From 3efc0623f603e73b5a1b984acd1ec9981c540138 Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Mon, 21 Oct 2024 13:13:08 +0200
Subject: [PATCH] update

---
 .../_build/.doctrees/environment.pickle       |  Bin 594149 -> 595314 bytes
 .../_build/.doctrees/week43.doctree           |  Bin 749637 -> 605735 bytes
 .../_build/html/_sources/week43.ipynb         | 1991 +++++++----
 doc/LectureNotes/_build/html/searchindex.js   |    2 +-
 doc/LectureNotes/_build/html/week43.html      |  610 +---
 .../_build/jupyter_execute/week43.ipynb       | 2913 ++++++++---------
 .../_build/jupyter_execute/week43.py          |   55 +-
 doc/LectureNotes/week43.ipynb                 | 1991 +++++++----
 doc/pub/week43/html/week43-bs.html            |    4 +-
 doc/pub/week43/html/week43-reveal.html        |    5 +-
 doc/pub/week43/html/week43-solarized.html     |    4 +-
 doc/pub/week43/html/week43.html               |    4 +-
 doc/pub/week43/ipynb/ipynb-week43-src.tar.gz  |  Bin 192 -> 192 bytes
 doc/pub/week43/ipynb/week43.ipynb             |  625 ++--
 doc/src/week43/week43.do.txt                  |    2 +-
 15 files changed, 4471 insertions(+), 3735 deletions(-)

diff --git a/doc/LectureNotes/_build/.doctrees/environment.pickle b/doc/LectureNotes/_build/.doctrees/environment.pickle
index 403cb743d4b14a595c3989728264801dd1690fca..21be02a4c0202bc72f4b934f69f8e0a5f76041e3 100644
GIT binary patch
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diff --git a/doc/LectureNotes/_build/.doctrees/week43.doctree b/doc/LectureNotes/_build/.doctrees/week43.doctree
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diff --git a/doc/LectureNotes/_build/html/_sources/week43.ipynb b/doc/LectureNotes/_build/html/_sources/week43.ipynb
index 47032b0fe..202263be5 100644
--- a/doc/LectureNotes/_build/html/_sources/week43.ipynb
+++ b/doc/LectureNotes/_build/html/_sources/week43.ipynb
@@ -2,8 +2,10 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "cda62a86",
-   "metadata": {},
+   "id": "677a195d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
     "doconce format html week43.do.txt --no_mako -->\n",
@@ -12,8 +14,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bdae1fa5",
-   "metadata": {},
+   "id": "e943e8f0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "# Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations\n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n",
@@ -23,8 +27,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e2c09dd5",
-   "metadata": {},
+   "id": "22cdced0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Plans for week 43\n",
     "\n",
@@ -39,8 +45,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7de8bfe0",
-   "metadata": {},
+   "id": "a57ef6df",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Exercises and lab session week 43\n",
     "**Lab sessions on Tuesday and Wednesday.**\n",
@@ -54,8 +62,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2664d901",
-   "metadata": {},
+   "id": "c4a134ee",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematics of deep learning\n",
     "\n",
@@ -68,8 +78,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46bb5558",
-   "metadata": {},
+   "id": "dd73045e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Reminder on books with hands-on material and codes\n",
     "* Sebastian Rashcka et al, Machine learning with Scikit-Learn and PyTorch at <https://sebastianraschka.com/blog/2022/ml-pytorch-book.html>"
@@ -77,8 +89,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c6ad86d",
-   "metadata": {},
+   "id": "372f4aa4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Reading recommendations\n",
     "\n",
@@ -89,8 +103,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9fbf4898",
-   "metadata": {},
+   "id": "05efbc6f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using Automatic differentiation\n",
     "\n",
@@ -100,8 +116,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "135a7122",
-   "metadata": {},
+   "id": "d04b0948",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Back propagation and automatic differentiation\n",
     "\n",
@@ -115,16 +133,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45236eaf",
-   "metadata": {},
+   "id": "b9d41f5c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Lecture Monday  October 21"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "8997a10d",
-   "metadata": {},
+   "id": "68606991",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the back propagation algorithm and algorithm for a feed forward NN, initalizations\n",
     "This is a reminder from where we ended last week.\n",
@@ -148,8 +170,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df88cb72",
-   "metadata": {},
+   "id": "a564a394",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the back propagation algorithm, part 1\n",
     "\n",
@@ -169,8 +193,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46d7ebde",
-   "metadata": {},
+   "id": "43ab4381",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the back propagation algorithm, part 2\n",
     "\n",
@@ -179,8 +205,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ad237f5",
-   "metadata": {},
+   "id": "f578cee4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\delta_j^L = \\sigma'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)}.\n",
@@ -189,16 +217,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f6906530",
-   "metadata": {},
+   "id": "fbc05943",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Then we compute the back propagate error for each $l=L-1,L-2,\\dots,1$ as"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e9613a49",
-   "metadata": {},
+   "id": "6ad3c28f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}\\sigma'(z_j^l).\n",
@@ -207,8 +239,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dba468b9",
-   "metadata": {},
+   "id": "135513b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the Back propagation algorithm, part 3\n",
     "\n",
@@ -219,8 +253,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "21c684a1",
-   "metadata": {},
+   "id": "f643ecdf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "w_{ij}^l\\leftarrow  = w_{ij}^l- \\eta \\delta_j^la_i^{l-1},\n",
@@ -229,8 +265,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6acf04a3",
-   "metadata": {},
+   "id": "077ef1c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n",
@@ -239,16 +277,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b0558fbe",
-   "metadata": {},
+   "id": "50cf7472",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $\\eta$ being the learning rate."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6b424064",
-   "metadata": {},
+   "id": "a10f406c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Updating the gradients\n",
     "\n",
@@ -257,8 +299,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7bc86e31",
-   "metadata": {},
+   "id": "626cba8f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}\\sigma'(z_j^l),\n",
@@ -267,16 +311,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7a10087",
-   "metadata": {},
+   "id": "2ebe05ad",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "we update the weights and the biases using gradient descent for each $l=L-1,L-2,\\dots,1$ and update the weights and biases according to the rules"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "2bf12837",
-   "metadata": {},
+   "id": "bfbbac35",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "w_{ij}^l\\leftarrow  = w_{ij}^l- \\eta \\delta_j^la_i^{l-1},\n",
@@ -285,8 +333,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ad07731e",
-   "metadata": {},
+   "id": "ac515399",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n",
@@ -295,8 +345,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "30c6ae90",
-   "metadata": {},
+   "id": "4703cc51",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Activation functions\n",
     "\n",
@@ -316,8 +368,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5dfa6d1c",
-   "metadata": {},
+   "id": "cab6ad03",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions, examples\n",
     "\n",
@@ -326,8 +380,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8d0be63",
-   "metadata": {},
+   "id": "ad6042eb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\sigma(x) = \\frac{1}{1 + e^{-x}},\n",
@@ -336,16 +392,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3ec0efa",
-   "metadata": {},
+   "id": "1e96b7e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and the *hyperbolic tangent* function"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "78c46915",
-   "metadata": {},
+   "id": "c600792f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\sigma(x) = \\tanh(x)\n",
@@ -354,8 +414,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87e6973b",
-   "metadata": {},
+   "id": "76d1da8e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The RELU function family\n",
     "\n",
@@ -373,8 +435,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c990bc8",
-   "metadata": {},
+   "id": "8e7e0e0c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## ELU function\n",
     "\n",
@@ -385,8 +449,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b7760f9",
-   "metadata": {},
+   "id": "4b1f77d6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "ELU(z) = \\left\\{\\begin{array}{cc} \\alpha\\left( \\exp{(z)}-1\\right) & z < 0,\\\\  z & z \\ge 0.\\end{array}\\right.\n",
@@ -395,8 +461,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47927a82",
-   "metadata": {},
+   "id": "10826ba9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Which activation function should we use?\n",
     "\n",
@@ -415,8 +483,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52554330",
-   "metadata": {},
+   "id": "79d307b6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More on activation functions, output layers\n",
     "\n",
@@ -435,8 +505,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b7d3292",
-   "metadata": {},
+   "id": "429b8d4e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up a Multi-layer perceptron model for classification\n",
     "\n",
@@ -461,8 +533,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38715b52",
-   "metadata": {},
+   "id": "90d9f195",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = \\frac{1}{1 + \\exp{(- \\boldsymbol{x}})} ,\n",
@@ -471,16 +545,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcc0cbfa",
-   "metadata": {},
+   "id": "73d2763e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c686ecf6",
-   "metadata": {},
+   "id": "e2a70a54",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(y = 1 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = 1 - P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) ,\n",
@@ -489,8 +567,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79a8b207",
-   "metadata": {},
+   "id": "7ed6c0dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $y \\in \\{0, 1\\}$  and $\\boldsymbol{\\theta}$ represents the weights and biases\n",
     "of our network."
@@ -498,8 +578,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3218b074",
-   "metadata": {},
+   "id": "a42826b9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Defining the cost function\n",
     "\n",
@@ -508,8 +590,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0e50336",
-   "metadata": {},
+   "id": "d8e401c5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = - \\sum_{i=1}^n\n",
@@ -519,8 +603,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79138403",
-   "metadata": {},
+   "id": "17808105",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This last equality means that we can interpret our *cost* function as a sum over the *loss* function\n",
     "for each point in the dataset $\\mathcal{L}_i(\\boldsymbol{\\theta})$.  \n",
@@ -542,8 +628,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b3db35e",
-   "metadata": {},
+   "id": "5a9b90ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(y_{ic} = 1 \\mid \\boldsymbol{x}_i, \\boldsymbol{\\theta}) = \\frac{\\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_c)}}\n",
@@ -553,8 +641,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90626f76",
-   "metadata": {},
+   "id": "57f33029",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which reduces to the logistic function in the binary case.  \n",
     "The likelihood of this $C$-class classifier\n",
@@ -563,8 +653,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "596eb444",
-   "metadata": {},
+   "id": "422eb23f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = \\prod_{i=1}^n \\prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .\n",
@@ -573,16 +665,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5529d979",
-   "metadata": {},
+   "id": "0eb634c3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Again we take the negative log-likelihood to define our cost function:"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "f7d2523f",
-   "metadata": {},
+   "id": "b3b208fc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\log{P(\\mathcal{D} \\mid \\boldsymbol{\\theta})}.\n",
@@ -591,8 +687,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d8d61f1",
-   "metadata": {},
+   "id": "3788aba1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "See the logistic regression lectures for a full definition of the cost function.\n",
     "\n",
@@ -601,8 +699,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9751fb82",
-   "metadata": {},
+   "id": "4d38ceec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: binary classification problem\n",
     "\n",
@@ -611,8 +711,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e6587c7",
-   "metadata": {},
+   "id": "cee503b9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\beta}) = - \\sum_{i=1}^n \\left(y_i\\log{p(y_i \\vert x_i,\\boldsymbol{\\beta})}+(1-y_i)\\log{1-p(y_i \\vert x_i,\\boldsymbol{\\beta})}\\right),\n",
@@ -621,16 +723,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39bb5ba4",
-   "metadata": {},
+   "id": "19b29e02",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we had defined the logistic (sigmoid) function"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "fcb1f3d9",
-   "metadata": {},
+   "id": "19507159",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(y_i =1\\vert x_i,\\boldsymbol{\\beta})=\\frac{\\exp{(\\beta_0+\\beta_1 x_i)}}{1+\\exp{(\\beta_0+\\beta_1 x_i)}},\n",
@@ -639,16 +745,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20fc130a",
-   "metadata": {},
+   "id": "a15191e4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "66c7c0e9",
-   "metadata": {},
+   "id": "c9df7a22",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(y_i =0\\vert x_i,\\boldsymbol{\\beta})=1-p(y_i =1\\vert x_i,\\boldsymbol{\\beta}).\n",
@@ -657,8 +767,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e757c738",
-   "metadata": {},
+   "id": "0cae75ec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The parameters $\\boldsymbol{\\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. \n",
     "\n",
@@ -668,8 +780,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d048e79e",
-   "metadata": {},
+   "id": "36b0506b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "a_i^l = y_i = \\frac{\\exp{(z_i^l)}}{1+\\exp{(z_i^l)}},\n",
@@ -678,16 +792,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b97827e7",
-   "metadata": {},
+   "id": "0c729c48",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c11528eb",
-   "metadata": {},
+   "id": "060813af",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "z_i^l = \\sum_{j}w_{ij}^l a_j^{l-1}+b_i^l,\n",
@@ -696,8 +814,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94839c96",
-   "metadata": {},
+   "id": "f2a5059b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where the superscript $l-1$ indicates that these are the outputs from layer $l-1$.\n",
     "Our cost function at the final layer $l=L$ is now"
@@ -705,8 +825,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "694596c9",
-   "metadata": {},
+   "id": "6763074d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(1-t_i)\\log{(1-a_i^L)}\\right),\n",
@@ -715,16 +837,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b4c8232e",
-   "metadata": {},
+   "id": "f498b6b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have defined the targets $t_i$. The derivatives of the cost function with respect to the output $a_i^L$ are then easily calculated and we get"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "9d611a08",
-   "metadata": {},
+   "id": "fedce928",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial \\mathcal{C}(\\boldsymbol{W})}{\\partial a_i^L} = \\frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.\n",
@@ -733,16 +859,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb7847ef",
-   "metadata": {},
+   "id": "429c11ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In case we use another activation function than the logistic one, we need to evaluate other derivatives."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "cd5be179",
-   "metadata": {},
+   "id": "ddde8370",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The Softmax function\n",
     "In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation $z_i^l$, that is we need"
@@ -750,8 +880,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96b7fe79",
-   "metadata": {},
+   "id": "637bd194",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial f(z_i^l)}{\\partial w_{jk}^l} =\n",
@@ -761,16 +893,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1040c590",
-   "metadata": {},
+   "id": "0792109c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "For the Softmax function we have"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3162bd5e",
-   "metadata": {},
+   "id": "10f14691",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(z_i^l) = \\frac{\\exp{(z_i^l)}}{\\sum_{m=1}^K\\exp{(z_m^l)}}.\n",
@@ -779,16 +915,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b7f2b7b8",
-   "metadata": {},
+   "id": "186529b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Its derivative with respect to $z_j^l$ gives"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "735fd9c0",
-   "metadata": {},
+   "id": "68afc0da",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial f(z_i^l)}{\\partial z_j^l}= f(z_i^l)\\left(\\delta_{ij}-f(z_j^l)\\right),\n",
@@ -797,16 +937,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3cbbb04",
-   "metadata": {},
+   "id": "cf48ea60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which in case of the simply binary model reduces to  having $i=j$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6462edbb",
-   "metadata": {},
+   "id": "861a3bbe",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Developing a code for doing neural networks with back propagation\n",
     "\n",
@@ -827,8 +971,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7915dc1d",
-   "metadata": {},
+   "id": "c8007ce7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Collect and pre-process data\n",
     "\n",
@@ -875,8 +1021,11 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "eb736d79",
-   "metadata": {},
+   "id": "29678f97",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "%matplotlib inline\n",
@@ -927,8 +1076,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01fcb50b",
-   "metadata": {},
+   "id": "3ba6d7d6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Train and test datasets\n",
     "\n",
@@ -946,8 +1097,11 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "e6b7f2e3",
-   "metadata": {},
+   "id": "7df51dd1",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn.model_selection import train_test_split\n",
@@ -981,8 +1135,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ca032f8",
-   "metadata": {},
+   "id": "249898fd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Define model and architecture\n",
     "\n",
@@ -1023,8 +1179,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6e4e1e18",
-   "metadata": {},
+   "id": "2d30ddd3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Layers\n",
     "\n",
@@ -1061,8 +1219,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab0ee6d8",
-   "metadata": {},
+   "id": "ce9f14e4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Weights and biases\n",
     "\n",
@@ -1080,8 +1240,11 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "15ad1599",
-   "metadata": {},
+   "id": "c3f75b32",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# building our neural network\n",
@@ -1103,8 +1266,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3efd576a",
-   "metadata": {},
+   "id": "4ebf4f68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Feed-forward pass\n",
     "\n",
@@ -1129,8 +1294,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "715c5d46",
-   "metadata": {},
+   "id": "c6760d1f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Matrix multiplications\n",
     "\n",
@@ -1164,8 +1331,11 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "ecaa833e",
-   "metadata": {},
+   "id": "98f3a5d5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# setup the feed-forward pass, subscript h = hidden layer\n",
@@ -1207,8 +1377,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0319e65",
-   "metadata": {},
+   "id": "19cd49ec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Choose cost function and optimizer\n",
     "\n",
@@ -1236,8 +1408,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98c6696e",
-   "metadata": {},
+   "id": "b0342f54",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Optimizing the cost function\n",
     "\n",
@@ -1272,8 +1446,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5d1145a",
-   "metadata": {},
+   "id": "7219731b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Regularization\n",
     "\n",
@@ -1304,8 +1480,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b73247fd",
-   "metadata": {},
+   "id": "248590b9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Matrix  multiplication\n",
     "\n",
@@ -1343,8 +1521,11 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "3d61438f",
-   "metadata": {},
+   "id": "1810a36c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# to categorical turns our integer vector into a onehot representation\n",
@@ -1419,8 +1600,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a20a495",
-   "metadata": {},
+   "id": "e094a404",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Improving performance\n",
     "\n",
@@ -1438,8 +1621,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "717b63a1",
-   "metadata": {},
+   "id": "1fb3aab5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Full object-oriented implementation\n",
     "\n",
@@ -1450,8 +1635,11 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "9d6c9929",
-   "metadata": {},
+   "id": "20b3c187",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "class NeuralNetwork:\n",
@@ -1557,8 +1745,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e70667c5",
-   "metadata": {},
+   "id": "f85564ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Evaluate model performance on test data\n",
     "\n",
@@ -1574,8 +1764,11 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "083dfe41",
-   "metadata": {},
+   "id": "9be7082e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "epochs = 100\n",
@@ -1598,8 +1791,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bffeadd3",
-   "metadata": {},
+   "id": "255b5b3d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Adjust hyperparameters\n",
     "\n",
@@ -1610,8 +1805,11 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "6513ac74",
-   "metadata": {},
+   "id": "fc014642",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "eta_vals = np.logspace(-5, 1, 7)\n",
@@ -1638,8 +1836,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a6e305f6",
-   "metadata": {},
+   "id": "96089af8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Visualization"
    ]
@@ -1647,8 +1847,11 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "d920e285",
-   "metadata": {},
+   "id": "04c4d29a",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# visual representation of grid search\n",
@@ -1688,8 +1891,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0f1aaadd",
-   "metadata": {},
+   "id": "472a5060",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## scikit-learn implementation\n",
     "\n",
@@ -1709,8 +1914,11 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "156764f3",
-   "metadata": {},
+   "id": "42e40777",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn.neural_network import MLPClassifier\n",
@@ -1733,8 +1941,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e5fec48",
-   "metadata": {},
+   "id": "57fc5d93",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Visualization"
    ]
@@ -1742,8 +1952,11 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "ace47e70",
-   "metadata": {},
+   "id": "90477fe7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# optional\n",
@@ -1784,8 +1997,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d327f9b",
-   "metadata": {},
+   "id": "29af8aff",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Building neural networks in Tensorflow and Keras\n",
     "\n",
@@ -1800,8 +2015,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2280cbce",
-   "metadata": {},
+   "id": "a70cf999",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Tensorflow\n",
     "\n",
@@ -1833,8 +2050,11 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "dff81198",
-   "metadata": {},
+   "id": "812c98fe",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "pip3 install tensorflow"
@@ -1842,8 +2062,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9bf9cac",
-   "metadata": {},
+   "id": "694c0bd7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and/or if you use **anaconda**, just write (or install from the graphical user interface)\n",
     "(current release of CPU-only TensorFlow)"
@@ -1852,8 +2074,11 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "1ccb8dba",
-   "metadata": {},
+   "id": "1ecd18cc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "conda create -n tf tensorflow\n",
@@ -1862,8 +2087,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efc3f4e2",
-   "metadata": {},
+   "id": "584ab0ab",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "To install the current release of GPU TensorFlow"
    ]
@@ -1871,8 +2098,11 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "01556b01",
-   "metadata": {},
+   "id": "a811e23d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "conda create -n tf-gpu tensorflow-gpu\n",
@@ -1881,8 +2111,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b900f015",
-   "metadata": {},
+   "id": "ab99008f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using Keras\n",
     "\n",
@@ -1894,8 +2126,11 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "3fd1f12f",
-   "metadata": {},
+   "id": "fe547415",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "conda install keras"
@@ -1903,8 +2138,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20ec35c5",
-   "metadata": {},
+   "id": "ed1e0fc6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "You can look up the [instructions here](https://keras.io/) for more information.\n",
     "\n",
@@ -1913,8 +2150,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "249e56f7",
-   "metadata": {},
+   "id": "6aebcb51",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Collect and pre-process data\n",
     "\n",
@@ -1924,8 +2163,11 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "0ff66efc",
-   "metadata": {},
+   "id": "a4a7d68d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# import necessary packages\n",
@@ -1976,8 +2218,11 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "2806c62b",
-   "metadata": {},
+   "id": "21335418",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from tensorflow.keras.layers import Input\n",
@@ -2002,8 +2247,11 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "3bf4c3f6",
-   "metadata": {},
+   "id": "e81d58de",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\n",
@@ -2020,7 +2268,7 @@
     "    model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))\n",
     "    model.add(Dense(n_categories, activation='softmax'))\n",
     "    \n",
-    "    sgd = optimizers.SGD(lr=eta)\n",
+    "    sgd = optimizers.SGD(learning_rate=eta)\n",
     "    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n",
     "    \n",
     "    return model"
@@ -2029,8 +2277,11 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "81a46485",
-   "metadata": {},
+   "id": "b91287cc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
@@ -2053,8 +2304,11 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "6e619c14",
-   "metadata": {},
+   "id": "d108674e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# optional\n",
@@ -2092,8 +2346,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c303d97b",
-   "metadata": {},
+   "id": "1198d799",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The Breast Cancer Data, now with Keras"
    ]
@@ -2101,8 +2357,11 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "03a57bfd",
-   "metadata": {},
+   "id": "eb1eb4fb",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\n",
@@ -2215,7 +2474,7 @@
     "        else:                       #Subsequent layers are capable of automatic shape inferencing\n",
     "            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda)))\n",
     "    model.add(Dense(2,activation='softmax'))  #2 outputs - ordered and disordered (softmax for prob)\n",
-    "    sgd=optimizers.SGD(lr=eta)\n",
+    "    sgd=optimizers.SGD(learning_rate=eta)\n",
     "    model.compile(loss='categorical_crossentropy',optimizer=sgd,metrics=['accuracy'])\n",
     "    return model\n",
     "\n",
@@ -2275,8 +2534,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9ad1085",
-   "metadata": {},
+   "id": "92834502",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Building a neural network code\n",
     "\n",
@@ -2292,8 +2553,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf4f3c14",
-   "metadata": {},
+   "id": "deb24cc1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Learning rate methods\n",
     "\n",
@@ -2312,8 +2575,11 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "id": "467ea7a2",
-   "metadata": {},
+   "id": "d3619281",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2450,8 +2716,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6af64d5a",
-   "metadata": {},
+   "id": "f37fd7bc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Usage of the above learning rate schedulers\n",
     "\n",
@@ -2464,8 +2732,11 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "id": "290e0d00",
-   "metadata": {},
+   "id": "5db34b9b",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "momentum_scheduler = Momentum(eta=1e-3, momentum=0.9)\n",
@@ -2474,8 +2745,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1f43cc5",
-   "metadata": {},
+   "id": "8b25a24d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Here is a small example for how a segment of code using schedulers\n",
     "could look. Switching out the schedulers is simple."
@@ -2484,8 +2757,11 @@
   {
    "cell_type": "code",
    "execution_count": 24,
-   "id": "0def5cec",
-   "metadata": {},
+   "id": "2d5f2887",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "weights = np.ones((3,3))\n",
@@ -2503,8 +2779,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b27dcd7",
-   "metadata": {},
+   "id": "9070c2d3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Cost functions\n",
     "\n",
@@ -2517,8 +2795,11 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "id": "4217839c",
-   "metadata": {},
+   "id": "c360c736",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2552,8 +2833,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ef5f9fe9",
-   "metadata": {},
+   "id": "42c7ec61",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Below we give a short example of how these cost function may be used\n",
     "to obtain results if you wish to test them out on your own using\n",
@@ -2563,8 +2846,11 @@
   {
    "cell_type": "code",
    "execution_count": 26,
-   "id": "305e1479",
-   "metadata": {},
+   "id": "cd9cb3a5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from autograd import grad\n",
@@ -2581,8 +2867,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1499b193",
-   "metadata": {},
+   "id": "796aab4a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions\n",
     "\n",
@@ -2595,8 +2883,11 @@
   {
    "cell_type": "code",
    "execution_count": 27,
-   "id": "e7b59b25",
-   "metadata": {},
+   "id": "5ea4891d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2650,8 +2941,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57599619",
-   "metadata": {},
+   "id": "2ff3c57c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Below follows a short demonstration of how to use an activation\n",
     "function. The derivative of the activation function will be important\n",
@@ -2663,8 +2956,11 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "id": "5ee68acd",
-   "metadata": {},
+   "id": "34289210",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "z = np.array([[4, 5, 6]]).T\n",
@@ -2681,8 +2977,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d3295d9",
-   "metadata": {},
+   "id": "0839f98b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### The Neural Network\n",
     "\n",
@@ -2703,8 +3001,11 @@
   {
    "cell_type": "code",
    "execution_count": 29,
-   "id": "c4cfc50a",
-   "metadata": {},
+   "id": "0fdc2707",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import math\n",
@@ -3172,8 +3473,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e6e81c1",
-   "metadata": {},
+   "id": "17bc192e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Before we make a model, we will quickly generate a dataset we can use\n",
     "for our linear regression problem as shown below"
@@ -3182,8 +3485,11 @@
   {
    "cell_type": "code",
    "execution_count": 30,
-   "id": "0d4f1ff8",
-   "metadata": {},
+   "id": "f3f5d088",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -3223,8 +3529,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8f1940f",
-   "metadata": {},
+   "id": "53c3b4c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Now that we have our dataset ready for the regression, we can create\n",
     "our regressor. Note that with the seed parameter, we can make sure our\n",
@@ -3237,8 +3545,11 @@
   {
    "cell_type": "code",
    "execution_count": 31,
-   "id": "ff6bd29b",
-   "metadata": {},
+   "id": "890d682f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -3249,8 +3560,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7b906df",
-   "metadata": {},
+   "id": "dc4da852",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We then fit our model with our training data using the scheduler of our choice."
    ]
@@ -3258,8 +3571,11 @@
   {
    "cell_type": "code",
    "execution_count": 32,
-   "id": "db7a5bf2",
-   "metadata": {},
+   "id": "1e98a3f8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -3270,8 +3586,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "508c351b",
-   "metadata": {},
+   "id": "68c5d793",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Due to the progress bar we can see the MSE (train_error) throughout\n",
     "the FFNN's training. Note that the fit() function has some optional\n",
@@ -3284,8 +3602,11 @@
   {
    "cell_type": "code",
    "execution_count": 33,
-   "id": "6b0562b2",
-   "metadata": {},
+   "id": "e735086e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -3295,8 +3616,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f03172d9",
-   "metadata": {},
+   "id": "360468f6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We see that given more epochs to train on, the regressor reaches a lower MSE.\n",
     "\n",
@@ -3308,8 +3631,11 @@
   {
    "cell_type": "code",
    "execution_count": 34,
-   "id": "26d1d1c3",
-   "metadata": {},
+   "id": "c5937c59",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn.datasets import load_breast_cancer\n",
@@ -3331,8 +3657,11 @@
   {
    "cell_type": "code",
    "execution_count": 35,
-   "id": "6a78c633",
-   "metadata": {},
+   "id": "2e06b929",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -3343,8 +3672,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5feaced2",
-   "metadata": {},
+   "id": "94140fb1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We will now make use of our validation data by passing it into our fit function as a keyword argument"
    ]
@@ -3352,8 +3683,11 @@
   {
    "cell_type": "code",
    "execution_count": 36,
-   "id": "6a9b1538",
-   "metadata": {},
+   "id": "da82b266",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "logistic_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -3364,8 +3698,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90c7f8f3",
-   "metadata": {},
+   "id": "19e8d4c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Finally, we will create a neural network with 2 hidden layers with activation functions."
    ]
@@ -3373,8 +3709,11 @@
   {
    "cell_type": "code",
    "execution_count": 37,
-   "id": "58954140",
-   "metadata": {},
+   "id": "4744accd",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -3390,8 +3729,11 @@
   {
    "cell_type": "code",
    "execution_count": 38,
-   "id": "89536ca9",
-   "metadata": {},
+   "id": "f5b5b198",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "neural_network.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -3402,8 +3744,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "803f4791",
-   "metadata": {},
+   "id": "1f5fc0a0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Multiclass classification\n",
     "\n",
@@ -3415,8 +3759,11 @@
   {
    "cell_type": "code",
    "execution_count": 39,
-   "id": "50405951",
-   "metadata": {},
+   "id": "4308d82f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn.datasets import load_digits\n",
@@ -3449,8 +3796,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d906edf4",
-   "metadata": {},
+   "id": "96fc3508",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Testing the XOR gate and other gates\n",
     "\n",
@@ -3460,8 +3809,11 @@
   {
    "cell_type": "code",
    "execution_count": 40,
-   "id": "414ee306",
-   "metadata": {},
+   "id": "5aa9a2a4",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)\n",
@@ -3480,18 +3832,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "982d1747",
-   "metadata": {},
+   "id": "d57346ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Not bad, but the results depend strongly on the learning reate. Try different learning rates."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "616eae3e",
-   "metadata": {},
+   "id": "0219b252",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "## Solving ODEs with Deep Learning\n",
+    "## Solving differential equations  with Deep Learning\n",
     "\n",
     "The Universal Approximation Theorem states that a neural network can\n",
     "approximate any function at a single hidden layer along with one input\n",
@@ -3513,10 +3869,12 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43fb869c",
-   "metadata": {},
+   "id": "80032cfc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "## Ordinary Differential Equations\n",
+    "## Ordinary Differential Equations first\n",
     "\n",
     "An ordinary differential equation (ODE) is an equation involving functions having one variable.\n",
     "\n",
@@ -3525,8 +3883,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4855aef1",
-   "metadata": {},
+   "id": "3c5546df",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"ode\"></div>\n",
@@ -3540,8 +3900,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d31c26fc",
-   "metadata": {},
+   "id": "e4f540a5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(x)$ is the function to find, and $g^{(n)}(x)$ is the $n$-th derivative of $g(x)$.\n",
     "\n",
@@ -3554,8 +3916,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08d629ec",
-   "metadata": {},
+   "id": "75ec2cfe",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "\n",
@@ -3564,8 +3928,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2cfd7bd",
-   "metadata": {},
+   "id": "a71e7eb8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto1\"></div>\n",
@@ -3580,8 +3946,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4cd106f",
-   "metadata": {},
+   "id": "9b06d2bf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $h_1(x)$ is a function that makes $g_t(x)$ satisfy a given set\n",
     "of conditions, $N(x,P)$ a neural network with weights and biases\n",
@@ -3599,8 +3967,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74da655f",
-   "metadata": {},
+   "id": "0aea2f3e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Minimization process\n",
     "\n",
@@ -3614,8 +3984,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efe0ec18",
-   "metadata": {},
+   "id": "a21c6a43",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(x, P\\right) = \\big(f\\left(x, \\, g(x), \\, g'(x), \\, g''(x), \\, \\dots \\, , \\, g^{(n)}(x)\\right)\\big)^2\n",
@@ -3624,8 +3996,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9c1643a",
-   "metadata": {},
+   "id": "ff939582",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If $N$ inputs are given as a vector $\\boldsymbol{x}$ with elements $x_i$ for $i = 1,\\dots,N$,\n",
     "the cost function becomes"
@@ -3633,8 +4007,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b900e26",
-   "metadata": {},
+   "id": "9f63085a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"cost\"></div>\n",
@@ -3648,8 +4024,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82e8e341",
-   "metadata": {},
+   "id": "2875658a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The neural net should then find the parameters $P$ that minimizes the cost function in\n",
     "([3](#cost)) for a set of $N$ training samples $x_i$."
@@ -3657,8 +4035,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b89f2f97",
-   "metadata": {},
+   "id": "8a63e4c6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Minimizing the cost function using gradient descent and automatic differentiation\n",
     "\n",
@@ -3671,8 +4051,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc38c37f",
-   "metadata": {},
+   "id": "2d5b4c88",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Exponential decay\n",
     "\n",
@@ -3681,8 +4063,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c5f0410",
-   "metadata": {},
+   "id": "daab1d5e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solve_expdec\"></div>\n",
@@ -3696,8 +4080,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4531d4a4",
-   "metadata": {},
+   "id": "fc2cedc3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $g(0) = g_0$ for some chosen initial value $g_0$.\n",
     "\n",
@@ -3706,8 +4092,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d580caea",
-   "metadata": {},
+   "id": "da284bc1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto2\"></div>\n",
@@ -3722,16 +4110,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f384ec5",
-   "metadata": {},
+   "id": "04c2531a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of ([4](#solve_expdec))."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e650af49",
-   "metadata": {},
+   "id": "62a110db",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The function to solve for\n",
     "\n",
@@ -3740,8 +4132,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68e3a73b",
-   "metadata": {},
+   "id": "7b5b722c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solveode\"></div>\n",
@@ -3755,8 +4149,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61f7dce9",
-   "metadata": {},
+   "id": "02446b0e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(0) = g_0$ with $\\gamma$ and $g_0$ being some chosen values.\n",
     "\n",
@@ -3765,8 +4161,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47e985ed",
-   "metadata": {},
+   "id": "205c8e89",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "To begin with, a trial solution $g_t(t)$ must be chosen. A general trial solution for ordinary differential equations could be"
@@ -3774,8 +4172,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5787755",
-   "metadata": {},
+   "id": "9e46aee1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x, P) = h_1(x) + h_2(x, N(x, P))\n",
@@ -3784,16 +4184,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efd0d663",
-   "metadata": {},
+   "id": "cb0d1f30",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $h_1(x)$ ensuring that $g_t(x)$ satisfies some conditions and $h_2(x,N(x, P))$ an expression involving $x$ and the output from the neural network $N(x,P)$ with $P $ being the collection of the weights and biases for each layer. For now, it is assumed that the network consists of one input layer, one hidden layer, and one output layer."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "de4cfa12",
-   "metadata": {},
+   "id": "8485bdd3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setup of Network\n",
     "\n",
@@ -3810,8 +4214,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4de8eeb1",
-   "metadata": {},
+   "id": "730e057b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"trial\"></div>\n",
@@ -3825,8 +4231,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3076a5d",
-   "metadata": {},
+   "id": "db8907ef",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Reformulating the problem\n",
     "\n",
@@ -3842,8 +4250,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00459420",
-   "metadata": {},
+   "id": "ce4a7022",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x, P) = g_0 + x \\cdot N(x, P)\n",
@@ -3852,16 +4262,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "493318e4",
-   "metadata": {},
+   "id": "b17ab00d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "has been chosen such that it already solves the condition $g(0) = g_0$. What remains, is to find $P$ such that"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b1cd6594",
-   "metadata": {},
+   "id": "f4af75e0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"nnmin\"></div>\n",
@@ -3875,16 +4289,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf2aa493",
-   "metadata": {},
+   "id": "4ea72b19",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "is fulfilled as *best as possible*."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5eda172b",
-   "metadata": {},
+   "id": "428cf327",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More technicalities\n",
     "\n",
@@ -3897,8 +4315,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2bfc8161",
-   "metadata": {},
+   "id": "1b4c9872",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P}\\Big\\{ \\big(g_t'(x, P) - ( -\\gamma g_t(x, P) \\big)^2 \\Big\\}\n",
@@ -3907,8 +4327,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9af6a125",
-   "metadata": {},
+   "id": "f12896dd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "(the notation $\\min_{P}\\{ f(x, P) \\}$ means that we desire to find $P$ that yields the minimum of $f(x, P)$)\n",
     "\n",
@@ -3917,8 +4339,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bea03f10",
-   "metadata": {},
+   "id": "70e2187e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P_{\\text{hidden} }, \\ P_{\\text{output} }}\\Big\\{ \\big(g_t'(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) - ( -\\gamma g_t(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) \\big)^2 \\Big\\}\n",
@@ -3927,16 +4351,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "352fb11e",
-   "metadata": {},
+   "id": "e0136d5f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for an input value $x$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "98d5219e",
-   "metadata": {},
+   "id": "ff915c59",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More details\n",
     "\n",
@@ -3945,8 +4373,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "83d7b299",
-   "metadata": {},
+   "id": "ca46667e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"min\"></div>\n",
@@ -3960,16 +4390,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ba53d11",
-   "metadata": {},
+   "id": "3efa1dc6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Letting $\\boldsymbol{x}$ be a vector with elements $x_i$ and $C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i  \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2$ denote the cost function, the minimization problem that our network must solve, becomes"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3953e778",
-   "metadata": {},
+   "id": "a3d800e8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P} C(\\boldsymbol{x}, P)\n",
@@ -3978,8 +4412,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "706a1978",
-   "metadata": {},
+   "id": "8fb679f5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In terms of $P_{\\text{hidden} }$ and $P_{\\text{output} }$, this could also be expressed as\n",
     "\n",
@@ -3990,8 +4426,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8ff57d1a",
-   "metadata": {},
+   "id": "08b2a19b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## A possible implementation of a neural network\n",
     "\n",
@@ -4004,8 +4442,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb487d3d",
-   "metadata": {},
+   "id": "082074c8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Technicalities\n",
     "\n",
@@ -4014,8 +4454,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d6ac6a6",
-   "metadata": {},
+   "id": "b69f9148",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4034,8 +4476,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fee86c29",
-   "metadata": {},
+   "id": "9feeefde",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities I\n",
     "\n",
@@ -4044,8 +4488,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "317dd762",
-   "metadata": {},
+   "id": "cde763a7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4065,8 +4511,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4641c716",
-   "metadata": {},
+   "id": "3c83e5dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities II\n",
     "\n",
@@ -4079,8 +4527,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a28fd5d3",
-   "metadata": {},
+   "id": "4566531c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(z) = \\frac{1}{1 + \\exp{(-z)}}\n",
@@ -4089,8 +4539,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2c6ce13",
-   "metadata": {},
+   "id": "e316d1e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "It is possible to use other activations functions for the hidden layer also.\n",
     "\n",
@@ -4111,8 +4563,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5bf0304c",
-   "metadata": {},
+   "id": "41ac9a1c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities III\n",
     "\n",
@@ -4121,8 +4575,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4ee906f",
-   "metadata": {},
+   "id": "b0a8a3c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4140,8 +4596,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "454cd32f",
-   "metadata": {},
+   "id": "67447b23",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities IV\n",
     "\n",
@@ -4150,8 +4608,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "49b52638",
-   "metadata": {},
+   "id": "12d3e1ee",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{z}_{1}^{\\text{output}} =\n",
@@ -4167,16 +4627,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75d1e0dc",
-   "metadata": {},
+   "id": "562a122c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In this case we seek a continuous range of values since we are approximating a function. This means that after computing $\\boldsymbol{z}_{1}^{\\text{output}}$ the neural network has finished its feed forward step, and $\\boldsymbol{z}_{1}^{\\text{output}}$ is the final output of the network."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "243508b9",
-   "metadata": {},
+   "id": "78789a96",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Back propagation\n",
     "\n",
@@ -4187,8 +4651,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cfaa5264",
-   "metadata": {},
+   "id": "76b734fb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i  \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2\n",
@@ -4197,8 +4663,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "188a58e4",
-   "metadata": {},
+   "id": "e2911f97",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In order to minimize the cost function, an optimization method must be chosen.\n",
     "\n",
@@ -4207,8 +4675,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f3c7251",
-   "metadata": {},
+   "id": "5e0c281c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Gradient descent\n",
     "\n",
@@ -4222,8 +4692,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b48662af",
-   "metadata": {},
+   "id": "077e3318",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\omega}_{\\text{new} } = \\boldsymbol{\\omega} - \\lambda \\nabla_{\\boldsymbol{\\omega}} C(\\boldsymbol{x}, \\boldsymbol{\\omega})\n",
@@ -4232,8 +4704,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46cc1b9b",
-   "metadata": {},
+   "id": "b6e9387d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for a number of iterations or until $ \\big|\\big| \\boldsymbol{\\omega}_{\\text{new} } - \\boldsymbol{\\omega} \\big|\\big|$ becomes smaller than some given tolerance.\n",
     "\n",
@@ -4252,8 +4726,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "018877f6",
-   "metadata": {},
+   "id": "3fa21e60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4265,8 +4741,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "35e348bd",
-   "metadata": {},
+   "id": "e05e6028",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The code for solving the ODE"
    ]
@@ -4274,8 +4752,11 @@
   {
    "cell_type": "code",
    "execution_count": 41,
-   "id": "dafe8d25",
-   "metadata": {},
+   "id": "eb77d1cf",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -4426,8 +4907,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65e4f300",
-   "metadata": {},
+   "id": "bbd6562b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The network with one input layer, specified number of hidden layers, and one output layer\n",
     "\n",
@@ -4439,8 +4922,11 @@
   {
    "cell_type": "code",
    "execution_count": 42,
-   "id": "5ef5f766",
-   "metadata": {},
+   "id": "24ba1afd",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -4455,8 +4941,8 @@
     "# but with number of hidden layers specified by the user.\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consists of\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
     "                                        # parameters to all the hidden\n",
     "                                        # layers AND the output layer.\n",
     "\n",
@@ -4605,8 +5091,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7ad45ef",
-   "metadata": {},
+   "id": "3974040a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Population growth\n",
     "\n",
@@ -4616,8 +5104,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d1376bc",
-   "metadata": {},
+   "id": "a9d203ea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"log\"></div>\n",
@@ -4631,8 +5121,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f039785",
-   "metadata": {},
+   "id": "ede35f92",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(t)$ is the population density at time $t$, $\\alpha > 0$ the growth rate and $A > 0$ is the maximum population number in the environment.\n",
     "Also, at $t = 0$ the population has the size $g(0) = g_0$, where $g_0$ is some chosen constant.\n",
@@ -4645,8 +5137,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8dfcfb5e",
-   "metadata": {},
+   "id": "a9720dfc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the problem\n",
     "\n",
@@ -4656,8 +5150,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cb5e674",
-   "metadata": {},
+   "id": "5ef6b555",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solveode_population\"></div>\n",
@@ -4671,8 +5167,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "56581c9f",
-   "metadata": {},
+   "id": "bd5c646e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(0) = g_0$.\n",
     "\n",
@@ -4681,8 +5179,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ebf7032a",
-   "metadata": {},
+   "id": "cdc5561b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "\n",
@@ -4706,8 +5206,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a943c5c6",
-   "metadata": {},
+   "id": "cebde164",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The program using Autograd\n",
     "\n",
@@ -4717,8 +5219,11 @@
   {
    "cell_type": "code",
    "execution_count": 43,
-   "id": "a3620769",
-   "metadata": {},
+   "id": "c71a9592",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -4737,9 +5242,12 @@
     "    g0 = 1.2\n",
     "    return alpha, A, g0\n",
     "\n",
-    "def deep_neural_network(P, x):\n",
+    "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(P) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -4756,7 +5264,7 @@
     "\n",
     "    for l in range(N_hidden):\n",
     "        # From the list of parameters P; find the correct weigths and bias for this layer\n",
-    "        w_hidden = P[l]\n",
+    "        w_hidden = deep_params[l]\n",
     "\n",
     "        # Add a row of ones to include bias\n",
     "        x_prev = np.concatenate((np.ones((1,num_values)), x_prev ), axis = 0)\n",
@@ -4770,7 +5278,7 @@
     "    ## Output layer:\n",
     "\n",
     "    # Get the weights and bias for this layer\n",
-    "    w_output = P[-1]\n",
+    "    w_output = deep_params[-1]\n",
     "\n",
     "    # Include bias:\n",
     "    x_prev = np.concatenate((np.ones((1,num_values)), x_prev), axis = 0)\n",
@@ -4781,6 +5289,8 @@
     "    return x_output\n",
     "\n",
     "\n",
+    "\n",
+    "\n",
     "def cost_function_deep(P, x):\n",
     "\n",
     "    # Evaluate the trial function with the current parameters P\n",
@@ -4888,8 +5398,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a21afc2",
-   "metadata": {},
+   "id": "bd70d6cc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using forward Euler to solve the ODE\n",
     "\n",
@@ -4906,8 +5418,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a8ad46c",
-   "metadata": {},
+   "id": "ee3bdd02",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4919,8 +5433,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b83336b",
-   "metadata": {},
+   "id": "d81b6054",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "along with the condition that $g(0) = g_0$.\n",
     "\n",
@@ -4931,8 +5447,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea68eaac",
-   "metadata": {},
+   "id": "0d7a2272",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4945,16 +5463,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c8a2f92c",
-   "metadata": {},
+   "id": "ca29846f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Now, if $g_i = g(t_i)$ then"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "4f1a2187",
-   "metadata": {},
+   "id": "1a51d849",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"odenum\"></div>\n",
@@ -4973,8 +5495,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb87fc93",
-   "metadata": {},
+   "id": "700a9bac",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for $i \\geq 1$ and $g_0 = g(t_0) = g(0) = g_0$.\n",
     "\n",
@@ -4985,8 +5509,11 @@
   {
    "cell_type": "code",
    "execution_count": 44,
-   "id": "f8c976e7",
-   "metadata": {},
+   "id": "482cf93c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# Assume that all function definitions from the example program using Autograd\n",
@@ -5058,8 +5585,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23756e15",
-   "metadata": {},
+   "id": "4ed3cefd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Solving the one dimensional Poisson equation\n",
     "\n",
@@ -5068,8 +5597,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a68185f",
-   "metadata": {},
+   "id": "d0bdfcdb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"poisson\"></div>\n",
@@ -5083,8 +5614,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc784286",
-   "metadata": {},
+   "id": "656240e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $f(x)$ is a given function for $x \\in (0,1)$.\n",
     "\n",
@@ -5093,8 +5626,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e0f7d593",
-   "metadata": {},
+   "id": "fb310d7c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -5106,8 +5641,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4cacfaeb",
-   "metadata": {},
+   "id": "e6b102dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This equation can be solved numerically using programs where e.g Autograd and TensorFlow are used.\n",
     "The results from the networks can then be compared to the analytical solution.\n",
@@ -5116,8 +5653,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69ba705a",
-   "metadata": {},
+   "id": "797d4bb8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The specific equation to solve for\n",
     "\n",
@@ -5126,8 +5665,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "995cfbc9",
-   "metadata": {},
+   "id": "da2e90b8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "-g''(x) = f(x),\\qquad x \\in (0,1)\n",
@@ -5136,16 +5677,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "769f9670",
-   "metadata": {},
+   "id": "318f8f3a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $f(x)$ is a given function, along with the chosen conditions"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "855cddbb",
-   "metadata": {},
+   "id": "c5e8ac9e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"cond\"></div>\n",
@@ -5159,8 +5704,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7006cb54",
-   "metadata": {},
+   "id": "220ceeb4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In this example, we consider the case when $f(x) = (3x + x^2)\\exp(x)$.\n",
     "\n",
@@ -5169,8 +5716,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5216ca22",
-   "metadata": {},
+   "id": "ec8b38dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x) = x \\cdot (1-x) \\cdot N(P,x)\n",
@@ -5179,16 +5728,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b77670be",
-   "metadata": {},
+   "id": "0ed927a9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The analytical solution for this problem is"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "bf2bed23",
-   "metadata": {},
+   "id": "3a51ddcc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g(x) = x(1 - x)\\exp(x)\n",
@@ -5197,8 +5750,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a22ccb78",
-   "metadata": {},
+   "id": "d5392b8d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Solving the equation using Autograd"
    ]
@@ -5206,8 +5761,11 @@
   {
    "cell_type": "code",
    "execution_count": 45,
-   "id": "7b3b5f5a",
-   "metadata": {},
+   "id": "95059f71",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -5220,7 +5778,10 @@
     "\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -5261,6 +5822,7 @@
     "\n",
     "    return x_output\n",
     "\n",
+    "\n",
     "def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
     "    # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
     "\n",
@@ -5364,8 +5926,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6668b7ef",
-   "metadata": {},
+   "id": "7c568bf3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Comparing with a numerical scheme\n",
     "\n",
@@ -5384,8 +5948,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec1adda2",
-   "metadata": {},
+   "id": "eab0bb68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"approx\"></div>\n",
@@ -5399,16 +5965,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33486af4",
-   "metadata": {},
+   "id": "c0ada0c0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If $x_i = i \\Delta x = x_{i-1} + \\Delta x$ and $g_i = g(x_i)$ for $i = 1,\\dots N_x - 2$ with $N_x$ being the number of values for $x$, ([15](#approx)) becomes"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "42c3ef84",
-   "metadata": {},
+   "id": "b483eace",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -5420,16 +5990,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f454dbea",
-   "metadata": {},
+   "id": "30d45122",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Since we know from our problem that"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "7411a707",
-   "metadata": {},
+   "id": "52c68e05",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -5441,8 +6015,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c47c3822",
-   "metadata": {},
+   "id": "1657934d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "along with the conditions $g(0) = g(1) = 0$,\n",
     "the following scheme can be used to find an approximate solution for $g(x)$ numerically:"
@@ -5450,8 +6026,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1cca824c",
-   "metadata": {},
+   "id": "9fc46a1b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"odesys\"></div>\n",
@@ -5468,8 +6046,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82ecd5a1",
-   "metadata": {},
+   "id": "cd79f75c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for $i = 1, \\dots, N_x - 2$ where $g_0 = g_{N_x - 1} = 0$ and $f(x_i) = (3x_i + x_i^2)\\exp(x_i)$, which is given for our specific problem.\n",
     "\n",
@@ -5478,8 +6058,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39f5fe07",
-   "metadata": {},
+   "id": "501ac880",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -5513,16 +6095,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ac54c35",
-   "metadata": {},
+   "id": "8551615b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which makes it possible to solve for the vector $\\boldsymbol{g}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "79ad3ebc",
-   "metadata": {},
+   "id": "dbd6d2a1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the code\n",
     "\n",
@@ -5532,8 +6118,11 @@
   {
    "cell_type": "code",
    "execution_count": 46,
-   "id": "be03bf2d",
-   "metadata": {},
+   "id": "c71a3063",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -5546,7 +6135,10 @@
     "\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -5587,6 +6179,7 @@
     "\n",
     "    return x_output\n",
     "\n",
+    "\n",
     "def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
     "    # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
     "\n",
@@ -5730,8 +6323,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "faa0daa4",
-   "metadata": {},
+   "id": "da58cdec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Partial Differential Equations\n",
     "\n",
@@ -5745,8 +6340,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb7b7ff6",
-   "metadata": {},
+   "id": "df991968",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"PDE\"></div>\n",
@@ -5760,16 +6357,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71da1640",
-   "metadata": {},
+   "id": "59ef3099",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $f$ is an expression involving all kinds of possible mixed derivatives of $g(x_1,\\dots,x_N)$ up to an order $n$. In order for the solution to be unique, some additional conditions must also be given."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c77e6225",
-   "metadata": {},
+   "id": "a580ae0f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Type of problem\n",
     "\n",
@@ -5781,8 +6382,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98f82ea2",
-   "metadata": {},
+   "id": "a56f3fe1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -5793,8 +6396,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc33501c",
-   "metadata": {},
+   "id": "69586714",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $h_1(x_1,\\dots,x_N)$ is a function that ensures $g_t(x_1,\\dots,x_N)$ satisfies some given conditions.\n",
     "The neural network $N(x_1,\\dots,x_N,P)$ has weights and biases described by $P$ and $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$ is an expression using the output from the neural network in some way.\n",
@@ -5804,8 +6409,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "818e8900",
-   "metadata": {},
+   "id": "d8374dce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Network requirements\n",
     "\n",
@@ -5822,8 +6429,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "526d5428",
-   "metadata": {},
+   "id": "f3fe961e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(x_1, \\dots, x_N, P\\right) = \\left(  f\\left(x_1, \\, \\dots \\, , x_N, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1}, \\dots , \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_N}, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(x_1,\\dots,x_N) }{\\partial x_N^n} \\right) \\right)^2\n",
@@ -5832,8 +6441,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "279b9296",
-   "metadata": {},
+   "id": "4e453aa1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More details\n",
     "\n",
@@ -5842,8 +6453,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcb8ce40",
-   "metadata": {},
+   "id": "e1ebf5bd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(\\boldsymbol{x}, P\\right) = f\\left( \\left( \\boldsymbol{x}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}) }{\\partial x_N^n} \\right) \\right)^2\n",
@@ -5852,16 +6465,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6549ea7b",
-   "metadata": {},
+   "id": "b8c35553",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If we also have $M$ different sets of values for $x_1, \\dots, x_N$, that is $\\boldsymbol{x}_i = \\big(x_1^{(i)}, \\dots, x_N^{(i)}\\big)$ for $i = 1,\\dots,M$ being the rows in matrix $X$, the cost function can be generalized into"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "0956062e",
-   "metadata": {},
+   "id": "22a123d5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(X, P \\right) = \\sum_{i=1}^M f\\left( \\left( \\boldsymbol{x}_i, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}_i) }{\\partial x_N^n} \\right) \\right)^2.\n",
@@ -5870,8 +6487,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8fca0166",
-   "metadata": {},
+   "id": "b15eedf5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: The diffusion equation\n",
     "\n",
@@ -5880,8 +6499,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58ad6f25",
-   "metadata": {},
+   "id": "1a92cc8c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial g(x,t)}{\\partial t} = \\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
@@ -5890,16 +6511,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6e5728e",
-   "metadata": {},
+   "id": "e4862313",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where a possible choice of conditions are"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6921faa1",
-   "metadata": {},
+   "id": "5c186d68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -5912,16 +6537,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80e632ef",
-   "metadata": {},
+   "id": "57d4f000",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $u(x)$ being some given function."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a2711421",
-   "metadata": {},
+   "id": "7c2cdc6b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Defining the problem\n",
     "\n",
@@ -5930,8 +6559,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "981da4af",
-   "metadata": {},
+   "id": "bde064ea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"diffonedim\"></div>\n",
@@ -5945,16 +6576,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1b8c16d",
-   "metadata": {},
+   "id": "7a558c97",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b8ed6509",
-   "metadata": {},
+   "id": "534a4844",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -5967,8 +6602,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "200050ac",
-   "metadata": {},
+   "id": "a07e0730",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $u(x) = \\sin(\\pi x)$.\n",
     "\n",
@@ -5979,8 +6616,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5dca99d2",
-   "metadata": {},
+   "id": "74b72286",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the network using Autograd\n",
     "\n",
@@ -5996,8 +6635,11 @@
   {
    "cell_type": "code",
    "execution_count": 47,
-   "id": "85f4b843",
-   "metadata": {},
+   "id": "4a0c57e9",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "def sigmoid(z):\n",
@@ -6011,7 +6653,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -6048,8 +6690,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9dd68ff8",
-   "metadata": {},
+   "id": "350b1d3d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the network using Autograd; The trial solution\n",
     "\n",
@@ -6076,8 +6720,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65f68c5a",
-   "metadata": {},
+   "id": "9fd438b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Why the jacobian?\n",
     "\n",
@@ -6103,8 +6749,11 @@
   {
    "cell_type": "code",
    "execution_count": 48,
-   "id": "91612f4f",
-   "metadata": {},
+   "id": "d1c81690",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# Set up the trial function:\n",
@@ -6147,8 +6796,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff9df4ba",
-   "metadata": {},
+   "id": "ca22d9ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the network using Autograd; The full program\n",
     "\n",
@@ -6171,8 +6822,11 @@
   {
    "cell_type": "code",
    "execution_count": 49,
-   "id": "e6451b9e",
-   "metadata": {},
+   "id": "5a9146bc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -6195,7 +6849,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -6338,7 +6992,7 @@
     "    T,X = np.meshgrid(t,x)\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))\n",
     "    s = ax.plot_surface(T,X,g_dnn_ag,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -6346,14 +7000,14 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Analytical solution')\n",
     "    s = ax.plot_surface(T,X,G_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
     "    ax.set_ylabel('Position $x$');\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Difference')\n",
     "    s = ax.plot_surface(T,X,diff_ag,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -6402,8 +7056,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7f867cf2",
-   "metadata": {},
+   "id": "e59d2116",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Solving the wave equation with Neural Networks\n",
     "\n",
@@ -6412,8 +7068,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ded83be1",
-   "metadata": {},
+   "id": "e2ffdbaf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial^2 g(x,t)}{\\partial t^2} = c^2\\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
@@ -6422,8 +7080,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0aba0c9",
-   "metadata": {},
+   "id": "37b2cc03",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $c$ being the specified wave speed.\n",
     "\n",
@@ -6432,8 +7092,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28a48fe7",
-   "metadata": {},
+   "id": "524df5d3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -6447,16 +7109,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61ded78d",
-   "metadata": {},
+   "id": "d175b25f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $\\frac{\\partial g(x,t)}{\\partial t} \\Big |_{t = 0}$ means the derivative of $g(x,t)$ with respect to $t$ is evaluated at $t = 0$, and $u(x)$ and $v(x)$ being given functions."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "990695ea",
-   "metadata": {},
+   "id": "11b3289e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The problem to solve for\n",
     "\n",
@@ -6465,8 +7131,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58841089",
-   "metadata": {},
+   "id": "e469d65e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"wave\"></div>\n",
@@ -6480,8 +7148,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "303eb900",
-   "metadata": {},
+   "id": "5f773fa8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $c$ is the given wave speed.\n",
     "The chosen conditions for this equation are"
@@ -6489,8 +7159,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce5c5167",
-   "metadata": {},
+   "id": "2952f7b4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"condwave\"></div>\n",
@@ -6507,16 +7179,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "609a7556",
-   "metadata": {},
+   "id": "99057b48",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In this example, let $c = 1$ and $u(x) = \\sin(\\pi x)$ and $v(x) = -\\pi\\sin(\\pi x)$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5edb8797",
-   "metadata": {},
+   "id": "7debdfea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "Setting up the network is done in similar matter as for the example of solving the diffusion equation.\n",
@@ -6539,8 +7215,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6be7518",
-   "metadata": {},
+   "id": "2d5d5c44",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The analytical solution\n",
     "\n",
@@ -6553,8 +7231,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "368bb540",
-   "metadata": {},
+   "id": "f97806ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Solving the wave equation - the full program using Autograd"
    ]
@@ -6562,8 +7242,11 @@
   {
    "cell_type": "code",
    "execution_count": 50,
-   "id": "65085f11",
-   "metadata": {},
+   "id": "9337b7c7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -6620,7 +7303,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -6725,7 +7408,7 @@
     "    T,X = np.meshgrid(t,x)\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))\n",
     "    s = ax.plot_surface(T,X,res,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -6733,7 +7416,7 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Analytical solution')\n",
     "    s = ax.plot_surface(T,X,res_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -6741,7 +7424,7 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Difference')\n",
     "    s = ax.plot_surface(T,X,diff,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -6790,8 +7473,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "41011c90",
-   "metadata": {},
+   "id": "6071d006",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resources on differential equations and deep learning\n",
     "\n",
@@ -6805,25 +7490,7 @@
    ]
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.9.15"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 5
 }
diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js
index d29a47560..bb364a7d0 100644
--- a/doc/LectureNotes/_build/html/searchindex.js
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Week 42: Logistic Regression and Optimization, reminders from week 38 and week 40","<span class=\"section-number\">3. </span>Linear Regression","<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network","<span class=\"section-number\">15. </span>Solving Differential Equations  with Deep Learning","<span class=\"section-number\">16. </span>Convolutional Neural Networks","<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view","<span class=\"section-number\">4. </span>Ridge and Lasso Regression","<span class=\"section-number\">5. </span>Resampling Methods","<span class=\"section-number\">6. </span>Logistic Regression","<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims","<span class=\"section-number\">9. </span>Decision trees, overarching aims","<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)","<span class=\"section-number\">13. </span>Neural networks","<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm","<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Exercises week 41","Exercises week 42","Applied Data Analysis and Machine Learning","<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Project 2 on Machine Learning, deadline November 4 (Midnight)","Teaching schedule with links to material","<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Regression and Statistical interpretations","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and  Gradient Methods","Week 40: Gradient descent methods (continued) and start Neural networks","Week 41 Neural networks and constructing a neural network code","Week 42 Constructing a Neural Network code with examples","Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations"],titleterms:{"0":40,"1":[1,16,17,18,19,23,26,32,33,39,40,41],"11":39,"14":40,"16":36,"2":[1,16,17,18,19,23,27,32,33,34,39,40,41],"2023":30,"2024":[26,37,38,39,40],"21":41,"23":37,"26":33,"27":37,"3":[1,16,17,23,32,33,39,40,41],"30":38,"34":[16,32],"35":[17,33],"36":[18,34],"37":[19,35],"38":[0,20,36],"39":[21,22,37],"4":[1,23,27,33,40],"40":[0,22,38],"41":[22,39],"42":[0,23,40],"43":41,"5":[1,23],"6":23,"7":[23,26,39],"9":35,"case":[9,11,29,33,34,36,37],"class":[0,36,39],"do":[2,34,35,37,38,39,40,41],"final":[13,22,27,33,34,37,38,39,40,41],"float":39,"function":[0,1,2,7,8,9,11,12,13,14,22,26,27,29,32,33,34,35,36,37,38,39,40,41],"import":[6,22,25,32,33,34,38,39,40],"new":[5,34,35,39],A:[0,1,2,5,9,10,22,32,34,35,36,38,39,40,41],AND:[38,39],And:[22,32,33,34,36,37,38],But:[22,37,38],For:33,In:[30,39],Is:[39,40],Ising:7,OR:[38,39],The:[0,1,2,3,4,6,7,8,9,10,12,13,18,24,32,33,34,35,36,37,38,39,40,41],To:[32,33],With:[5,34],about:[32,33],abov:[34,39,40,41],activ:[2,13,23,27,34,38,39,40,41],ad:[1,7,18,26,32,33,38,39,40],adaboost:11,adagrad:[14,22,37,38],adam:[14,22,37,38],adapt:[11,22,37,38],adjust:[2,40,41],advanc:[22,38],adversari:5,again:[0,4,10,36],ai:[26,32],aim:[9,10,18,19,20,21,22,23,32],aka:[32,33],al:[22,38],algebra:[25,32],algorithm:[10,11,12,13,22,27,33,37,38,39,40,41],algortithm:[14,36,37],all:[9,39,40],an:[1,5,11,32,39],analys:[6,33],analysi:[1,6,7,12,24,26,27,29,32,33,34,35,39],analyt:[1,17,18,22,41],analyz:[39,40],ani:[14,36,37],anoth:[10,34,35],appli:24,approach:[1,9,15,32,35,37,38],approxim:[13,39],architectur:[2,40,41],argument:[37,38],arrai:[25,32],artifici:[38,39],assist:30,assumpt:[34,35],august:33,autocorrel:29,autograd:[3,14,22,37,38,41],automat:[14,22,37,38,39,41],avoid:[],b:[18,26,27,37],back:[2,12,13,39,40,41],background:[24,26,27,35],bag:11,base:[14,22,35,37,38],basic:[1,6,8,10,11,12,25,33,34,35,36,39],batch:[2,37,38,39,40],bay:[6,34,35],befor:12,bengio:[39,40],beta:[34,35],better:[9,38,39],bia:[7,26,35],bias:[39,40,41],binari:[2,40,41],bind:32,bird:11,boldsymbol:[33,34,35],book:[39,40,41],boost:11,bootstrap:[7,11,35],boston:1,breast:[2,40,41],brief:[32,35,36,37],bring:[13,39,40],build:[2,4,10,40,41],c:[26,27,32],calcul:33,can:[22,32,35,37,38,39],cancer:[0,2,8,10,12,36,40,41],cart:10,center:33,central:[14,24,29,35,36,37],chain:[13,39,40],challeng:36,chang:11,channel:32,chi:[1,32],choic:[39,40],choos:[2,40,41],cifar01:4,classic:12,classif:[0,2,10,11,27,36,40,41],classifi:[9,36],clip:[2,39,40],cluster:15,cnn:4,code:[1,2,3,6,10,12,13,14,15,22,27,32,33,34,35,36,37,38,39,40,41],collect:[2,4,40,41],come:36,commun:32,compact:[0,36,39,40],compar:[3,11,41],comparison:34,compet:[22,37,38],complet:[33,39,40],complex:[1,7,26,33],complic:[7,37,38,39],compon:12,comput:[10,37,38],computation:35,computerlab:32,con:10,concept:29,condit:[34,35,36,37],confid:35,conjug:[14,37],consider:[39,40],construct:[39,40,41],continu:38,contn:32,convex:[9,14,36,37],convolut:[4,13,38,39],correctli:[34,35],correl:[0,12,33,36],correspond:[36,37],cost:[0,2,11,33,34,35,36,37,39,40,41],count:39,cours:[24,31,32],covari:[6,12,29,33],cover:32,critic:27,cross:[0,7,26,35,36],custom:23,cython:32,d:[26,27],data:[0,1,2,4,7,8,10,12,16,17,23,24,26,29,32,33,34,36,39,40,41],dataset:[2,4,40,41],deadlin:[26,27,32],decai:[3,37,38,41],decis:[10,11],decomposit:[6,12,18,25,33],deep:[2,3,32,36,39,40,41],defin:[2,32,39,40,41],definit:[39,40],degre:[1,33],deliveri:[26,27],delta:35,dens:[1,32],deriv:[6,13,33,34,35,36,37,39,40],descent:[0,3,11,14,22,27,36,37,38,41],descript:26,design:33,detail:[4,32,41],develop:[2,40,41],diagon:12,differ:[9,27,37,38],different:22,differenti:[3,14,37,38,39,41],diffus:[3,41],dimension:[3,4,9,26,33,41],directli:[37,38],disadvantag:10,discret:29,discuss:[0,36],distribut:[6,29,34,35],distrubut:35,doe:[33,34,38,39],domain:29,dot:37,down:[2,39,40],dropout:[2,39,40],e:[26,27],each:[23,36],economi:33,electron:[26,27],element:[1,29,32,37,38],elimin:25,elu:[39,40,41],energi:32,ensembl:11,entri:[39,40],entropi:[0,10,36],environ:[1,16,32],equat:[1,3,13,32,33,34,36,37,39,40,41],error:[1,11,32,33,35],essenti:32,estim:[34,35],et:[22,38],etc:32,euler:[3,41],evalu:[2,27,39,40,41],exampl:[0,1,2,3,4,5,7,8,9,10,11,22,32,33,34,35,36,37,38,39,40,41],exercis:[0,1,7,16,17,18,19,20,21,22,23,32,33,39,41],expect:[19,29,34,35],expens:35,experi:29,explicit:[39,40],explod:[39,40],explor:[1,16,17,32],exponenti:[3,41],express:[0,18,19,33,36,37,39,40],extend:[0,36,37,39],extrapol:5,extrem:[11,32],ey:11,f:[26,27],fall:30,famili:[2,32,33,39,40,41],famou:25,fantast:33,featur:[10,25,33],feed:[2,13,38,39,40,41],find:[35,37],fine:[2,39,40],first:[5,13,27,32,33,34,36,37,39,40],fit:[1,11,32,34],fix:33,fold:[35,36],forc:4,forest:11,format:[26,27,32],forward:[2,3,13,38,39,40,41],fourier:4,frank:[7,26,33],freedom:[1,33],frequent:33,frequentist:[1,32],fridai:[],from:[0,6,11,13,22,27,33,34,35,36,37,38,39,40],full:[3,40,41],funtion:[39,40],further:[4,6,33],g:26,gan:5,gate:[38,39,40,41],gaussian:25,gd:[14,22,37,38],gener:[5,10,32,39],geometr:[12,36,37],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Week 42: Logistic Regression and Optimization, reminders from week 38 and week 40","<span class=\"section-number\">3. </span>Linear Regression","<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network","<span class=\"section-number\">15. </span>Solving Differential Equations  with Deep Learning","<span class=\"section-number\">16. </span>Convolutional Neural Networks","<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view","<span class=\"section-number\">4. </span>Ridge and Lasso Regression","<span class=\"section-number\">5. </span>Resampling Methods","<span class=\"section-number\">6. </span>Logistic Regression","<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims","<span class=\"section-number\">9. </span>Decision trees, overarching aims","<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)","<span class=\"section-number\">13. </span>Neural networks","<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm","<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Exercises week 41","Exercises week 42","Applied Data Analysis and Machine Learning","<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Project 2 on Machine Learning, deadline November 4 (Midnight)","Teaching schedule with links to material","<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Regression and Statistical interpretations","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and  Gradient Methods","Week 40: Gradient descent methods (continued) and start Neural networks","Week 41 Neural networks and constructing a neural network code","Week 42 Constructing a Neural Network code with examples","Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations"],titleterms:{"0":40,"1":[1,16,17,18,19,23,26,32,33,39,40,41],"11":39,"14":40,"16":36,"2":[1,16,17,18,19,23,27,32,33,34,39,40,41],"2023":30,"2024":[26,37,38,39,40],"21":41,"23":37,"26":33,"27":37,"3":[1,16,17,23,32,33,39,40,41],"30":38,"34":[16,32],"35":[17,33],"36":[18,34],"37":[19,35],"38":[0,20,36],"39":[21,22,37],"4":[1,23,27,33,40],"40":[0,22,38],"41":[22,39],"42":[0,23,40],"43":41,"5":[1,23],"6":23,"7":[23,26,39],"9":35,"case":[9,11,29,33,34,36,37],"class":[0,36,39],"do":[2,34,35,37,38,39,40,41],"final":[13,22,27,33,34,37,38,39,40,41],"float":39,"function":[0,1,2,7,8,9,11,12,13,14,22,26,27,29,32,33,34,35,36,37,38,39,40,41],"import":[6,22,25,32,33,34,38,39,40],"new":[5,34,35,39],A:[0,1,2,5,9,10,22,32,34,35,36,38,39,40,41],AND:[38,39],And:[22,32,33,34,36,37,38],But:[22,37,38],For:33,In:[30,39],Is:[39,40],Ising:7,OR:[38,39],The:[0,1,2,3,4,6,7,8,9,10,12,13,18,24,32,33,34,35,36,37,38,39,40,41],To:[32,33],With:[5,34],about:[32,33],abov:[34,39,40,41],activ:[2,13,23,27,34,38,39,40,41],ad:[1,7,18,26,32,33,38,39,40],adaboost:11,adagrad:[14,22,37,38],adam:[14,22,37,38],adapt:[11,22,37,38],adjust:[2,40,41],advanc:[22,38],adversari:5,again:[0,4,10,36],ai:[26,32],aim:[9,10,18,19,20,21,22,23,32],aka:[32,33],al:[22,38],algebra:[25,32],algorithm:[10,11,12,13,22,27,33,37,38,39,40,41],algortithm:[14,36,37],all:[9,39,40],an:[1,5,11,32,39],analys:[6,33],analysi:[1,6,7,12,24,26,27,29,32,33,34,35,39],analyt:[1,17,18,22,41],analyz:[39,40],ani:[14,36,37],anoth:[10,34,35],appli:24,approach:[1,9,15,32,35,37,38],approxim:[13,39],architectur:[2,40,41],argument:[37,38],arrai:[25,32],artifici:[38,39],assist:30,assumpt:[34,35],august:33,autocorrel:29,autograd:[3,14,22,37,38,41],automat:[14,22,37,38,39,41],avoid:[],b:[18,26,27,37],back:[2,12,13,39,40,41],background:[24,26,27,35],bag:11,base:[14,22,35,37,38],basic:[1,6,8,10,11,12,25,33,34,35,36,39],batch:[2,37,38,39,40],bay:[6,34,35],befor:12,bengio:[39,40],beta:[34,35],better:[9,38,39],bia:[7,26,35],bias:[39,40,41],binari:[2,40,41],bind:32,bird:11,boldsymbol:[33,34,35],book:[39,40,41],boost:11,bootstrap:[7,11,35],boston:1,breast:[2,40,41],brief:[32,35,36,37],bring:[13,39,40],build:[2,4,10,40,41],c:[26,27,32],calcul:33,can:[22,32,35,37,38,39],cancer:[0,2,8,10,12,36,40,41],cart:10,center:33,central:[14,24,29,35,36,37],chain:[13,39,40],challeng:36,chang:11,channel:32,chi:[1,32],choic:[39,40],choos:[2,40,41],cifar01:4,classic:12,classif:[0,2,10,11,27,36,40,41],classifi:[9,36],clip:[2,39,40],cluster:15,cnn:4,code:[1,2,3,6,10,12,13,14,15,22,27,32,33,34,35,36,37,38,39,40,41],collect:[2,4,40,41],come:36,commun:32,compact:[0,36,39,40],compar:[3,11,41],comparison:34,compet:[22,37,38],complet:[33,39,40],complex:[1,7,26,33],complic:[7,37,38,39],compon:12,comput:[10,37,38],computation:35,computerlab:32,con:10,concept:29,condit:[34,35,36,37],confid:35,conjug:[14,37],consider:[39,40],construct:[39,40,41],continu:38,contn:32,convex:[9,14,36,37],convolut:[4,13,38,39],correctli:[34,35],correl:[0,12,33,36],correspond:[36,37],cost:[0,2,11,33,34,35,36,37,39,40,41],count:39,cours:[24,31,32],covari:[6,12,29,33],cover:32,critic:27,cross:[0,7,26,35,36],custom:23,cython:32,d:[26,27],data:[0,1,2,4,7,8,10,12,16,17,23,24,26,29,32,33,34,36,39,40,41],dataset:[2,4,40,41],deadlin:[26,27,32],decai:[3,37,38,41],decis:[10,11],decomposit:[6,12,18,25,33],deep:[2,3,32,36,39,40,41],defin:[2,32,39,40,41],definit:[39,40],degre:[1,33],deliveri:[26,27],delta:35,dens:[1,32],deriv:[6,13,33,34,35,36,37,39,40],descent:[0,3,11,14,22,27,36,37,38,41],descript:26,design:33,detail:[4,32,41],develop:[2,40,41],diagon:12,differ:[9,27,37,38],different:22,differenti:[3,14,37,38,39,41],diffus:[3,41],dimension:[3,4,9,26,33,41],directli:[37,38],disadvantag:10,discret:29,discuss:[0,36],distribut:[6,29,34,35],distrubut:35,doe:[33,34,38,39],domain:29,dot:37,down:[2,39,40],dropout:[2,39,40],e:[26,27],each:[23,36],economi:33,electron:[26,27],element:[1,29,32,37,38],elimin:25,elu:[39,40,41],energi:32,ensembl:11,entri:[39,40],entropi:[0,10,36],environ:[1,16,32],equat:[1,3,13,32,33,34,36,37,39,40,41],error:[1,11,32,33,35],essenti:32,estim:[34,35],et:[22,38],etc:32,euler:[3,41],evalu:[2,27,39,40,41],exampl:[0,1,2,3,4,5,7,8,9,10,11,22,32,33,34,35,36,37,38,39,40,41],exercis:[0,1,7,16,17,18,19,20,21,22,23,32,33,39,41],expect:[19,29,34,35],expens:35,experi:29,explicit:[39,40],explod:[39,40],explor:[1,16,17,32],exponenti:[3,41],express:[0,18,19,33,36,37,39,40],extend:[0,36,37,39],extrapol:5,extrem:[11,32],ey:11,f:[26,27],fall:30,famili:[2,32,33,39,40,41],famou:25,fantast:33,featur:[10,25,33],feed:[2,13,38,39,40,41],find:[35,37],fine:[2,39,40],first:[5,13,27,32,33,34,36,37,39,40,41],fit:[1,11,32,34],fix:33,fold:[35,36],forc:4,forest:11,format:[26,27,32],forward:[2,3,13,38,39,40,41],fourier:4,frank:[7,26,33],freedom:[1,33],frequent:33,frequentist:[1,32],fridai:[],from:[0,6,11,13,22,27,33,34,35,36,37,38,39,40],full:[3,40,41],funtion:[39,40],further:[4,6,33],g:26,gan:5,gate:[38,39,40,41],gaussian:25,gd:[14,22,37,38],gener:[5,10,32,39],geometr:[12,36,37],get:[22,38,39],gini:10,glorot:[39,40],good:[1,32],goodfellow:[22,38],grade:[30,32],gradient:[0,2,3,11,14,22,27,36,37,38,39,40,41],grid:36,group:36,growth:[3,41],ha:24,hand:[39,40,41],handl:[25,32,33],happen:[34,35],hard:[],hessian:[33,36,37],hidden:[3,39,40,41],histogram:35,homework:[36,37],homogen:[39,40],hous:1,how:36,hyperbol:[38,39,40],hyperparamet:[2,39,40,41],hyperplan:9,i:[2,41],id3:10,idea:12,ideal:[36,37],ident:[34,35],identifi:35,ii:[32,41],iid:[34,35],iii:41,illustr:[34,38,39],implement:[2,38,40,41],implic:[6,33],improv:[2,37,40,41],includ:[0,14,22,36,37,38,39],increment:12,independ:[34,35],index:10,inform:30,ingredi:39,init:[40,41],input:[3,23,39,40,41],insight:[39,40],instal:[24,26,32],instructor:30,intercept:33,intermedi:39,interpret:[6,12,32,33,34,35,36,37],interv:35,introduc:[12,14,22,33,37,38],introduct:[1,7,24,25,26,27,32,38,39],invers:[6,25,34],invert:33,iter:[11,37],its:33,iv:41,jacobian:[33,41],jax:[14,22,37,38],job:[38,39],julia:32,jungl:11,k:[35,36,39,40],kera:[2,4,40,41],kernel:[9,12],l:[39,40],lab:[35,36,37,38,41],lagrangian:9,lambda:36,lasso:[6,7,26,33,34,35,36,38],last:[33,36,38,39,40],later:[6,33,40],layer:[2,3,4,13,23,39,40,41],layout:[39,40],learn:[1,2,3,12,14,15,16,17,22,24,26,27,32,33,34,35,36,37,38,39,40,41],least:[6,7,19,26,32,33,34],lectur:[32,33,34,35,36,37,38,39,40,41],level:11,librari:[24,32],likelihood:[0,8,34,35,36],limit:[2,14,29,35,36,37,38,39,40],linear:[1,9,14,25,27,32,33,34,36],link:[6,12,28,31,33,34,35],list:[39,40],literatur:[26,27],logist:[0,8,27,32,36,37,38,39,40],loop:[37,38],loss:[33,36,37],lu:25,machin:[1,9,14,24,26,27,32,36,37],made:[34,35],main:[29,32],make:[1,10,11,16,17,32,33],mani:[11,13],manipul:33,margin:[34,35],mass:32,materi:[26,28,32,33,34,35,36,39,40,41],math:[6,33],mathemat:[4,6,9,33,37,38,39,40,41],matric:[6,25,32,34],matrix:[0,2,6,12,13,25,32,33,34,36,37,38,40,41],matter:[1,32],max:33,maximum:[34,35,36],mean:[1,33,34,36],measur:[0,36],meet:[6,11,29,32,33],mercer:9,method:[7,10,11,14,22,26,32,35,36,37,38,40,41],midnight:[26,27],min:33,mini:[37,38],minibatch:[22,37,38],minim:[0,32,36,41],ml:32,mle:[34,35],mlp:13,mnist:[4,5],mode:39,model:[1,2,5,7,13,32,38,39,40,41],moment:[37,38],momentum:[14,22,37,38],mondai:[33,34,35,36,37,38,39,41],moon:[9,10],more:[0,4,7,22,25,26,32,33,34,35,36,37,38,39,40,41],multi:[38,39,40,41],multiclass:[40,41],multilay:[13,38,39],multipl:[2,4,23,40,41],multipli:9,multivari:39,need:[26,32],network:[0,2,3,4,5,8,13,27,32,36,38,39,40,41],neural:[2,3,4,5,8,13,27,32,38,39,40,41],neuron:[38,39],newton:[22,36,37,38],nn:[39,40,41],node:[39,40],noeds:40,noen:22,non:9,none:[37,38],normal:[1,2,35,39,40],notat:[13,38],note:[22,26,33,34,38],novemb:27,now:[2,10,14,22,34,35,37,38,40,41],nuclear:[1,32],nueral:[0,36],numba:32,number:[1,3,22,29,33,37,38,39,41],numer:[3,26,27,29,41],numpi:[22,25,32,37,38],object:[4,40,41],observ:[39,40],obtain:12,octob:[26,39,40,41],od:[3,41],off:[7,26],ol:[6,7,22,26,34,35,37,38],onc:23,one:[3,13,36,37,39,40,41],ones:[38,39,40],oper:[25,39],optim:[0,2,9,14,24,32,33,36,37,38,39,40,41],option:23,order:[14,22,37,38],ordinari:[6,7,19,26,32,33,34,41],organ:[1,32],orient:[40,41],oslo:31,other:[0,5,10,12,13,25,26,32,33,36,38,39,40,41],ouput:[39,40],our:[1,5,6,12,14,32,33,36,37,39,40],outcom:[24,32],output:[3,39,40,41],over:[39,40],overarch:[1,5,9,10,18,19,20,21,22,23,32,33,39],overview:[11,32,37,38],own:[1,11,12,16,17,27,32,33],packag:[25,32],panda:[32,33],paper:[26,39,40],parallel:39,paramet:[0,32,33,36,37,38,39,40],part:[14,24,26,27,33,36,37,39,40,41],partial:[3,41],pass:[2,40,41],pca:12,pdf:29,pencil:26,percepetron:[39,40],perceptron:[13,38,39,40,41],perform:[2,10,40,41],period:4,perspect:[2,39,40],plan:[33,34,35,36,37,38,39,41],plot:[35,36],point:[5,39],poisson:[3,41],polynomi:[4,34],popul:[3,41],popular:32,possibl:41,practic:[14,22,30,32,37,38],pre:[2,4,40,41],preambl:26,predict:[5,23],predictor:[0,36],preprocess:33,prerequisit:[4,24,32],princip:12,principl:4,pro:10,probabl:[6,29,34,35],problem:[2,3,14,22,32,33,34,36,37,38,39,40,41],procedur:[10,32],process:[2,4,23,40,41],product:37,program:[3,14,26,27,36,37,39,41],project:[7,26,27,32,36],prop:[14,37,38],propag:[2,13,39,40,41],properti:[6,29,33,36],python:[1,10,16,24,25,32],quick:9,r:32,random:[11,12,29,36],raphson:[36,37],rate:[22,37,38,40,41],read:[10,32,33,35,36,38,39,40,41],real:[7,23,26,32,39],recommend:[32,33,39,40,41],rectangular:34,recurr:[5,13,38,39],recurs:[37,38],reduc:[1,33,39],reduct:4,refer:26,reformul:[3,41],regress:[0,1,6,7,8,10,11,14,18,19,26,27,32,33,34,35,36,37,38,39],regular:[2,36,40,41],relat:33,relev:[31,33,36,38,39,40],relu:[2,39,40,41],remark:4,remind:[0,7,9,32,36,37,39,40,41],repeat:33,replac:[14,37,38],report:[26,27],repositori:35,repres:[],requir:[3,24,41],resampl:[7,26,35],rescal:[7,34],residu:33,resourc:[3,41],result:[33,34,39,40],revers:39,revisit:[14,36,37],rewrit:[32,33,35],rewritten:36,ridg:[1,6,7,18,19,26,33,34,35,36,37,38],rm:[14,37,38],rmsprop:[22,37,38],root:[39,40],rule:[13,39,40],s:[9,11,22,35,36,37,38],same:[14,22,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\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/week43.html b/doc/LectureNotes/_build/html/week43.html
index 8c52d4663..acc647cab 100644
--- a/doc/LectureNotes/_build/html/week43.html
+++ b/doc/LectureNotes/_build/html/week43.html
@@ -711,13 +711,13 @@ const thebe_selector_output = ".output, .cell_output"
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#solving-odes-with-deep-learning">
-   Solving ODEs with Deep Learning
+  <a class="reference internal nav-link" href="#solving-differential-equations-with-deep-learning">
+   Solving differential equations  with Deep Learning
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ordinary-differential-equations">
-   Ordinary Differential Equations
+  <a class="reference internal nav-link" href="#ordinary-differential-equations-first">
+   Ordinary Differential Equations first
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
@@ -1250,13 +1250,13 @@ const thebe_selector_output = ".output, .cell_output"
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#solving-odes-with-deep-learning">
-   Solving ODEs with Deep Learning
+  <a class="reference internal nav-link" href="#solving-differential-equations-with-deep-learning">
+   Solving differential equations  with Deep Learning
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ordinary-differential-equations">
-   Ordinary Differential Equations
+  <a class="reference internal nav-link" href="#ordinary-differential-equations-first">
+   Ordinary Differential Equations first
   </a>
  </li>
  <li class="toc-h2 nav-item toc-entry">
@@ -2346,7 +2346,7 @@ the <em>Hadamard product</em>, meaning element-wise multiplication.</p>
 <div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Old accuracy on training data: 0.1440501043841336
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 </pre></div>
 </div>
@@ -2682,7 +2682,7 @@ Lambda =  10.0
 Accuracy score on test set:  0.19166666666666668
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 </pre></div>
 </div>
@@ -2691,7 +2691,7 @@ Lambda =  1e-05
 Accuracy score on test set:  0.10555555555555556
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 </pre></div>
 </div>
@@ -2700,7 +2700,7 @@ Lambda =  0.0001
 Accuracy score on test set:  0.08611111111111111
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 </pre></div>
 </div>
@@ -2709,7 +2709,7 @@ Lambda =  0.001
 Accuracy score on test set:  0.10555555555555556
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 </pre></div>
 </div>
@@ -2718,7 +2718,7 @@ Lambda =  0.01
 Accuracy score on test set:  0.08888888888888889
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 </pre></div>
 </div>
@@ -2727,7 +2727,7 @@ Lambda =  0.1
 Accuracy score on test set:  0.08611111111111111
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 </pre></div>
 </div>
@@ -2736,7 +2736,7 @@ Lambda =  1.0
 Accuracy score on test set:  0.08888888888888889
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 </pre></div>
 </div>
@@ -2745,11 +2745,11 @@ Lambda =  10.0
 Accuracy score on test set:  0.09166666666666666
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 </pre></div>
 </div>
@@ -2758,11 +2758,11 @@ Lambda =  1e-05
 Accuracy score on test set:  0.07777777777777778
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 </pre></div>
 </div>
@@ -2771,11 +2771,11 @@ Lambda =  0.0001
 Accuracy score on test set:  0.07777777777777778
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 </pre></div>
 </div>
@@ -2784,11 +2784,11 @@ Lambda =  0.001
 Accuracy score on test set:  0.07777777777777778
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 </pre></div>
 </div>
@@ -2797,130 +2797,37 @@ Lambda =  0.01
 Accuracy score on test set:  0.07777777777777778
 </pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
+/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  0.1
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  1.0
-Accuracy score on test set:  0.10555555555555556
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  10.0
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  1e-05
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  0.0001
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  0.001
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  0.01
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  0.1
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  1.0
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  10.0
-Accuracy score on test set:  0.07777777777777778
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">KeyboardInterrupt</span><span class="g g-Whitespace">                         </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">8</span><span class="p">],</span> <span class="n">line</span> <span class="mi">11</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">lmbd</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">lmbd_vals</span><span class="p">):</span>
+<span class="g g-Whitespace">      </span><span class="mi">9</span>     <span class="n">dnn</span> <span class="o">=</span> <span class="n">NeuralNetwork</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">Y_train_onehot</span><span class="p">,</span> <span class="n">eta</span><span class="o">=</span><span class="n">eta</span><span class="p">,</span> <span class="n">lmbd</span><span class="o">=</span><span class="n">lmbd</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="n">epochs</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">,</span>
+<span class="g g-Whitespace">     </span><span class="mi">10</span>                         <span class="n">n_hidden_neurons</span><span class="o">=</span><span class="n">n_hidden_neurons</span><span class="p">,</span> <span class="n">n_categories</span><span class="o">=</span><span class="n">n_categories</span><span class="p">)</span>
+<span class="ne">---&gt; </span><span class="mi">11</span>     <span class="n">dnn</span><span class="o">.</span><span class="n">train</span><span class="p">()</span>
+<span class="g g-Whitespace">     </span><span class="mi">13</span>     <span class="n">DNN_numpy</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dnn</span>
+<span class="g g-Whitespace">     </span><span class="mi">15</span>     <span class="n">test_predict</span> <span class="o">=</span> <span class="n">dnn</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
+
+<span class="nn">Cell In[6], line 99,</span> in <span class="ni">NeuralNetwork.train</span><span class="nt">(self)</span>
+<span class="g g-Whitespace">     </span><span class="mi">96</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data_full</span><span class="p">[</span><span class="n">chosen_datapoints</span><span class="p">]</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="bp">self</span><span class="o">.</span><span class="n">feed_forward</span><span class="p">()</span>
+<span class="ne">---&gt; </span><span class="mi">99</span> <span class="bp">self</span><span class="o">.</span><span class="n">backpropagation</span><span class="p">()</span>
+
+<span class="nn">Cell In[6], line 64,</span> in <span class="ni">NeuralNetwork.backpropagation</span><span class="nt">(self)</span>
+<span class="g g-Whitespace">     </span><span class="mi">61</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_weights_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">a_h</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">error_output</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">62</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_bias_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">error_output</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+<span class="ne">---&gt; </span><span class="mi">64</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_weights_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">X_data</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">error_hidden</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">65</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_bias_gradient</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">error_hidden</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">67</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">lmbd</span> <span class="o">&gt;</span> <span class="mf">0.0</span><span class="p">:</span>
+
+<span class="ne">KeyboardInterrupt</span>: 
 </pre></div>
 </div>
 </div>
@@ -2966,22 +2873,6 @@ Accuracy score on test set:  0.07777777777777778
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
-</div>
-<img alt="_images/week43_96_1.png" src="_images/week43_96_1.png" />
-<img alt="_images/week43_96_2.png" src="_images/week43_96_2.png" />
-</div>
 </div>
 </div>
 <div class="section" id="scikit-learn-implementation">
@@ -3017,328 +2908,6 @@ performance overall.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  1e-05
-Accuracy score on test set:  0.18333333333333332
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.0001
-Accuracy score on test set:  0.18611111111111112
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.001
-Accuracy score on test set:  0.13055555555555556
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.01
-Accuracy score on test set:  0.24444444444444444
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.1
-Accuracy score on test set:  0.23333333333333334
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  1.0
-Accuracy score on test set:  0.12777777777777777
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  10.0
-Accuracy score on test set:  0.1527777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  1e-05
-Accuracy score on test set:  0.9111111111111111
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  0.0001
-Accuracy score on test set:  0.8888888888888888
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  0.001
-Accuracy score on test set:  0.8722222222222222
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  0.01
-Accuracy score on test set:  0.8305555555555556
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
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-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  1.0
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-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  10.0
-Accuracy score on test set:  0.8944444444444445
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  1e-05
-Accuracy score on test set:  0.975
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  0.0001
-Accuracy score on test set:  0.9777777777777777
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
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-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
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-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
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-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
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-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
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-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
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-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
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-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
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-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
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-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
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-Accuracy score on test set:  0.9888888888888889
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
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-Accuracy score on test set:  0.9722222222222222
-
-Learning rate  =  0.01
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-Accuracy score on test set:  0.9527777777777777
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
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-
-Learning rate  =  0.1
-Lambda =  0.0001
-Accuracy score on test set:  0.8583333333333333
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
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-
-Learning rate  =  0.1
-Lambda =  0.01
-Accuracy score on test set:  0.9055555555555556
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
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-
-Learning rate  =  0.1
-Lambda =  1.0
-Accuracy score on test set:  0.8722222222222222
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
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-
-Learning rate  =  1.0
-Lambda =  1e-05
-Accuracy score on test set:  0.08611111111111111
-
-Learning rate  =  1.0
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-Accuracy score on test set:  0.10555555555555556
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
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-
-Learning rate  =  1.0
-Lambda =  0.01
-Accuracy score on test set:  0.17777777777777778
-
-Learning rate  =  1.0
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-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  1.0
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-
-Learning rate  =  1.0
-Lambda =  10.0
-Accuracy score on test set:  0.09444444444444444
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  1e-05
-Accuracy score on test set:  0.17222222222222222
-
-Learning rate  =  10.0
-Lambda =  0.0001
-Accuracy score on test set:  0.11666666666666667
-
-Learning rate  =  10.0
-Lambda =  0.001
-Accuracy score on test set:  0.10555555555555556
-
-Learning rate  =  10.0
-Lambda =  0.01
-Accuracy score on test set:  0.1388888888888889
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  0.1
-Accuracy score on test set:  0.11388888888888889
-
-Learning rate  =  10.0
-Lambda =  1.0
-Accuracy score on test set:  0.10555555555555556
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  10.0
-Accuracy score on test set:  0.09444444444444444
-</pre></div>
-</div>
-</div>
 </div>
 </div>
 <div class="section" id="id1">
@@ -3382,10 +2951,6 @@ Accuracy score on test set:  0.09444444444444444
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week43_100_0.png" src="_images/week43_100_0.png" />
-<img alt="_images/week43_100_1.png" src="_images/week43_100_1.png" />
-</div>
 </div>
 </div>
 <div class="section" id="building-neural-networks-in-tensorflow-and-keras">
@@ -3424,14 +2989,6 @@ how simple solving a machine learning problem can be.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span>  <span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">12</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
-    <span class="n">pip3</span> <span class="n">install</span> <span class="n">tensorflow</span>
-         <span class="o">^</span>
-<span class="ne">SyntaxError</span>: invalid syntax
-</pre></div>
-</div>
-</div>
 </div>
 <p>and/or if you use <strong>anaconda</strong>, just write (or install from the graphical user interface)
 (current release of CPU-only TensorFlow)</p>
@@ -3558,7 +3115,7 @@ If you have Anaconda installed you may run the following command</p>
     <span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">Dense</span><span class="p">(</span><span class="n">n_neurons_layer2</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">&#39;sigmoid&#39;</span><span class="p">,</span> <span class="n">kernel_regularizer</span><span class="o">=</span><span class="n">regularizers</span><span class="o">.</span><span class="n">l2</span><span class="p">(</span><span class="n">lmbd</span><span class="p">)))</span>
     <span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">Dense</span><span class="p">(</span><span class="n">n_categories</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">&#39;softmax&#39;</span><span class="p">))</span>
     
-    <span class="n">sgd</span> <span class="o">=</span> <span class="n">optimizers</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">lr</span><span class="o">=</span><span class="n">eta</span><span class="p">)</span>
+    <span class="n">sgd</span> <span class="o">=</span> <span class="n">optimizers</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">learning_rate</span><span class="o">=</span><span class="n">eta</span><span class="p">)</span>
     <span class="n">model</span><span class="o">.</span><span class="n">compile</span><span class="p">(</span><span class="n">loss</span><span class="o">=</span><span class="s1">&#39;categorical_crossentropy&#39;</span><span class="p">,</span> <span class="n">optimizer</span><span class="o">=</span><span class="n">sgd</span><span class="p">,</span> <span class="n">metrics</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;accuracy&#39;</span><span class="p">])</span>
     
     <span class="k">return</span> <span class="n">model</span>
@@ -3738,7 +3295,7 @@ If you have Anaconda installed you may run the following command</p>
         <span class="k">else</span><span class="p">:</span>                       <span class="c1">#Subsequent layers are capable of automatic shape inferencing</span>
             <span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">Dense</span><span class="p">(</span><span class="n">n_neuron</span><span class="p">,</span><span class="n">activation</span><span class="o">=</span><span class="s1">&#39;relu&#39;</span><span class="p">,</span><span class="n">kernel_regularizer</span><span class="o">=</span><span class="n">regularizers</span><span class="o">.</span><span class="n">l2</span><span class="p">(</span><span class="n">lamda</span><span class="p">)))</span>
     <span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">Dense</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="n">activation</span><span class="o">=</span><span class="s1">&#39;softmax&#39;</span><span class="p">))</span>  <span class="c1">#2 outputs - ordered and disordered (softmax for prob)</span>
-    <span class="n">sgd</span><span class="o">=</span><span class="n">optimizers</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">lr</span><span class="o">=</span><span class="n">eta</span><span class="p">)</span>
+    <span class="n">sgd</span><span class="o">=</span><span class="n">optimizers</span><span class="o">.</span><span class="n">SGD</span><span class="p">(</span><span class="n">learning_rate</span><span class="o">=</span><span class="n">eta</span><span class="p">)</span>
     <span class="n">model</span><span class="o">.</span><span class="n">compile</span><span class="p">(</span><span class="n">loss</span><span class="o">=</span><span class="s1">&#39;categorical_crossentropy&#39;</span><span class="p">,</span><span class="n">optimizer</span><span class="o">=</span><span class="n">sgd</span><span class="p">,</span><span class="n">metrics</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;accuracy&#39;</span><span class="p">])</span>
     <span class="k">return</span> <span class="n">model</span>
 
@@ -4828,8 +4385,8 @@ digits between the range of 0 to 9.</p>
 </div>
 <p>Not bad, but the results depend strongly on the learning reate. Try different learning rates.</p>
 </div>
-<div class="section" id="solving-odes-with-deep-learning">
-<h2>Solving ODEs with Deep Learning<a class="headerlink" href="#solving-odes-with-deep-learning" title="Permalink to this headline">¶</a></h2>
+<div class="section" id="solving-differential-equations-with-deep-learning">
+<h2>Solving differential equations  with Deep Learning<a class="headerlink" href="#solving-differential-equations-with-deep-learning" title="Permalink to this headline">¶</a></h2>
 <p>The Universal Approximation Theorem states that a neural network can
 approximate any function at a single hidden layer along with one input
 and output layer to any given precision.</p>
@@ -4841,8 +4398,8 @@ and output layer to any given precision.</p>
 <p>The lectures on differential equations were developed by Kristine Baluka Hein, now PhD student at IFI.
 A great thanks to Kristine.</p>
 </div>
-<div class="section" id="ordinary-differential-equations">
-<h2>Ordinary Differential Equations<a class="headerlink" href="#ordinary-differential-equations" title="Permalink to this headline">¶</a></h2>
+<div class="section" id="ordinary-differential-equations-first">
+<h2>Ordinary Differential Equations first<a class="headerlink" href="#ordinary-differential-equations-first" title="Permalink to this headline">¶</a></h2>
 <p>An ordinary differential equation (ODE) is an equation involving functions having one variable.</p>
 <p>In general, an ordinary differential equation looks like</p>
 <!-- Equation labels as ordinary links -->
@@ -5350,8 +4907,8 @@ P_{\text{output},\text{new}} &amp;= P_{\text{output}} - \lambda \nabla_{P_{\text
 <span class="c1"># but with number of hidden layers specified by the user.</span>
 <span class="k">def</span> <span class="nf">deep_neural_network</span><span class="p">(</span><span class="n">deep_params</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
     <span class="c1"># N_hidden is the number of hidden layers</span>
-
-    <span class="n">N_hidden</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consists of</span>
+    <span class="c1"># deep_params is a list, len() should be used</span>
+    <span class="n">N_hidden</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consists of</span>
                                         <span class="c1"># parameters to all the hidden</span>
                                         <span class="c1"># layers AND the output layer.</span>
 
@@ -5572,9 +5129,12 @@ g(t) = \frac{Ag_0}{g_0 + (A - g_0)\exp(-\alpha A t)}
     <span class="n">g0</span> <span class="o">=</span> <span class="mf">1.2</span>
     <span class="k">return</span> <span class="n">alpha</span><span class="p">,</span> <span class="n">A</span><span class="p">,</span> <span class="n">g0</span>
 
-<span class="k">def</span> <span class="nf">deep_neural_network</span><span class="p">(</span><span class="n">P</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
+<span class="k">def</span> <span class="nf">deep_neural_network</span><span class="p">(</span><span class="n">deep_params</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
     <span class="c1"># N_hidden is the number of hidden layers</span>
-    <span class="n">N_hidden</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">P</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consist of parameters to all the hidden layers AND the output layer</span>
+    <span class="c1"># deep_params is a list, len() should be used</span>
+    <span class="n">N_hidden</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consists of</span>
+                                        <span class="c1"># parameters to all the hidden</span>
+                                        <span class="c1"># layers AND the output layer.</span>
 
     <span class="c1"># Assumes input x being an one-dimensional array</span>
     <span class="n">num_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
@@ -5591,7 +5151,7 @@ g(t) = \frac{Ag_0}{g_0 + (A - g_0)\exp(-\alpha A t)}
 
     <span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_hidden</span><span class="p">):</span>
         <span class="c1"># From the list of parameters P; find the correct weigths and bias for this layer</span>
-        <span class="n">w_hidden</span> <span class="o">=</span> <span class="n">P</span><span class="p">[</span><span class="n">l</span><span class="p">]</span>
+        <span class="n">w_hidden</span> <span class="o">=</span> <span class="n">deep_params</span><span class="p">[</span><span class="n">l</span><span class="p">]</span>
 
         <span class="c1"># Add a row of ones to include bias</span>
         <span class="n">x_prev</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span><span class="n">num_values</span><span class="p">)),</span> <span class="n">x_prev</span> <span class="p">),</span> <span class="n">axis</span> <span class="o">=</span> <span class="mi">0</span><span class="p">)</span>
@@ -5605,7 +5165,7 @@ g(t) = \frac{Ag_0}{g_0 + (A - g_0)\exp(-\alpha A t)}
     <span class="c1">## Output layer:</span>
 
     <span class="c1"># Get the weights and bias for this layer</span>
-    <span class="n">w_output</span> <span class="o">=</span> <span class="n">P</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+    <span class="n">w_output</span> <span class="o">=</span> <span class="n">deep_params</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
 
     <span class="c1"># Include bias:</span>
     <span class="n">x_prev</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span><span class="n">num_values</span><span class="p">)),</span> <span class="n">x_prev</span><span class="p">),</span> <span class="n">axis</span> <span class="o">=</span> <span class="mi">0</span><span class="p">)</span>
@@ -5616,6 +5176,8 @@ g(t) = \frac{Ag_0}{g_0 + (A - g_0)\exp(-\alpha A t)}
     <span class="k">return</span> <span class="n">x_output</span>
 
 
+
+
 <span class="k">def</span> <span class="nf">cost_function_deep</span><span class="p">(</span><span class="n">P</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
 
     <span class="c1"># Evaluate the trial function with the current parameters P</span>
@@ -5906,7 +5468,10 @@ g(x) = x(1 - x)\exp(x)
 
 <span class="k">def</span> <span class="nf">deep_neural_network</span><span class="p">(</span><span class="n">deep_params</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
     <span class="c1"># N_hidden is the number of hidden layers</span>
-    <span class="n">N_hidden</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consist of parameters to all the hidden layers AND the output layer</span>
+    <span class="c1"># deep_params is a list, len() should be used</span>
+    <span class="n">N_hidden</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consists of</span>
+                                        <span class="c1"># parameters to all the hidden</span>
+                                        <span class="c1"># layers AND the output layer.</span>
 
     <span class="c1"># Assumes input x being an one-dimensional array</span>
     <span class="n">num_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
@@ -5947,6 +5512,7 @@ g(x) = x(1 - x)\exp(x)
 
     <span class="k">return</span> <span class="n">x_output</span>
 
+
 <span class="k">def</span> <span class="nf">solve_ode_deep_neural_network</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">num_neurons</span><span class="p">,</span> <span class="n">num_iter</span><span class="p">,</span> <span class="n">lmb</span><span class="p">):</span>
     <span class="c1"># num_hidden_neurons is now a list of number of neurons within each hidden layer</span>
 
@@ -6146,7 +5712,10 @@ f(x_{N_x - 2})
 
 <span class="k">def</span> <span class="nf">deep_neural_network</span><span class="p">(</span><span class="n">deep_params</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
     <span class="c1"># N_hidden is the number of hidden layers</span>
-    <span class="n">N_hidden</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consist of parameters to all the hidden layers AND the output layer</span>
+    <span class="c1"># deep_params is a list, len() should be used</span>
+    <span class="n">N_hidden</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consists of</span>
+                                        <span class="c1"># parameters to all the hidden</span>
+                                        <span class="c1"># layers AND the output layer.</span>
 
     <span class="c1"># Assumes input x being an one-dimensional array</span>
     <span class="n">num_values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
@@ -6187,6 +5756,7 @@ f(x_{N_x - 2})
 
     <span class="k">return</span> <span class="n">x_output</span>
 
+
 <span class="k">def</span> <span class="nf">solve_ode_deep_neural_network</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">num_neurons</span><span class="p">,</span> <span class="n">num_iter</span><span class="p">,</span> <span class="n">lmb</span><span class="p">):</span>
     <span class="c1"># num_hidden_neurons is now a list of number of neurons within each hidden layer</span>
 
@@ -6456,7 +6026,7 @@ network at each possible pair <span class="math notranslate nohighlight">\((x,t)
     <span class="n">num_points</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
 
     <span class="c1"># N_hidden is the number of hidden layers</span>
-    <span class="n">N_hidden</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consist of parameters to all the hidden layers AND the output layer</span>
+    <span class="n">N_hidden</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consist of parameters to all the hidden layers AND the output layer</span>
 
     <span class="c1"># Assume that the input layer does nothing to the input x</span>
     <span class="n">x_input</span> <span class="o">=</span> <span class="n">x</span>
@@ -6607,7 +6177,7 @@ Using TensorFlow results in a much better execution time. Try it!</p>
     <span class="n">num_points</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
 
     <span class="c1"># N_hidden is the number of hidden layers</span>
-    <span class="n">N_hidden</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consist of parameters to all the hidden layers AND the output layer</span>
+    <span class="n">N_hidden</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consist of parameters to all the hidden layers AND the output layer</span>
 
     <span class="c1"># Assume that the input layer does nothing to the input x</span>
     <span class="n">x_input</span> <span class="o">=</span> <span class="n">x</span>
@@ -6750,7 +6320,7 @@ Using TensorFlow results in a much better execution time. Try it!</p>
     <span class="n">T</span><span class="p">,</span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="n">x</span><span class="p">)</span>
 
     <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">))</span>
-    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
+    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_suplot</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;Solution from the deep neural network w/ </span><span class="si">%d</span><span class="s1"> layer&#39;</span><span class="o">%</span><span class="k">len</span>(num_hidden_neurons))
     <span class="n">s</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="n">X</span><span class="p">,</span><span class="n">g_dnn_ag</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span><span class="n">cmap</span><span class="o">=</span><span class="n">cm</span><span class="o">.</span><span class="n">viridis</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;Time $t$&#39;</span><span class="p">)</span>
@@ -6758,14 +6328,14 @@ Using TensorFlow results in a much better execution time. Try it!</p>
 
 
     <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">))</span>
-    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
+    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_suplot</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;Analytical solution&#39;</span><span class="p">)</span>
     <span class="n">s</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="n">X</span><span class="p">,</span><span class="n">G_analytical</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span><span class="n">cmap</span><span class="o">=</span><span class="n">cm</span><span class="o">.</span><span class="n">viridis</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;Time $t$&#39;</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">&#39;Position $x$&#39;</span><span class="p">);</span>
 
     <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">))</span>
-    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
+    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_suplot</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;Difference&#39;</span><span class="p">)</span>
     <span class="n">s</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="n">X</span><span class="p">,</span><span class="n">diff_ag</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span><span class="n">cmap</span><span class="o">=</span><span class="n">cm</span><span class="o">.</span><span class="n">viridis</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;Time $t$&#39;</span><span class="p">)</span>
@@ -6943,7 +6513,7 @@ g(x,t) = \sin(\pi x)\cos(\pi t) - \sin(\pi x)\sin(\pi t)
     <span class="n">num_points</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
 
     <span class="c1"># N_hidden is the number of hidden layers</span>
-    <span class="n">N_hidden</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consist of parameters to all the hidden layers AND the output layer</span>
+    <span class="n">N_hidden</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deep_params</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="c1"># -1 since params consist of parameters to all the hidden layers AND the output layer</span>
 
     <span class="c1"># Assume that the input layer does nothing to the input x</span>
     <span class="n">x_input</span> <span class="o">=</span> <span class="n">x</span>
@@ -7048,7 +6618,7 @@ g(x,t) = \sin(\pi x)\cos(\pi t) - \sin(\pi x)\sin(\pi t)
     <span class="n">T</span><span class="p">,</span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="n">x</span><span class="p">)</span>
 
     <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">))</span>
-    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
+    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_suplot</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;Solution from the deep neural network w/ </span><span class="si">%d</span><span class="s1"> layer&#39;</span><span class="o">%</span><span class="k">len</span>(num_hidden_neurons))
     <span class="n">s</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="n">X</span><span class="p">,</span><span class="n">res</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span><span class="n">cmap</span><span class="o">=</span><span class="n">cm</span><span class="o">.</span><span class="n">viridis</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;Time $t$&#39;</span><span class="p">)</span>
@@ -7056,7 +6626,7 @@ g(x,t) = \sin(\pi x)\cos(\pi t) - \sin(\pi x)\sin(\pi t)
 
 
     <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">))</span>
-    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
+    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_suplot</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;Analytical solution&#39;</span><span class="p">)</span>
     <span class="n">s</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="n">X</span><span class="p">,</span><span class="n">res_analytical</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span><span class="n">cmap</span><span class="o">=</span><span class="n">cm</span><span class="o">.</span><span class="n">viridis</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;Time $t$&#39;</span><span class="p">)</span>
@@ -7064,7 +6634,7 @@ g(x,t) = \sin(\pi x)\cos(\pi t) - \sin(\pi x)\sin(\pi t)
 
 
     <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="mi">10</span><span class="p">))</span>
-    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
+    <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_suplot</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">&#39;3d&#39;</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;Difference&#39;</span><span class="p">)</span>
     <span class="n">s</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="n">X</span><span class="p">,</span><span class="n">diff</span><span class="p">,</span><span class="n">linewidth</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="n">antialiased</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span><span class="n">cmap</span><span class="o">=</span><span class="n">cm</span><span class="o">.</span><span class="n">viridis</span><span class="p">)</span>
     <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;Time $t$&#39;</span><span class="p">)</span>
diff --git a/doc/LectureNotes/_build/jupyter_execute/week43.ipynb b/doc/LectureNotes/_build/jupyter_execute/week43.ipynb
index 035fa507f..0824e4c7e 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week43.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week43.ipynb
@@ -2,8 +2,10 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "cda62a86",
-   "metadata": {},
+   "id": "677a195d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
     "doconce format html week43.do.txt --no_mako -->\n",
@@ -12,8 +14,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bdae1fa5",
-   "metadata": {},
+   "id": "e943e8f0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "# Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations\n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n",
@@ -23,8 +27,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e2c09dd5",
-   "metadata": {},
+   "id": "22cdced0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Plans for week 43\n",
     "\n",
@@ -39,8 +45,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7de8bfe0",
-   "metadata": {},
+   "id": "a57ef6df",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Exercises and lab session week 43\n",
     "**Lab sessions on Tuesday and Wednesday.**\n",
@@ -54,8 +62,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2664d901",
-   "metadata": {},
+   "id": "c4a134ee",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematics of deep learning\n",
     "\n",
@@ -68,8 +78,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46bb5558",
-   "metadata": {},
+   "id": "dd73045e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Reminder on books with hands-on material and codes\n",
     "* Sebastian Rashcka et al, Machine learning with Scikit-Learn and PyTorch at <https://sebastianraschka.com/blog/2022/ml-pytorch-book.html>"
@@ -77,8 +89,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c6ad86d",
-   "metadata": {},
+   "id": "372f4aa4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Reading recommendations\n",
     "\n",
@@ -89,8 +103,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9fbf4898",
-   "metadata": {},
+   "id": "05efbc6f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using Automatic differentiation\n",
     "\n",
@@ -100,8 +116,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "135a7122",
-   "metadata": {},
+   "id": "d04b0948",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Back propagation and automatic differentiation\n",
     "\n",
@@ -115,16 +133,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45236eaf",
-   "metadata": {},
+   "id": "b9d41f5c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Lecture Monday  October 21"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "8997a10d",
-   "metadata": {},
+   "id": "68606991",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the back propagation algorithm and algorithm for a feed forward NN, initalizations\n",
     "This is a reminder from where we ended last week.\n",
@@ -148,8 +170,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df88cb72",
-   "metadata": {},
+   "id": "a564a394",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the back propagation algorithm, part 1\n",
     "\n",
@@ -169,8 +193,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46d7ebde",
-   "metadata": {},
+   "id": "43ab4381",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the back propagation algorithm, part 2\n",
     "\n",
@@ -179,8 +205,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ad237f5",
-   "metadata": {},
+   "id": "f578cee4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\delta_j^L = \\sigma'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)}.\n",
@@ -189,16 +217,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f6906530",
-   "metadata": {},
+   "id": "fbc05943",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Then we compute the back propagate error for each $l=L-1,L-2,\\dots,1$ as"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e9613a49",
-   "metadata": {},
+   "id": "6ad3c28f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}\\sigma'(z_j^l).\n",
@@ -207,8 +239,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dba468b9",
-   "metadata": {},
+   "id": "135513b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the Back propagation algorithm, part 3\n",
     "\n",
@@ -219,8 +253,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "21c684a1",
-   "metadata": {},
+   "id": "f643ecdf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "w_{ij}^l\\leftarrow  = w_{ij}^l- \\eta \\delta_j^la_i^{l-1},\n",
@@ -229,8 +265,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6acf04a3",
-   "metadata": {},
+   "id": "077ef1c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n",
@@ -239,16 +277,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b0558fbe",
-   "metadata": {},
+   "id": "50cf7472",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $\\eta$ being the learning rate."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6b424064",
-   "metadata": {},
+   "id": "a10f406c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Updating the gradients\n",
     "\n",
@@ -257,8 +299,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7bc86e31",
-   "metadata": {},
+   "id": "626cba8f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}\\sigma'(z_j^l),\n",
@@ -267,16 +311,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7a10087",
-   "metadata": {},
+   "id": "2ebe05ad",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "we update the weights and the biases using gradient descent for each $l=L-1,L-2,\\dots,1$ and update the weights and biases according to the rules"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "2bf12837",
-   "metadata": {},
+   "id": "bfbbac35",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "w_{ij}^l\\leftarrow  = w_{ij}^l- \\eta \\delta_j^la_i^{l-1},\n",
@@ -285,8 +333,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ad07731e",
-   "metadata": {},
+   "id": "ac515399",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n",
@@ -295,8 +345,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "30c6ae90",
-   "metadata": {},
+   "id": "4703cc51",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Activation functions\n",
     "\n",
@@ -316,8 +368,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5dfa6d1c",
-   "metadata": {},
+   "id": "cab6ad03",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions, examples\n",
     "\n",
@@ -326,8 +380,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8d0be63",
-   "metadata": {},
+   "id": "ad6042eb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\sigma(x) = \\frac{1}{1 + e^{-x}},\n",
@@ -336,16 +392,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3ec0efa",
-   "metadata": {},
+   "id": "1e96b7e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and the *hyperbolic tangent* function"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "78c46915",
-   "metadata": {},
+   "id": "c600792f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\sigma(x) = \\tanh(x)\n",
@@ -354,8 +414,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87e6973b",
-   "metadata": {},
+   "id": "76d1da8e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The RELU function family\n",
     "\n",
@@ -373,8 +435,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c990bc8",
-   "metadata": {},
+   "id": "8e7e0e0c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## ELU function\n",
     "\n",
@@ -385,8 +449,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b7760f9",
-   "metadata": {},
+   "id": "4b1f77d6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "ELU(z) = \\left\\{\\begin{array}{cc} \\alpha\\left( \\exp{(z)}-1\\right) & z < 0,\\\\  z & z \\ge 0.\\end{array}\\right.\n",
@@ -395,8 +461,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47927a82",
-   "metadata": {},
+   "id": "10826ba9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Which activation function should we use?\n",
     "\n",
@@ -415,8 +483,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52554330",
-   "metadata": {},
+   "id": "79d307b6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More on activation functions, output layers\n",
     "\n",
@@ -435,8 +505,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b7d3292",
-   "metadata": {},
+   "id": "429b8d4e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up a Multi-layer perceptron model for classification\n",
     "\n",
@@ -461,8 +533,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38715b52",
-   "metadata": {},
+   "id": "90d9f195",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = \\frac{1}{1 + \\exp{(- \\boldsymbol{x}})} ,\n",
@@ -471,16 +545,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcc0cbfa",
-   "metadata": {},
+   "id": "73d2763e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c686ecf6",
-   "metadata": {},
+   "id": "e2a70a54",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(y = 1 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = 1 - P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) ,\n",
@@ -489,8 +567,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79a8b207",
-   "metadata": {},
+   "id": "7ed6c0dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $y \\in \\{0, 1\\}$  and $\\boldsymbol{\\theta}$ represents the weights and biases\n",
     "of our network."
@@ -498,8 +578,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3218b074",
-   "metadata": {},
+   "id": "a42826b9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Defining the cost function\n",
     "\n",
@@ -508,8 +590,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0e50336",
-   "metadata": {},
+   "id": "d8e401c5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = - \\sum_{i=1}^n\n",
@@ -519,8 +603,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79138403",
-   "metadata": {},
+   "id": "17808105",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This last equality means that we can interpret our *cost* function as a sum over the *loss* function\n",
     "for each point in the dataset $\\mathcal{L}_i(\\boldsymbol{\\theta})$.  \n",
@@ -542,8 +628,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b3db35e",
-   "metadata": {},
+   "id": "5a9b90ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(y_{ic} = 1 \\mid \\boldsymbol{x}_i, \\boldsymbol{\\theta}) = \\frac{\\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_c)}}\n",
@@ -553,8 +641,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90626f76",
-   "metadata": {},
+   "id": "57f33029",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which reduces to the logistic function in the binary case.  \n",
     "The likelihood of this $C$-class classifier\n",
@@ -563,8 +653,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "596eb444",
-   "metadata": {},
+   "id": "422eb23f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = \\prod_{i=1}^n \\prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .\n",
@@ -573,16 +665,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5529d979",
-   "metadata": {},
+   "id": "0eb634c3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Again we take the negative log-likelihood to define our cost function:"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "f7d2523f",
-   "metadata": {},
+   "id": "b3b208fc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\log{P(\\mathcal{D} \\mid \\boldsymbol{\\theta})}.\n",
@@ -591,8 +687,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d8d61f1",
-   "metadata": {},
+   "id": "3788aba1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "See the logistic regression lectures for a full definition of the cost function.\n",
     "\n",
@@ -601,8 +699,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9751fb82",
-   "metadata": {},
+   "id": "4d38ceec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: binary classification problem\n",
     "\n",
@@ -611,8 +711,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e6587c7",
-   "metadata": {},
+   "id": "cee503b9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\beta}) = - \\sum_{i=1}^n \\left(y_i\\log{p(y_i \\vert x_i,\\boldsymbol{\\beta})}+(1-y_i)\\log{1-p(y_i \\vert x_i,\\boldsymbol{\\beta})}\\right),\n",
@@ -621,16 +723,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39bb5ba4",
-   "metadata": {},
+   "id": "19b29e02",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we had defined the logistic (sigmoid) function"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "fcb1f3d9",
-   "metadata": {},
+   "id": "19507159",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(y_i =1\\vert x_i,\\boldsymbol{\\beta})=\\frac{\\exp{(\\beta_0+\\beta_1 x_i)}}{1+\\exp{(\\beta_0+\\beta_1 x_i)}},\n",
@@ -639,16 +745,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20fc130a",
-   "metadata": {},
+   "id": "a15191e4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "66c7c0e9",
-   "metadata": {},
+   "id": "c9df7a22",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(y_i =0\\vert x_i,\\boldsymbol{\\beta})=1-p(y_i =1\\vert x_i,\\boldsymbol{\\beta}).\n",
@@ -657,8 +767,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e757c738",
-   "metadata": {},
+   "id": "0cae75ec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The parameters $\\boldsymbol{\\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. \n",
     "\n",
@@ -668,8 +780,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d048e79e",
-   "metadata": {},
+   "id": "36b0506b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "a_i^l = y_i = \\frac{\\exp{(z_i^l)}}{1+\\exp{(z_i^l)}},\n",
@@ -678,16 +792,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b97827e7",
-   "metadata": {},
+   "id": "0c729c48",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c11528eb",
-   "metadata": {},
+   "id": "060813af",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "z_i^l = \\sum_{j}w_{ij}^l a_j^{l-1}+b_i^l,\n",
@@ -696,8 +814,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94839c96",
-   "metadata": {},
+   "id": "f2a5059b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where the superscript $l-1$ indicates that these are the outputs from layer $l-1$.\n",
     "Our cost function at the final layer $l=L$ is now"
@@ -705,8 +825,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "694596c9",
-   "metadata": {},
+   "id": "6763074d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(1-t_i)\\log{(1-a_i^L)}\\right),\n",
@@ -715,16 +837,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b4c8232e",
-   "metadata": {},
+   "id": "f498b6b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have defined the targets $t_i$. The derivatives of the cost function with respect to the output $a_i^L$ are then easily calculated and we get"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "9d611a08",
-   "metadata": {},
+   "id": "fedce928",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial \\mathcal{C}(\\boldsymbol{W})}{\\partial a_i^L} = \\frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.\n",
@@ -733,16 +859,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb7847ef",
-   "metadata": {},
+   "id": "429c11ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In case we use another activation function than the logistic one, we need to evaluate other derivatives."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "cd5be179",
-   "metadata": {},
+   "id": "ddde8370",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The Softmax function\n",
     "In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation $z_i^l$, that is we need"
@@ -750,8 +880,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96b7fe79",
-   "metadata": {},
+   "id": "637bd194",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial f(z_i^l)}{\\partial w_{jk}^l} =\n",
@@ -761,16 +893,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1040c590",
-   "metadata": {},
+   "id": "0792109c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "For the Softmax function we have"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3162bd5e",
-   "metadata": {},
+   "id": "10f14691",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(z_i^l) = \\frac{\\exp{(z_i^l)}}{\\sum_{m=1}^K\\exp{(z_m^l)}}.\n",
@@ -779,16 +915,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b7f2b7b8",
-   "metadata": {},
+   "id": "186529b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Its derivative with respect to $z_j^l$ gives"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "735fd9c0",
-   "metadata": {},
+   "id": "68afc0da",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial f(z_i^l)}{\\partial z_j^l}= f(z_i^l)\\left(\\delta_{ij}-f(z_j^l)\\right),\n",
@@ -797,16 +937,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3cbbb04",
-   "metadata": {},
+   "id": "cf48ea60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which in case of the simply binary model reduces to  having $i=j$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6462edbb",
-   "metadata": {},
+   "id": "861a3bbe",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Developing a code for doing neural networks with back propagation\n",
     "\n",
@@ -827,8 +971,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7915dc1d",
-   "metadata": {},
+   "id": "c8007ce7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Collect and pre-process data\n",
     "\n",
@@ -875,8 +1021,11 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "eb736d79",
-   "metadata": {},
+   "id": "29678f97",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -951,8 +1100,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01fcb50b",
-   "metadata": {},
+   "id": "3ba6d7d6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Train and test datasets\n",
     "\n",
@@ -970,8 +1121,11 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "e6b7f2e3",
-   "metadata": {},
+   "id": "7df51dd1",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1014,8 +1168,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ca032f8",
-   "metadata": {},
+   "id": "249898fd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Define model and architecture\n",
     "\n",
@@ -1056,8 +1212,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6e4e1e18",
-   "metadata": {},
+   "id": "2d30ddd3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Layers\n",
     "\n",
@@ -1094,8 +1252,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab0ee6d8",
-   "metadata": {},
+   "id": "ce9f14e4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Weights and biases\n",
     "\n",
@@ -1113,8 +1273,11 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "15ad1599",
-   "metadata": {},
+   "id": "c3f75b32",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# building our neural network\n",
@@ -1136,8 +1299,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3efd576a",
-   "metadata": {},
+   "id": "4ebf4f68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Feed-forward pass\n",
     "\n",
@@ -1162,8 +1327,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "715c5d46",
-   "metadata": {},
+   "id": "c6760d1f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Matrix multiplications\n",
     "\n",
@@ -1197,8 +1364,11 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "ecaa833e",
-   "metadata": {},
+   "id": "98f3a5d5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1257,8 +1427,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0319e65",
-   "metadata": {},
+   "id": "19cd49ec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Choose cost function and optimizer\n",
     "\n",
@@ -1286,8 +1458,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98c6696e",
-   "metadata": {},
+   "id": "b0342f54",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Optimizing the cost function\n",
     "\n",
@@ -1322,8 +1496,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5d1145a",
-   "metadata": {},
+   "id": "7219731b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Regularization\n",
     "\n",
@@ -1354,8 +1530,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b73247fd",
-   "metadata": {},
+   "id": "248590b9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Matrix  multiplication\n",
     "\n",
@@ -1393,8 +1571,11 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "3d61438f",
-   "metadata": {},
+   "id": "1810a36c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1407,7 +1588,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1492,8 +1673,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a20a495",
-   "metadata": {},
+   "id": "e094a404",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Improving performance\n",
     "\n",
@@ -1511,8 +1694,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "717b63a1",
-   "metadata": {},
+   "id": "1fb3aab5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Full object-oriented implementation\n",
     "\n",
@@ -1523,8 +1708,11 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "9d6c9929",
-   "metadata": {},
+   "id": "20b3c187",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "class NeuralNetwork:\n",
@@ -1630,8 +1818,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e70667c5",
-   "metadata": {},
+   "id": "f85564ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Evaluate model performance on test data\n",
     "\n",
@@ -1647,8 +1837,11 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "083dfe41",
-   "metadata": {},
+   "id": "9be7082e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1679,8 +1872,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bffeadd3",
-   "metadata": {},
+   "id": "255b5b3d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Adjust hyperparameters\n",
     "\n",
@@ -1691,8 +1886,11 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "6513ac74",
-   "metadata": {},
+   "id": "fc014642",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1978,7 +2176,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -1996,7 +2194,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -2014,7 +2212,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -2032,7 +2230,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -2050,7 +2248,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -2068,7 +2266,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -2086,7 +2284,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n"
      ]
     },
@@ -2104,11 +2302,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -2126,11 +2324,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -2148,11 +2346,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -2170,11 +2368,11 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
@@ -2192,216 +2390,25 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
       "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
       "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
+      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_92604/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
       "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
      ]
     },
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/1630775253.py:44: RuntimeWarning: invalid value encountered in divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
+     "ename": "KeyboardInterrupt",
+     "evalue": "",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[8], line 11\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m j, lmbd \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(lmbd_vals):\n\u001b[1;32m      9\u001b[0m     dnn \u001b[38;5;241m=\u001b[39m NeuralNetwork(X_train, Y_train_onehot, eta\u001b[38;5;241m=\u001b[39meta, lmbd\u001b[38;5;241m=\u001b[39mlmbd, epochs\u001b[38;5;241m=\u001b[39mepochs, batch_size\u001b[38;5;241m=\u001b[39mbatch_size,\n\u001b[1;32m     10\u001b[0m                         n_hidden_neurons\u001b[38;5;241m=\u001b[39mn_hidden_neurons, n_categories\u001b[38;5;241m=\u001b[39mn_categories)\n\u001b[0;32m---> 11\u001b[0m     \u001b[43mdnn\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtrain\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     13\u001b[0m     DNN_numpy[i][j] \u001b[38;5;241m=\u001b[39m dnn\n\u001b[1;32m     15\u001b[0m     test_predict \u001b[38;5;241m=\u001b[39m dnn\u001b[38;5;241m.\u001b[39mpredict(X_test)\n",
+      "Cell \u001b[0;32mIn[6], line 99\u001b[0m, in \u001b[0;36mNeuralNetwork.train\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     96\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mY_data \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mY_data_full[chosen_datapoints]\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfeed_forward()\n\u001b[0;32m---> 99\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mbackpropagation\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
+      "Cell \u001b[0;32mIn[6], line 64\u001b[0m, in \u001b[0;36mNeuralNetwork.backpropagation\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     61\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39moutput_weights_gradient \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mmatmul(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39ma_h\u001b[38;5;241m.\u001b[39mT, error_output)\n\u001b[1;32m     62\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39moutput_bias_gradient \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39msum(error_output, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m)\n\u001b[0;32m---> 64\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mhidden_weights_gradient \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmatmul\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mX_data\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mT\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43merror_hidden\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     65\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mhidden_bias_gradient \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39msum(error_hidden, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m)\n\u001b[1;32m     67\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mlmbd \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m0.0\u001b[39m:\n",
+      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
      ]
     }
    ],
@@ -2430,8 +2437,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a6e305f6",
-   "metadata": {},
+   "id": "96089af8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Visualization"
    ]
@@ -2439,54 +2448,12 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "d920e285",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_87605/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 1000x1000 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week43_96_1.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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",
-      "text/plain": [
-       "<Figure size 1000x1000 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week43_96_2.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "id": "04c4d29a",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# visual representation of grid search\n",
     "# uses seaborn heatmap, you can also do this with matplotlib imshow\n",
@@ -2525,8 +2492,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0f1aaadd",
-   "metadata": {},
+   "id": "472a5060",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## scikit-learn implementation\n",
     "\n",
@@ -2546,598 +2515,12 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "156764f3",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.18333333333333332\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.18611111111111112\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.13055555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.24444444444444444\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.23333333333333334\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.12777777777777777\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.1527777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.9111111111111111\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.8888888888888888\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.8722222222222222\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.8305555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.8888888888888888\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.8805555555555555\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.8944444444444445\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.975\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.9777777777777777\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.9805555555555555\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.9861111111111112\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.9805555555555555\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.9777777777777777\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.9444444444444444\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.9861111111111112\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.9888888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.9888888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.9861111111111112\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.9888888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.9722222222222222\n",
-      "\n",
-      "Learning rate  =  0.01\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.9527777777777777\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.9027777777777778\n",
-      "\n",
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.8583333333333333\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.8722222222222222\n",
-      "\n",
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.9055555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.8805555555555555\n",
-      "\n",
-      "Learning rate  =  0.1\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.8722222222222222\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.8666666666666667\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.08611111111111111\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.17777777777777778\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.08333333333333333\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.08888888888888889\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.09444444444444444\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.17222222222222222\n",
-      "\n",
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.11666666666666667\n",
-      "\n",
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n",
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.1388888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.11388888888888889\n",
-      "\n",
-      "Learning rate  =  10.0\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.09444444444444444\n",
-      "\n"
-     ]
-    }
-   ],
+   "id": "42e40777",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "from sklearn.neural_network import MLPClassifier\n",
     "# store models for later use\n",
@@ -3159,8 +2542,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e5fec48",
-   "metadata": {},
+   "id": "57fc5d93",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Visualization"
    ]
@@ -3168,38 +2553,12 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "ace47e70",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 1000x1000 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week43_100_0.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
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",
-      "text/plain": [
-       "<Figure size 1000x1000 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week43_100_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "id": "90477fe7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "# optional\n",
     "# visual representation of grid search\n",
@@ -3239,8 +2598,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d327f9b",
-   "metadata": {},
+   "id": "29af8aff",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Building neural networks in Tensorflow and Keras\n",
     "\n",
@@ -3255,8 +2616,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2280cbce",
-   "metadata": {},
+   "id": "a70cf999",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Tensorflow\n",
     "\n",
@@ -3288,26 +2651,22 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "dff81198",
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "SyntaxError",
-     "evalue": "invalid syntax (2357089093.py, line 1)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;36m  Cell \u001b[0;32mIn[12], line 1\u001b[0;36m\u001b[0m\n\u001b[0;31m    pip3 install tensorflow\u001b[0m\n\u001b[0m         ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
-     ]
-    }
-   ],
+   "id": "812c98fe",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "pip3 install tensorflow"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e9bf9cac",
-   "metadata": {},
+   "id": "694c0bd7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and/or if you use **anaconda**, just write (or install from the graphical user interface)\n",
     "(current release of CPU-only TensorFlow)"
@@ -3316,8 +2675,11 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "1ccb8dba",
-   "metadata": {},
+   "id": "1ecd18cc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "conda create -n tf tensorflow\n",
@@ -3326,8 +2688,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efc3f4e2",
-   "metadata": {},
+   "id": "584ab0ab",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "To install the current release of GPU TensorFlow"
    ]
@@ -3335,8 +2699,11 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "01556b01",
-   "metadata": {},
+   "id": "a811e23d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "conda create -n tf-gpu tensorflow-gpu\n",
@@ -3345,8 +2712,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b900f015",
-   "metadata": {},
+   "id": "ab99008f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using Keras\n",
     "\n",
@@ -3358,8 +2727,11 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "3fd1f12f",
-   "metadata": {},
+   "id": "fe547415",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "conda install keras"
@@ -3367,8 +2739,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20ec35c5",
-   "metadata": {},
+   "id": "ed1e0fc6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "You can look up the [instructions here](https://keras.io/) for more information.\n",
     "\n",
@@ -3377,8 +2751,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "249e56f7",
-   "metadata": {},
+   "id": "6aebcb51",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Collect and pre-process data\n",
     "\n",
@@ -3388,8 +2764,11 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "0ff66efc",
-   "metadata": {},
+   "id": "a4a7d68d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# import necessary packages\n",
@@ -3440,8 +2819,11 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "2806c62b",
-   "metadata": {},
+   "id": "21335418",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from tensorflow.keras.layers import Input\n",
@@ -3466,8 +2848,11 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "3bf4c3f6",
-   "metadata": {},
+   "id": "e81d58de",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\n",
@@ -3484,7 +2869,7 @@
     "    model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))\n",
     "    model.add(Dense(n_categories, activation='softmax'))\n",
     "    \n",
-    "    sgd = optimizers.SGD(lr=eta)\n",
+    "    sgd = optimizers.SGD(learning_rate=eta)\n",
     "    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n",
     "    \n",
     "    return model"
@@ -3493,8 +2878,11 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "81a46485",
-   "metadata": {},
+   "id": "b91287cc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
@@ -3517,8 +2905,11 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "6e619c14",
-   "metadata": {},
+   "id": "d108674e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# optional\n",
@@ -3556,8 +2947,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c303d97b",
-   "metadata": {},
+   "id": "1198d799",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The Breast Cancer Data, now with Keras"
    ]
@@ -3565,8 +2958,11 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "03a57bfd",
-   "metadata": {},
+   "id": "eb1eb4fb",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\n",
@@ -3679,7 +3075,7 @@
     "        else:                       #Subsequent layers are capable of automatic shape inferencing\n",
     "            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda)))\n",
     "    model.add(Dense(2,activation='softmax'))  #2 outputs - ordered and disordered (softmax for prob)\n",
-    "    sgd=optimizers.SGD(lr=eta)\n",
+    "    sgd=optimizers.SGD(learning_rate=eta)\n",
     "    model.compile(loss='categorical_crossentropy',optimizer=sgd,metrics=['accuracy'])\n",
     "    return model\n",
     "\n",
@@ -3739,8 +3135,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9ad1085",
-   "metadata": {},
+   "id": "92834502",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Building a neural network code\n",
     "\n",
@@ -3756,8 +3154,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf4f3c14",
-   "metadata": {},
+   "id": "deb24cc1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Learning rate methods\n",
     "\n",
@@ -3776,8 +3176,11 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "id": "467ea7a2",
-   "metadata": {},
+   "id": "d3619281",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -3914,8 +3317,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6af64d5a",
-   "metadata": {},
+   "id": "f37fd7bc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Usage of the above learning rate schedulers\n",
     "\n",
@@ -3928,8 +3333,11 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "id": "290e0d00",
-   "metadata": {},
+   "id": "5db34b9b",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "momentum_scheduler = Momentum(eta=1e-3, momentum=0.9)\n",
@@ -3938,8 +3346,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1f43cc5",
-   "metadata": {},
+   "id": "8b25a24d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Here is a small example for how a segment of code using schedulers\n",
     "could look. Switching out the schedulers is simple."
@@ -3948,8 +3358,11 @@
   {
    "cell_type": "code",
    "execution_count": 24,
-   "id": "0def5cec",
-   "metadata": {},
+   "id": "2d5f2887",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "weights = np.ones((3,3))\n",
@@ -3967,8 +3380,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b27dcd7",
-   "metadata": {},
+   "id": "9070c2d3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Cost functions\n",
     "\n",
@@ -3981,8 +3396,11 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "id": "4217839c",
-   "metadata": {},
+   "id": "c360c736",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -4016,8 +3434,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ef5f9fe9",
-   "metadata": {},
+   "id": "42c7ec61",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Below we give a short example of how these cost function may be used\n",
     "to obtain results if you wish to test them out on your own using\n",
@@ -4027,8 +3447,11 @@
   {
    "cell_type": "code",
    "execution_count": 26,
-   "id": "305e1479",
-   "metadata": {},
+   "id": "cd9cb3a5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from autograd import grad\n",
@@ -4045,8 +3468,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1499b193",
-   "metadata": {},
+   "id": "796aab4a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions\n",
     "\n",
@@ -4059,8 +3484,11 @@
   {
    "cell_type": "code",
    "execution_count": 27,
-   "id": "e7b59b25",
-   "metadata": {},
+   "id": "5ea4891d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -4114,8 +3542,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57599619",
-   "metadata": {},
+   "id": "2ff3c57c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Below follows a short demonstration of how to use an activation\n",
     "function. The derivative of the activation function will be important\n",
@@ -4127,8 +3557,11 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "id": "5ee68acd",
-   "metadata": {},
+   "id": "34289210",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "z = np.array([[4, 5, 6]]).T\n",
@@ -4145,8 +3578,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d3295d9",
-   "metadata": {},
+   "id": "0839f98b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### The Neural Network\n",
     "\n",
@@ -4167,8 +3602,11 @@
   {
    "cell_type": "code",
    "execution_count": 29,
-   "id": "c4cfc50a",
-   "metadata": {},
+   "id": "0fdc2707",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import math\n",
@@ -4636,8 +4074,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e6e81c1",
-   "metadata": {},
+   "id": "17bc192e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Before we make a model, we will quickly generate a dataset we can use\n",
     "for our linear regression problem as shown below"
@@ -4646,8 +4086,11 @@
   {
    "cell_type": "code",
    "execution_count": 30,
-   "id": "0d4f1ff8",
-   "metadata": {},
+   "id": "f3f5d088",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -4687,8 +4130,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8f1940f",
-   "metadata": {},
+   "id": "53c3b4c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Now that we have our dataset ready for the regression, we can create\n",
     "our regressor. Note that with the seed parameter, we can make sure our\n",
@@ -4701,8 +4146,11 @@
   {
    "cell_type": "code",
    "execution_count": 31,
-   "id": "ff6bd29b",
-   "metadata": {},
+   "id": "890d682f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -4713,8 +4161,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7b906df",
-   "metadata": {},
+   "id": "dc4da852",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We then fit our model with our training data using the scheduler of our choice."
    ]
@@ -4722,8 +4172,11 @@
   {
    "cell_type": "code",
    "execution_count": 32,
-   "id": "db7a5bf2",
-   "metadata": {},
+   "id": "1e98a3f8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -4734,8 +4187,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "508c351b",
-   "metadata": {},
+   "id": "68c5d793",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Due to the progress bar we can see the MSE (train_error) throughout\n",
     "the FFNN's training. Note that the fit() function has some optional\n",
@@ -4748,8 +4203,11 @@
   {
    "cell_type": "code",
    "execution_count": 33,
-   "id": "6b0562b2",
-   "metadata": {},
+   "id": "e735086e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -4759,8 +4217,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f03172d9",
-   "metadata": {},
+   "id": "360468f6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We see that given more epochs to train on, the regressor reaches a lower MSE.\n",
     "\n",
@@ -4772,8 +4232,11 @@
   {
    "cell_type": "code",
    "execution_count": 34,
-   "id": "26d1d1c3",
-   "metadata": {},
+   "id": "c5937c59",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn.datasets import load_breast_cancer\n",
@@ -4795,8 +4258,11 @@
   {
    "cell_type": "code",
    "execution_count": 35,
-   "id": "6a78c633",
-   "metadata": {},
+   "id": "2e06b929",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -4807,8 +4273,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5feaced2",
-   "metadata": {},
+   "id": "94140fb1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We will now make use of our validation data by passing it into our fit function as a keyword argument"
    ]
@@ -4816,8 +4284,11 @@
   {
    "cell_type": "code",
    "execution_count": 36,
-   "id": "6a9b1538",
-   "metadata": {},
+   "id": "da82b266",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "logistic_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -4828,8 +4299,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90c7f8f3",
-   "metadata": {},
+   "id": "19e8d4c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Finally, we will create a neural network with 2 hidden layers with activation functions."
    ]
@@ -4837,8 +4310,11 @@
   {
    "cell_type": "code",
    "execution_count": 37,
-   "id": "58954140",
-   "metadata": {},
+   "id": "4744accd",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -4854,8 +4330,11 @@
   {
    "cell_type": "code",
    "execution_count": 38,
-   "id": "89536ca9",
-   "metadata": {},
+   "id": "f5b5b198",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "neural_network.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -4866,8 +4345,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "803f4791",
-   "metadata": {},
+   "id": "1f5fc0a0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Multiclass classification\n",
     "\n",
@@ -4879,8 +4360,11 @@
   {
    "cell_type": "code",
    "execution_count": 39,
-   "id": "50405951",
-   "metadata": {},
+   "id": "4308d82f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn.datasets import load_digits\n",
@@ -4913,8 +4397,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d906edf4",
-   "metadata": {},
+   "id": "96fc3508",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Testing the XOR gate and other gates\n",
     "\n",
@@ -4924,8 +4410,11 @@
   {
    "cell_type": "code",
    "execution_count": 40,
-   "id": "414ee306",
-   "metadata": {},
+   "id": "5aa9a2a4",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)\n",
@@ -4944,18 +4433,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "982d1747",
-   "metadata": {},
+   "id": "d57346ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Not bad, but the results depend strongly on the learning reate. Try different learning rates."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "616eae3e",
-   "metadata": {},
+   "id": "0219b252",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "## Solving ODEs with Deep Learning\n",
+    "## Solving differential equations  with Deep Learning\n",
     "\n",
     "The Universal Approximation Theorem states that a neural network can\n",
     "approximate any function at a single hidden layer along with one input\n",
@@ -4977,10 +4470,12 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43fb869c",
-   "metadata": {},
+   "id": "80032cfc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "## Ordinary Differential Equations\n",
+    "## Ordinary Differential Equations first\n",
     "\n",
     "An ordinary differential equation (ODE) is an equation involving functions having one variable.\n",
     "\n",
@@ -4989,8 +4484,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4855aef1",
-   "metadata": {},
+   "id": "3c5546df",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"ode\"></div>\n",
@@ -5004,8 +4501,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d31c26fc",
-   "metadata": {},
+   "id": "e4f540a5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(x)$ is the function to find, and $g^{(n)}(x)$ is the $n$-th derivative of $g(x)$.\n",
     "\n",
@@ -5018,8 +4517,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08d629ec",
-   "metadata": {},
+   "id": "75ec2cfe",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "\n",
@@ -5028,8 +4529,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2cfd7bd",
-   "metadata": {},
+   "id": "a71e7eb8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto1\"></div>\n",
@@ -5044,8 +4547,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4cd106f",
-   "metadata": {},
+   "id": "9b06d2bf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $h_1(x)$ is a function that makes $g_t(x)$ satisfy a given set\n",
     "of conditions, $N(x,P)$ a neural network with weights and biases\n",
@@ -5063,8 +4568,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74da655f",
-   "metadata": {},
+   "id": "0aea2f3e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Minimization process\n",
     "\n",
@@ -5078,8 +4585,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efe0ec18",
-   "metadata": {},
+   "id": "a21c6a43",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(x, P\\right) = \\big(f\\left(x, \\, g(x), \\, g'(x), \\, g''(x), \\, \\dots \\, , \\, g^{(n)}(x)\\right)\\big)^2\n",
@@ -5088,8 +4597,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9c1643a",
-   "metadata": {},
+   "id": "ff939582",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If $N$ inputs are given as a vector $\\boldsymbol{x}$ with elements $x_i$ for $i = 1,\\dots,N$,\n",
     "the cost function becomes"
@@ -5097,8 +4608,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b900e26",
-   "metadata": {},
+   "id": "9f63085a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"cost\"></div>\n",
@@ -5112,8 +4625,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82e8e341",
-   "metadata": {},
+   "id": "2875658a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The neural net should then find the parameters $P$ that minimizes the cost function in\n",
     "([3](#cost)) for a set of $N$ training samples $x_i$."
@@ -5121,8 +4636,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b89f2f97",
-   "metadata": {},
+   "id": "8a63e4c6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Minimizing the cost function using gradient descent and automatic differentiation\n",
     "\n",
@@ -5135,8 +4652,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc38c37f",
-   "metadata": {},
+   "id": "2d5b4c88",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Exponential decay\n",
     "\n",
@@ -5145,8 +4664,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c5f0410",
-   "metadata": {},
+   "id": "daab1d5e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solve_expdec\"></div>\n",
@@ -5160,8 +4681,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4531d4a4",
-   "metadata": {},
+   "id": "fc2cedc3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $g(0) = g_0$ for some chosen initial value $g_0$.\n",
     "\n",
@@ -5170,8 +4693,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d580caea",
-   "metadata": {},
+   "id": "da284bc1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto2\"></div>\n",
@@ -5186,16 +4711,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f384ec5",
-   "metadata": {},
+   "id": "04c2531a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of ([4](#solve_expdec))."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e650af49",
-   "metadata": {},
+   "id": "62a110db",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The function to solve for\n",
     "\n",
@@ -5204,8 +4733,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68e3a73b",
-   "metadata": {},
+   "id": "7b5b722c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solveode\"></div>\n",
@@ -5219,8 +4750,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61f7dce9",
-   "metadata": {},
+   "id": "02446b0e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(0) = g_0$ with $\\gamma$ and $g_0$ being some chosen values.\n",
     "\n",
@@ -5229,8 +4762,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47e985ed",
-   "metadata": {},
+   "id": "205c8e89",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "To begin with, a trial solution $g_t(t)$ must be chosen. A general trial solution for ordinary differential equations could be"
@@ -5238,8 +4773,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5787755",
-   "metadata": {},
+   "id": "9e46aee1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x, P) = h_1(x) + h_2(x, N(x, P))\n",
@@ -5248,16 +4785,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efd0d663",
-   "metadata": {},
+   "id": "cb0d1f30",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $h_1(x)$ ensuring that $g_t(x)$ satisfies some conditions and $h_2(x,N(x, P))$ an expression involving $x$ and the output from the neural network $N(x,P)$ with $P $ being the collection of the weights and biases for each layer. For now, it is assumed that the network consists of one input layer, one hidden layer, and one output layer."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "de4cfa12",
-   "metadata": {},
+   "id": "8485bdd3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setup of Network\n",
     "\n",
@@ -5274,8 +4815,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4de8eeb1",
-   "metadata": {},
+   "id": "730e057b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"trial\"></div>\n",
@@ -5289,8 +4832,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3076a5d",
-   "metadata": {},
+   "id": "db8907ef",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Reformulating the problem\n",
     "\n",
@@ -5306,8 +4851,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00459420",
-   "metadata": {},
+   "id": "ce4a7022",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x, P) = g_0 + x \\cdot N(x, P)\n",
@@ -5316,16 +4863,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "493318e4",
-   "metadata": {},
+   "id": "b17ab00d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "has been chosen such that it already solves the condition $g(0) = g_0$. What remains, is to find $P$ such that"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b1cd6594",
-   "metadata": {},
+   "id": "f4af75e0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"nnmin\"></div>\n",
@@ -5339,16 +4890,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf2aa493",
-   "metadata": {},
+   "id": "4ea72b19",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "is fulfilled as *best as possible*."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5eda172b",
-   "metadata": {},
+   "id": "428cf327",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More technicalities\n",
     "\n",
@@ -5361,8 +4916,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2bfc8161",
-   "metadata": {},
+   "id": "1b4c9872",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P}\\Big\\{ \\big(g_t'(x, P) - ( -\\gamma g_t(x, P) \\big)^2 \\Big\\}\n",
@@ -5371,8 +4928,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9af6a125",
-   "metadata": {},
+   "id": "f12896dd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "(the notation $\\min_{P}\\{ f(x, P) \\}$ means that we desire to find $P$ that yields the minimum of $f(x, P)$)\n",
     "\n",
@@ -5381,8 +4940,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bea03f10",
-   "metadata": {},
+   "id": "70e2187e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P_{\\text{hidden} }, \\ P_{\\text{output} }}\\Big\\{ \\big(g_t'(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) - ( -\\gamma g_t(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) \\big)^2 \\Big\\}\n",
@@ -5391,16 +4952,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "352fb11e",
-   "metadata": {},
+   "id": "e0136d5f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for an input value $x$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "98d5219e",
-   "metadata": {},
+   "id": "ff915c59",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More details\n",
     "\n",
@@ -5409,8 +4974,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "83d7b299",
-   "metadata": {},
+   "id": "ca46667e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"min\"></div>\n",
@@ -5424,16 +4991,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ba53d11",
-   "metadata": {},
+   "id": "3efa1dc6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Letting $\\boldsymbol{x}$ be a vector with elements $x_i$ and $C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i  \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2$ denote the cost function, the minimization problem that our network must solve, becomes"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3953e778",
-   "metadata": {},
+   "id": "a3d800e8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P} C(\\boldsymbol{x}, P)\n",
@@ -5442,8 +5013,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "706a1978",
-   "metadata": {},
+   "id": "8fb679f5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In terms of $P_{\\text{hidden} }$ and $P_{\\text{output} }$, this could also be expressed as\n",
     "\n",
@@ -5454,8 +5027,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8ff57d1a",
-   "metadata": {},
+   "id": "08b2a19b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## A possible implementation of a neural network\n",
     "\n",
@@ -5468,8 +5043,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb487d3d",
-   "metadata": {},
+   "id": "082074c8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Technicalities\n",
     "\n",
@@ -5478,8 +5055,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d6ac6a6",
-   "metadata": {},
+   "id": "b69f9148",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -5498,8 +5077,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fee86c29",
-   "metadata": {},
+   "id": "9feeefde",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities I\n",
     "\n",
@@ -5508,8 +5089,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "317dd762",
-   "metadata": {},
+   "id": "cde763a7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -5529,8 +5112,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4641c716",
-   "metadata": {},
+   "id": "3c83e5dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities II\n",
     "\n",
@@ -5543,8 +5128,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a28fd5d3",
-   "metadata": {},
+   "id": "4566531c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(z) = \\frac{1}{1 + \\exp{(-z)}}\n",
@@ -5553,8 +5140,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2c6ce13",
-   "metadata": {},
+   "id": "e316d1e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "It is possible to use other activations functions for the hidden layer also.\n",
     "\n",
@@ -5575,8 +5164,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5bf0304c",
-   "metadata": {},
+   "id": "41ac9a1c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities III\n",
     "\n",
@@ -5585,8 +5176,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4ee906f",
-   "metadata": {},
+   "id": "b0a8a3c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -5604,8 +5197,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "454cd32f",
-   "metadata": {},
+   "id": "67447b23",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities IV\n",
     "\n",
@@ -5614,8 +5209,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "49b52638",
-   "metadata": {},
+   "id": "12d3e1ee",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{z}_{1}^{\\text{output}} =\n",
@@ -5631,16 +5228,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75d1e0dc",
-   "metadata": {},
+   "id": "562a122c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In this case we seek a continuous range of values since we are approximating a function. This means that after computing $\\boldsymbol{z}_{1}^{\\text{output}}$ the neural network has finished its feed forward step, and $\\boldsymbol{z}_{1}^{\\text{output}}$ is the final output of the network."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "243508b9",
-   "metadata": {},
+   "id": "78789a96",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Back propagation\n",
     "\n",
@@ -5651,8 +5252,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cfaa5264",
-   "metadata": {},
+   "id": "76b734fb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i  \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2\n",
@@ -5661,8 +5264,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "188a58e4",
-   "metadata": {},
+   "id": "e2911f97",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In order to minimize the cost function, an optimization method must be chosen.\n",
     "\n",
@@ -5671,8 +5276,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f3c7251",
-   "metadata": {},
+   "id": "5e0c281c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Gradient descent\n",
     "\n",
@@ -5686,8 +5293,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b48662af",
-   "metadata": {},
+   "id": "077e3318",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\omega}_{\\text{new} } = \\boldsymbol{\\omega} - \\lambda \\nabla_{\\boldsymbol{\\omega}} C(\\boldsymbol{x}, \\boldsymbol{\\omega})\n",
@@ -5696,8 +5305,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46cc1b9b",
-   "metadata": {},
+   "id": "b6e9387d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for a number of iterations or until $ \\big|\\big| \\boldsymbol{\\omega}_{\\text{new} } - \\boldsymbol{\\omega} \\big|\\big|$ becomes smaller than some given tolerance.\n",
     "\n",
@@ -5716,8 +5327,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "018877f6",
-   "metadata": {},
+   "id": "3fa21e60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -5729,8 +5342,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "35e348bd",
-   "metadata": {},
+   "id": "e05e6028",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The code for solving the ODE"
    ]
@@ -5738,8 +5353,11 @@
   {
    "cell_type": "code",
    "execution_count": 41,
-   "id": "dafe8d25",
-   "metadata": {},
+   "id": "eb77d1cf",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -5890,8 +5508,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65e4f300",
-   "metadata": {},
+   "id": "bbd6562b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The network with one input layer, specified number of hidden layers, and one output layer\n",
     "\n",
@@ -5903,8 +5523,11 @@
   {
    "cell_type": "code",
    "execution_count": 42,
-   "id": "5ef5f766",
-   "metadata": {},
+   "id": "24ba1afd",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -5919,8 +5542,8 @@
     "# but with number of hidden layers specified by the user.\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consists of\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
     "                                        # parameters to all the hidden\n",
     "                                        # layers AND the output layer.\n",
     "\n",
@@ -6069,8 +5692,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7ad45ef",
-   "metadata": {},
+   "id": "3974040a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Population growth\n",
     "\n",
@@ -6080,8 +5705,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d1376bc",
-   "metadata": {},
+   "id": "a9d203ea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"log\"></div>\n",
@@ -6095,8 +5722,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f039785",
-   "metadata": {},
+   "id": "ede35f92",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(t)$ is the population density at time $t$, $\\alpha > 0$ the growth rate and $A > 0$ is the maximum population number in the environment.\n",
     "Also, at $t = 0$ the population has the size $g(0) = g_0$, where $g_0$ is some chosen constant.\n",
@@ -6109,8 +5738,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8dfcfb5e",
-   "metadata": {},
+   "id": "a9720dfc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the problem\n",
     "\n",
@@ -6120,8 +5751,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cb5e674",
-   "metadata": {},
+   "id": "5ef6b555",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solveode_population\"></div>\n",
@@ -6135,8 +5768,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "56581c9f",
-   "metadata": {},
+   "id": "bd5c646e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(0) = g_0$.\n",
     "\n",
@@ -6145,8 +5780,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ebf7032a",
-   "metadata": {},
+   "id": "cdc5561b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "\n",
@@ -6170,8 +5807,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a943c5c6",
-   "metadata": {},
+   "id": "cebde164",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The program using Autograd\n",
     "\n",
@@ -6181,8 +5820,11 @@
   {
    "cell_type": "code",
    "execution_count": 43,
-   "id": "a3620769",
-   "metadata": {},
+   "id": "c71a9592",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -6201,9 +5843,12 @@
     "    g0 = 1.2\n",
     "    return alpha, A, g0\n",
     "\n",
-    "def deep_neural_network(P, x):\n",
+    "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(P) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -6220,7 +5865,7 @@
     "\n",
     "    for l in range(N_hidden):\n",
     "        # From the list of parameters P; find the correct weigths and bias for this layer\n",
-    "        w_hidden = P[l]\n",
+    "        w_hidden = deep_params[l]\n",
     "\n",
     "        # Add a row of ones to include bias\n",
     "        x_prev = np.concatenate((np.ones((1,num_values)), x_prev ), axis = 0)\n",
@@ -6234,7 +5879,7 @@
     "    ## Output layer:\n",
     "\n",
     "    # Get the weights and bias for this layer\n",
-    "    w_output = P[-1]\n",
+    "    w_output = deep_params[-1]\n",
     "\n",
     "    # Include bias:\n",
     "    x_prev = np.concatenate((np.ones((1,num_values)), x_prev), axis = 0)\n",
@@ -6245,6 +5890,8 @@
     "    return x_output\n",
     "\n",
     "\n",
+    "\n",
+    "\n",
     "def cost_function_deep(P, x):\n",
     "\n",
     "    # Evaluate the trial function with the current parameters P\n",
@@ -6352,8 +5999,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a21afc2",
-   "metadata": {},
+   "id": "bd70d6cc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using forward Euler to solve the ODE\n",
     "\n",
@@ -6370,8 +6019,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a8ad46c",
-   "metadata": {},
+   "id": "ee3bdd02",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -6383,8 +6034,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b83336b",
-   "metadata": {},
+   "id": "d81b6054",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "along with the condition that $g(0) = g_0$.\n",
     "\n",
@@ -6395,8 +6048,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea68eaac",
-   "metadata": {},
+   "id": "0d7a2272",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -6409,16 +6064,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c8a2f92c",
-   "metadata": {},
+   "id": "ca29846f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Now, if $g_i = g(t_i)$ then"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "4f1a2187",
-   "metadata": {},
+   "id": "1a51d849",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"odenum\"></div>\n",
@@ -6437,8 +6096,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb87fc93",
-   "metadata": {},
+   "id": "700a9bac",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for $i \\geq 1$ and $g_0 = g(t_0) = g(0) = g_0$.\n",
     "\n",
@@ -6449,8 +6110,11 @@
   {
    "cell_type": "code",
    "execution_count": 44,
-   "id": "f8c976e7",
-   "metadata": {},
+   "id": "482cf93c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# Assume that all function definitions from the example program using Autograd\n",
@@ -6522,8 +6186,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23756e15",
-   "metadata": {},
+   "id": "4ed3cefd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Solving the one dimensional Poisson equation\n",
     "\n",
@@ -6532,8 +6198,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a68185f",
-   "metadata": {},
+   "id": "d0bdfcdb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"poisson\"></div>\n",
@@ -6547,8 +6215,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc784286",
-   "metadata": {},
+   "id": "656240e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $f(x)$ is a given function for $x \\in (0,1)$.\n",
     "\n",
@@ -6557,8 +6227,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e0f7d593",
-   "metadata": {},
+   "id": "fb310d7c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -6570,8 +6242,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4cacfaeb",
-   "metadata": {},
+   "id": "e6b102dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This equation can be solved numerically using programs where e.g Autograd and TensorFlow are used.\n",
     "The results from the networks can then be compared to the analytical solution.\n",
@@ -6580,8 +6254,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69ba705a",
-   "metadata": {},
+   "id": "797d4bb8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The specific equation to solve for\n",
     "\n",
@@ -6590,8 +6266,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "995cfbc9",
-   "metadata": {},
+   "id": "da2e90b8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "-g''(x) = f(x),\\qquad x \\in (0,1)\n",
@@ -6600,16 +6278,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "769f9670",
-   "metadata": {},
+   "id": "318f8f3a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $f(x)$ is a given function, along with the chosen conditions"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "855cddbb",
-   "metadata": {},
+   "id": "c5e8ac9e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"cond\"></div>\n",
@@ -6623,8 +6305,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7006cb54",
-   "metadata": {},
+   "id": "220ceeb4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In this example, we consider the case when $f(x) = (3x + x^2)\\exp(x)$.\n",
     "\n",
@@ -6633,8 +6317,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5216ca22",
-   "metadata": {},
+   "id": "ec8b38dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x) = x \\cdot (1-x) \\cdot N(P,x)\n",
@@ -6643,16 +6329,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b77670be",
-   "metadata": {},
+   "id": "0ed927a9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The analytical solution for this problem is"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "bf2bed23",
-   "metadata": {},
+   "id": "3a51ddcc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g(x) = x(1 - x)\\exp(x)\n",
@@ -6661,8 +6351,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a22ccb78",
-   "metadata": {},
+   "id": "d5392b8d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Solving the equation using Autograd"
    ]
@@ -6670,8 +6362,11 @@
   {
    "cell_type": "code",
    "execution_count": 45,
-   "id": "7b3b5f5a",
-   "metadata": {},
+   "id": "95059f71",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -6684,7 +6379,10 @@
     "\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -6725,6 +6423,7 @@
     "\n",
     "    return x_output\n",
     "\n",
+    "\n",
     "def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
     "    # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
     "\n",
@@ -6828,8 +6527,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6668b7ef",
-   "metadata": {},
+   "id": "7c568bf3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Comparing with a numerical scheme\n",
     "\n",
@@ -6848,8 +6549,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec1adda2",
-   "metadata": {},
+   "id": "eab0bb68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"approx\"></div>\n",
@@ -6863,16 +6566,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33486af4",
-   "metadata": {},
+   "id": "c0ada0c0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If $x_i = i \\Delta x = x_{i-1} + \\Delta x$ and $g_i = g(x_i)$ for $i = 1,\\dots N_x - 2$ with $N_x$ being the number of values for $x$, ([15](#approx)) becomes"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "42c3ef84",
-   "metadata": {},
+   "id": "b483eace",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -6884,16 +6591,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f454dbea",
-   "metadata": {},
+   "id": "30d45122",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Since we know from our problem that"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "7411a707",
-   "metadata": {},
+   "id": "52c68e05",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -6905,8 +6616,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c47c3822",
-   "metadata": {},
+   "id": "1657934d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "along with the conditions $g(0) = g(1) = 0$,\n",
     "the following scheme can be used to find an approximate solution for $g(x)$ numerically:"
@@ -6914,8 +6627,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1cca824c",
-   "metadata": {},
+   "id": "9fc46a1b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"odesys\"></div>\n",
@@ -6932,8 +6647,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82ecd5a1",
-   "metadata": {},
+   "id": "cd79f75c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for $i = 1, \\dots, N_x - 2$ where $g_0 = g_{N_x - 1} = 0$ and $f(x_i) = (3x_i + x_i^2)\\exp(x_i)$, which is given for our specific problem.\n",
     "\n",
@@ -6942,8 +6659,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39f5fe07",
-   "metadata": {},
+   "id": "501ac880",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -6977,16 +6696,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ac54c35",
-   "metadata": {},
+   "id": "8551615b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which makes it possible to solve for the vector $\\boldsymbol{g}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "79ad3ebc",
-   "metadata": {},
+   "id": "dbd6d2a1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the code\n",
     "\n",
@@ -6996,8 +6719,11 @@
   {
    "cell_type": "code",
    "execution_count": 46,
-   "id": "be03bf2d",
-   "metadata": {},
+   "id": "c71a3063",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -7010,7 +6736,10 @@
     "\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -7051,6 +6780,7 @@
     "\n",
     "    return x_output\n",
     "\n",
+    "\n",
     "def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
     "    # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
     "\n",
@@ -7194,8 +6924,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "faa0daa4",
-   "metadata": {},
+   "id": "da58cdec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Partial Differential Equations\n",
     "\n",
@@ -7209,8 +6941,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb7b7ff6",
-   "metadata": {},
+   "id": "df991968",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"PDE\"></div>\n",
@@ -7224,16 +6958,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71da1640",
-   "metadata": {},
+   "id": "59ef3099",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $f$ is an expression involving all kinds of possible mixed derivatives of $g(x_1,\\dots,x_N)$ up to an order $n$. In order for the solution to be unique, some additional conditions must also be given."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c77e6225",
-   "metadata": {},
+   "id": "a580ae0f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Type of problem\n",
     "\n",
@@ -7245,8 +6983,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98f82ea2",
-   "metadata": {},
+   "id": "a56f3fe1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -7257,8 +6997,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc33501c",
-   "metadata": {},
+   "id": "69586714",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $h_1(x_1,\\dots,x_N)$ is a function that ensures $g_t(x_1,\\dots,x_N)$ satisfies some given conditions.\n",
     "The neural network $N(x_1,\\dots,x_N,P)$ has weights and biases described by $P$ and $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$ is an expression using the output from the neural network in some way.\n",
@@ -7268,8 +7010,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "818e8900",
-   "metadata": {},
+   "id": "d8374dce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Network requirements\n",
     "\n",
@@ -7286,8 +7030,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "526d5428",
-   "metadata": {},
+   "id": "f3fe961e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(x_1, \\dots, x_N, P\\right) = \\left(  f\\left(x_1, \\, \\dots \\, , x_N, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1}, \\dots , \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_N}, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(x_1,\\dots,x_N) }{\\partial x_N^n} \\right) \\right)^2\n",
@@ -7296,8 +7042,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "279b9296",
-   "metadata": {},
+   "id": "4e453aa1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More details\n",
     "\n",
@@ -7306,8 +7054,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcb8ce40",
-   "metadata": {},
+   "id": "e1ebf5bd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(\\boldsymbol{x}, P\\right) = f\\left( \\left( \\boldsymbol{x}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}) }{\\partial x_N^n} \\right) \\right)^2\n",
@@ -7316,16 +7066,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6549ea7b",
-   "metadata": {},
+   "id": "b8c35553",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If we also have $M$ different sets of values for $x_1, \\dots, x_N$, that is $\\boldsymbol{x}_i = \\big(x_1^{(i)}, \\dots, x_N^{(i)}\\big)$ for $i = 1,\\dots,M$ being the rows in matrix $X$, the cost function can be generalized into"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "0956062e",
-   "metadata": {},
+   "id": "22a123d5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(X, P \\right) = \\sum_{i=1}^M f\\left( \\left( \\boldsymbol{x}_i, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}_i) }{\\partial x_N^n} \\right) \\right)^2.\n",
@@ -7334,8 +7088,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8fca0166",
-   "metadata": {},
+   "id": "b15eedf5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: The diffusion equation\n",
     "\n",
@@ -7344,8 +7100,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58ad6f25",
-   "metadata": {},
+   "id": "1a92cc8c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial g(x,t)}{\\partial t} = \\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
@@ -7354,16 +7112,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6e5728e",
-   "metadata": {},
+   "id": "e4862313",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where a possible choice of conditions are"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6921faa1",
-   "metadata": {},
+   "id": "5c186d68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -7376,16 +7138,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80e632ef",
-   "metadata": {},
+   "id": "57d4f000",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $u(x)$ being some given function."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a2711421",
-   "metadata": {},
+   "id": "7c2cdc6b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Defining the problem\n",
     "\n",
@@ -7394,8 +7160,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "981da4af",
-   "metadata": {},
+   "id": "bde064ea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"diffonedim\"></div>\n",
@@ -7409,16 +7177,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1b8c16d",
-   "metadata": {},
+   "id": "7a558c97",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b8ed6509",
-   "metadata": {},
+   "id": "534a4844",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -7431,8 +7203,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "200050ac",
-   "metadata": {},
+   "id": "a07e0730",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $u(x) = \\sin(\\pi x)$.\n",
     "\n",
@@ -7443,8 +7217,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5dca99d2",
-   "metadata": {},
+   "id": "74b72286",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the network using Autograd\n",
     "\n",
@@ -7460,8 +7236,11 @@
   {
    "cell_type": "code",
    "execution_count": 47,
-   "id": "85f4b843",
-   "metadata": {},
+   "id": "4a0c57e9",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "def sigmoid(z):\n",
@@ -7475,7 +7254,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -7512,8 +7291,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9dd68ff8",
-   "metadata": {},
+   "id": "350b1d3d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the network using Autograd; The trial solution\n",
     "\n",
@@ -7540,8 +7321,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65f68c5a",
-   "metadata": {},
+   "id": "9fd438b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Why the jacobian?\n",
     "\n",
@@ -7567,8 +7350,11 @@
   {
    "cell_type": "code",
    "execution_count": 48,
-   "id": "91612f4f",
-   "metadata": {},
+   "id": "d1c81690",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# Set up the trial function:\n",
@@ -7611,8 +7397,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff9df4ba",
-   "metadata": {},
+   "id": "ca22d9ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the network using Autograd; The full program\n",
     "\n",
@@ -7635,8 +7423,11 @@
   {
    "cell_type": "code",
    "execution_count": 49,
-   "id": "e6451b9e",
-   "metadata": {},
+   "id": "5a9146bc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -7659,7 +7450,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -7802,7 +7593,7 @@
     "    T,X = np.meshgrid(t,x)\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))\n",
     "    s = ax.plot_surface(T,X,g_dnn_ag,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -7810,14 +7601,14 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Analytical solution')\n",
     "    s = ax.plot_surface(T,X,G_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
     "    ax.set_ylabel('Position $x$');\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Difference')\n",
     "    s = ax.plot_surface(T,X,diff_ag,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -7866,8 +7657,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7f867cf2",
-   "metadata": {},
+   "id": "e59d2116",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Solving the wave equation with Neural Networks\n",
     "\n",
@@ -7876,8 +7669,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ded83be1",
-   "metadata": {},
+   "id": "e2ffdbaf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial^2 g(x,t)}{\\partial t^2} = c^2\\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
@@ -7886,8 +7681,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0aba0c9",
-   "metadata": {},
+   "id": "37b2cc03",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $c$ being the specified wave speed.\n",
     "\n",
@@ -7896,8 +7693,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28a48fe7",
-   "metadata": {},
+   "id": "524df5d3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -7911,16 +7710,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61ded78d",
-   "metadata": {},
+   "id": "d175b25f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $\\frac{\\partial g(x,t)}{\\partial t} \\Big |_{t = 0}$ means the derivative of $g(x,t)$ with respect to $t$ is evaluated at $t = 0$, and $u(x)$ and $v(x)$ being given functions."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "990695ea",
-   "metadata": {},
+   "id": "11b3289e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The problem to solve for\n",
     "\n",
@@ -7929,8 +7732,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58841089",
-   "metadata": {},
+   "id": "e469d65e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"wave\"></div>\n",
@@ -7944,8 +7749,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "303eb900",
-   "metadata": {},
+   "id": "5f773fa8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $c$ is the given wave speed.\n",
     "The chosen conditions for this equation are"
@@ -7953,8 +7760,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce5c5167",
-   "metadata": {},
+   "id": "2952f7b4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"condwave\"></div>\n",
@@ -7971,16 +7780,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "609a7556",
-   "metadata": {},
+   "id": "99057b48",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In this example, let $c = 1$ and $u(x) = \\sin(\\pi x)$ and $v(x) = -\\pi\\sin(\\pi x)$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5edb8797",
-   "metadata": {},
+   "id": "7debdfea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "Setting up the network is done in similar matter as for the example of solving the diffusion equation.\n",
@@ -8003,8 +7816,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6be7518",
-   "metadata": {},
+   "id": "2d5d5c44",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The analytical solution\n",
     "\n",
@@ -8017,8 +7832,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "368bb540",
-   "metadata": {},
+   "id": "f97806ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Solving the wave equation - the full program using Autograd"
    ]
@@ -8026,8 +7843,11 @@
   {
    "cell_type": "code",
    "execution_count": 50,
-   "id": "65085f11",
-   "metadata": {},
+   "id": "9337b7c7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -8084,7 +7904,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -8189,7 +8009,7 @@
     "    T,X = np.meshgrid(t,x)\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))\n",
     "    s = ax.plot_surface(T,X,res,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -8197,7 +8017,7 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Analytical solution')\n",
     "    s = ax.plot_surface(T,X,res_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -8205,7 +8025,7 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Difference')\n",
     "    s = ax.plot_surface(T,X,diff,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -8254,8 +8074,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "41011c90",
-   "metadata": {},
+   "id": "6071d006",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resources on differential equations and deep learning\n",
     "\n",
@@ -8270,11 +8092,6 @@
   }
  ],
  "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
   "language_info": {
    "codemirror_mode": {
     "name": "ipython",
diff --git a/doc/LectureNotes/_build/jupyter_execute/week43.py b/doc/LectureNotes/_build/jupyter_execute/week43.py
index f1ed0ece8..7e3c621a5 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week43.py
+++ b/doc/LectureNotes/_build/jupyter_execute/week43.py
@@ -1366,7 +1366,7 @@ def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories
     model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))
     model.add(Dense(n_categories, activation='softmax'))
     
-    sgd = optimizers.SGD(lr=eta)
+    sgd = optimizers.SGD(learning_rate=eta)
     model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
     
     return model
@@ -1542,7 +1542,7 @@ def NN_model(inputsize,n_layers,n_neuron,eta,lamda):
         else:                       #Subsequent layers are capable of automatic shape inferencing
             model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda)))
     model.add(Dense(2,activation='softmax'))  #2 outputs - ordered and disordered (softmax for prob)
-    sgd=optimizers.SGD(lr=eta)
+    sgd=optimizers.SGD(learning_rate=eta)
     model.compile(loss='categorical_crossentropy',optimizer=sgd,metrics=['accuracy'])
     return model
 
@@ -2623,7 +2623,7 @@ scores = logistic_regression.fit(X, yXOR, scheduler, epochs=1000)
 
 # Not bad, but the results depend strongly on the learning reate. Try different learning rates.
 
-# ## Solving ODEs with Deep Learning
+# ## Solving differential equations  with Deep Learning
 # 
 # The Universal Approximation Theorem states that a neural network can
 # approximate any function at a single hidden layer along with one input
@@ -2642,7 +2642,7 @@ scores = logistic_regression.fit(X, yXOR, scheduler, epochs=1000)
 # The lectures on differential equations were developed by Kristine Baluka Hein, now PhD student at IFI.
 # A great thanks to Kristine.
 
-# ## Ordinary Differential Equations
+# ## Ordinary Differential Equations first
 # 
 # An ordinary differential equation (ODE) is an equation involving functions having one variable.
 # 
@@ -3206,8 +3206,8 @@ def sigmoid(z):
 # but with number of hidden layers specified by the user.
 def deep_neural_network(deep_params, x):
     # N_hidden is the number of hidden layers
-
-    N_hidden = np.size(deep_params) - 1 # -1 since params consists of
+    # deep_params is a list, len() should be used
+    N_hidden = len(deep_params) - 1 # -1 since params consists of
                                         # parameters to all the hidden
                                         # layers AND the output layer.
 
@@ -3436,9 +3436,12 @@ def get_parameters():
     g0 = 1.2
     return alpha, A, g0
 
-def deep_neural_network(P, x):
+def deep_neural_network(deep_params, x):
     # N_hidden is the number of hidden layers
-    N_hidden = np.size(P) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer
+    # deep_params is a list, len() should be used
+    N_hidden = len(deep_params) - 1 # -1 since params consists of
+                                        # parameters to all the hidden
+                                        # layers AND the output layer.
 
     # Assumes input x being an one-dimensional array
     num_values = np.size(x)
@@ -3455,7 +3458,7 @@ def deep_neural_network(P, x):
 
     for l in range(N_hidden):
         # From the list of parameters P; find the correct weigths and bias for this layer
-        w_hidden = P[l]
+        w_hidden = deep_params[l]
 
         # Add a row of ones to include bias
         x_prev = np.concatenate((np.ones((1,num_values)), x_prev ), axis = 0)
@@ -3469,7 +3472,7 @@ def deep_neural_network(P, x):
     ## Output layer:
 
     # Get the weights and bias for this layer
-    w_output = P[-1]
+    w_output = deep_params[-1]
 
     # Include bias:
     x_prev = np.concatenate((np.ones((1,num_values)), x_prev), axis = 0)
@@ -3480,6 +3483,8 @@ def deep_neural_network(P, x):
     return x_output
 
 
+
+
 def cost_function_deep(P, x):
 
     # Evaluate the trial function with the current parameters P
@@ -3785,7 +3790,10 @@ def sigmoid(z):
 
 def deep_neural_network(deep_params, x):
     # N_hidden is the number of hidden layers
-    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer
+    # deep_params is a list, len() should be used
+    N_hidden = len(deep_params) - 1 # -1 since params consists of
+                                        # parameters to all the hidden
+                                        # layers AND the output layer.
 
     # Assumes input x being an one-dimensional array
     num_values = np.size(x)
@@ -3826,6 +3834,7 @@ def deep_neural_network(deep_params, x):
 
     return x_output
 
+
 def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):
     # num_hidden_neurons is now a list of number of neurons within each hidden layer
 
@@ -4035,7 +4044,10 @@ def sigmoid(z):
 
 def deep_neural_network(deep_params, x):
     # N_hidden is the number of hidden layers
-    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer
+    # deep_params is a list, len() should be used
+    N_hidden = len(deep_params) - 1 # -1 since params consists of
+                                        # parameters to all the hidden
+                                        # layers AND the output layer.
 
     # Assumes input x being an one-dimensional array
     num_values = np.size(x)
@@ -4076,6 +4088,7 @@ def deep_neural_network(deep_params, x):
 
     return x_output
 
+
 def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):
     # num_hidden_neurons is now a list of number of neurons within each hidden layer
 
@@ -4358,7 +4371,7 @@ def deep_neural_network(deep_params, x):
     num_points = np.size(x,1)
 
     # N_hidden is the number of hidden layers
-    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer
+    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer
 
     # Assume that the input layer does nothing to the input x
     x_input = x
@@ -4516,7 +4529,7 @@ def deep_neural_network(deep_params, x):
     num_points = np.size(x,1)
 
     # N_hidden is the number of hidden layers
-    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer
+    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer
 
     # Assume that the input layer does nothing to the input x
     x_input = x
@@ -4659,7 +4672,7 @@ if __name__ == '__main__':
     T,X = np.meshgrid(t,x)
 
     fig = plt.figure(figsize=(10,10))
-    ax = fig.gca(projection='3d')
+    ax = fig.add_suplot(projection='3d')
     ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))
     s = ax.plot_surface(T,X,g_dnn_ag,linewidth=0,antialiased=False,cmap=cm.viridis)
     ax.set_xlabel('Time $t$')
@@ -4667,14 +4680,14 @@ if __name__ == '__main__':
 
 
     fig = plt.figure(figsize=(10,10))
-    ax = fig.gca(projection='3d')
+    ax = fig.add_suplot(projection='3d')
     ax.set_title('Analytical solution')
     s = ax.plot_surface(T,X,G_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)
     ax.set_xlabel('Time $t$')
     ax.set_ylabel('Position $x$');
 
     fig = plt.figure(figsize=(10,10))
-    ax = fig.gca(projection='3d')
+    ax = fig.add_suplot(projection='3d')
     ax.set_title('Difference')
     s = ax.plot_surface(T,X,diff_ag,linewidth=0,antialiased=False,cmap=cm.viridis)
     ax.set_xlabel('Time $t$')
@@ -4859,7 +4872,7 @@ def deep_neural_network(deep_params, x):
     num_points = np.size(x,1)
 
     # N_hidden is the number of hidden layers
-    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer
+    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer
 
     # Assume that the input layer does nothing to the input x
     x_input = x
@@ -4964,7 +4977,7 @@ if __name__ == '__main__':
     T,X = np.meshgrid(t,x)
 
     fig = plt.figure(figsize=(10,10))
-    ax = fig.gca(projection='3d')
+    ax = fig.add_suplot(projection='3d')
     ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))
     s = ax.plot_surface(T,X,res,linewidth=0,antialiased=False,cmap=cm.viridis)
     ax.set_xlabel('Time $t$')
@@ -4972,7 +4985,7 @@ if __name__ == '__main__':
 
 
     fig = plt.figure(figsize=(10,10))
-    ax = fig.gca(projection='3d')
+    ax = fig.add_suplot(projection='3d')
     ax.set_title('Analytical solution')
     s = ax.plot_surface(T,X,res_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)
     ax.set_xlabel('Time $t$')
@@ -4980,7 +4993,7 @@ if __name__ == '__main__':
 
 
     fig = plt.figure(figsize=(10,10))
-    ax = fig.gca(projection='3d')
+    ax = fig.add_suplot(projection='3d')
     ax.set_title('Difference')
     s = ax.plot_surface(T,X,diff,linewidth=0,antialiased=False,cmap=cm.viridis)
     ax.set_xlabel('Time $t$')
diff --git a/doc/LectureNotes/week43.ipynb b/doc/LectureNotes/week43.ipynb
index 47032b0fe..202263be5 100644
--- a/doc/LectureNotes/week43.ipynb
+++ b/doc/LectureNotes/week43.ipynb
@@ -2,8 +2,10 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "cda62a86",
-   "metadata": {},
+   "id": "677a195d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
     "doconce format html week43.do.txt --no_mako -->\n",
@@ -12,8 +14,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bdae1fa5",
-   "metadata": {},
+   "id": "e943e8f0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "# Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations\n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n",
@@ -23,8 +27,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e2c09dd5",
-   "metadata": {},
+   "id": "22cdced0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Plans for week 43\n",
     "\n",
@@ -39,8 +45,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7de8bfe0",
-   "metadata": {},
+   "id": "a57ef6df",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Exercises and lab session week 43\n",
     "**Lab sessions on Tuesday and Wednesday.**\n",
@@ -54,8 +62,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2664d901",
-   "metadata": {},
+   "id": "c4a134ee",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Mathematics of deep learning\n",
     "\n",
@@ -68,8 +78,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46bb5558",
-   "metadata": {},
+   "id": "dd73045e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Reminder on books with hands-on material and codes\n",
     "* Sebastian Rashcka et al, Machine learning with Scikit-Learn and PyTorch at <https://sebastianraschka.com/blog/2022/ml-pytorch-book.html>"
@@ -77,8 +89,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c6ad86d",
-   "metadata": {},
+   "id": "372f4aa4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Reading recommendations\n",
     "\n",
@@ -89,8 +103,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9fbf4898",
-   "metadata": {},
+   "id": "05efbc6f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using Automatic differentiation\n",
     "\n",
@@ -100,8 +116,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "135a7122",
-   "metadata": {},
+   "id": "d04b0948",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Back propagation and automatic differentiation\n",
     "\n",
@@ -115,16 +133,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45236eaf",
-   "metadata": {},
+   "id": "b9d41f5c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Lecture Monday  October 21"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "8997a10d",
-   "metadata": {},
+   "id": "68606991",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the back propagation algorithm and algorithm for a feed forward NN, initalizations\n",
     "This is a reminder from where we ended last week.\n",
@@ -148,8 +170,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df88cb72",
-   "metadata": {},
+   "id": "a564a394",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the back propagation algorithm, part 1\n",
     "\n",
@@ -169,8 +193,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46d7ebde",
-   "metadata": {},
+   "id": "43ab4381",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the back propagation algorithm, part 2\n",
     "\n",
@@ -179,8 +205,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ad237f5",
-   "metadata": {},
+   "id": "f578cee4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\delta_j^L = \\sigma'(z_j^L)\\frac{\\partial {\\cal C}}{\\partial (a_j^L)}.\n",
@@ -189,16 +217,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f6906530",
-   "metadata": {},
+   "id": "fbc05943",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Then we compute the back propagate error for each $l=L-1,L-2,\\dots,1$ as"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e9613a49",
-   "metadata": {},
+   "id": "6ad3c28f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}\\sigma'(z_j^l).\n",
@@ -207,8 +239,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dba468b9",
-   "metadata": {},
+   "id": "135513b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the Back propagation algorithm, part 3\n",
     "\n",
@@ -219,8 +253,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "21c684a1",
-   "metadata": {},
+   "id": "f643ecdf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "w_{ij}^l\\leftarrow  = w_{ij}^l- \\eta \\delta_j^la_i^{l-1},\n",
@@ -229,8 +265,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6acf04a3",
-   "metadata": {},
+   "id": "077ef1c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n",
@@ -239,16 +277,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b0558fbe",
-   "metadata": {},
+   "id": "50cf7472",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $\\eta$ being the learning rate."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6b424064",
-   "metadata": {},
+   "id": "a10f406c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Updating the gradients\n",
     "\n",
@@ -257,8 +299,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7bc86e31",
-   "metadata": {},
+   "id": "626cba8f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\delta_j^l = \\sum_k \\delta_k^{l+1}w_{kj}^{l+1}\\sigma'(z_j^l),\n",
@@ -267,16 +311,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7a10087",
-   "metadata": {},
+   "id": "2ebe05ad",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "we update the weights and the biases using gradient descent for each $l=L-1,L-2,\\dots,1$ and update the weights and biases according to the rules"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "2bf12837",
-   "metadata": {},
+   "id": "bfbbac35",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "w_{ij}^l\\leftarrow  = w_{ij}^l- \\eta \\delta_j^la_i^{l-1},\n",
@@ -285,8 +333,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ad07731e",
-   "metadata": {},
+   "id": "ac515399",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "b_j^l \\leftarrow b_j^l-\\eta \\frac{\\partial {\\cal C}}{\\partial b_j^l}=b_j^l-\\eta \\delta_j^l,\n",
@@ -295,8 +345,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "30c6ae90",
-   "metadata": {},
+   "id": "4703cc51",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Activation functions\n",
     "\n",
@@ -316,8 +368,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5dfa6d1c",
-   "metadata": {},
+   "id": "cab6ad03",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions, examples\n",
     "\n",
@@ -326,8 +380,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8d0be63",
-   "metadata": {},
+   "id": "ad6042eb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\sigma(x) = \\frac{1}{1 + e^{-x}},\n",
@@ -336,16 +392,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3ec0efa",
-   "metadata": {},
+   "id": "1e96b7e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and the *hyperbolic tangent* function"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "78c46915",
-   "metadata": {},
+   "id": "c600792f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\sigma(x) = \\tanh(x)\n",
@@ -354,8 +414,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87e6973b",
-   "metadata": {},
+   "id": "76d1da8e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The RELU function family\n",
     "\n",
@@ -373,8 +435,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c990bc8",
-   "metadata": {},
+   "id": "8e7e0e0c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## ELU function\n",
     "\n",
@@ -385,8 +449,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b7760f9",
-   "metadata": {},
+   "id": "4b1f77d6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "ELU(z) = \\left\\{\\begin{array}{cc} \\alpha\\left( \\exp{(z)}-1\\right) & z < 0,\\\\  z & z \\ge 0.\\end{array}\\right.\n",
@@ -395,8 +461,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47927a82",
-   "metadata": {},
+   "id": "10826ba9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Which activation function should we use?\n",
     "\n",
@@ -415,8 +483,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52554330",
-   "metadata": {},
+   "id": "79d307b6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More on activation functions, output layers\n",
     "\n",
@@ -435,8 +505,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b7d3292",
-   "metadata": {},
+   "id": "429b8d4e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up a Multi-layer perceptron model for classification\n",
     "\n",
@@ -461,8 +533,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38715b52",
-   "metadata": {},
+   "id": "90d9f195",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = \\frac{1}{1 + \\exp{(- \\boldsymbol{x}})} ,\n",
@@ -471,16 +545,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcc0cbfa",
-   "metadata": {},
+   "id": "73d2763e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c686ecf6",
-   "metadata": {},
+   "id": "e2a70a54",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(y = 1 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) = 1 - P(y = 0 \\mid \\boldsymbol{x}, \\boldsymbol{\\theta}) ,\n",
@@ -489,8 +567,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79a8b207",
-   "metadata": {},
+   "id": "7ed6c0dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $y \\in \\{0, 1\\}$  and $\\boldsymbol{\\theta}$ represents the weights and biases\n",
     "of our network."
@@ -498,8 +578,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3218b074",
-   "metadata": {},
+   "id": "a42826b9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Defining the cost function\n",
     "\n",
@@ -508,8 +590,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0e50336",
-   "metadata": {},
+   "id": "d8e401c5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = - \\sum_{i=1}^n\n",
@@ -519,8 +603,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79138403",
-   "metadata": {},
+   "id": "17808105",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This last equality means that we can interpret our *cost* function as a sum over the *loss* function\n",
     "for each point in the dataset $\\mathcal{L}_i(\\boldsymbol{\\theta})$.  \n",
@@ -542,8 +628,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b3db35e",
-   "metadata": {},
+   "id": "5a9b90ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(y_{ic} = 1 \\mid \\boldsymbol{x}_i, \\boldsymbol{\\theta}) = \\frac{\\exp{((\\boldsymbol{a}_i^{hidden})^T \\boldsymbol{w}_c)}}\n",
@@ -553,8 +641,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90626f76",
-   "metadata": {},
+   "id": "57f33029",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which reduces to the logistic function in the binary case.  \n",
     "The likelihood of this $C$-class classifier\n",
@@ -563,8 +653,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "596eb444",
-   "metadata": {},
+   "id": "422eb23f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "P(\\mathcal{D} \\mid \\boldsymbol{\\theta}) = \\prod_{i=1}^n \\prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .\n",
@@ -573,16 +665,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5529d979",
-   "metadata": {},
+   "id": "0eb634c3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Again we take the negative log-likelihood to define our cost function:"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "f7d2523f",
-   "metadata": {},
+   "id": "b3b208fc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\theta}) = - \\log{P(\\mathcal{D} \\mid \\boldsymbol{\\theta})}.\n",
@@ -591,8 +687,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d8d61f1",
-   "metadata": {},
+   "id": "3788aba1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "See the logistic regression lectures for a full definition of the cost function.\n",
     "\n",
@@ -601,8 +699,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9751fb82",
-   "metadata": {},
+   "id": "4d38ceec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: binary classification problem\n",
     "\n",
@@ -611,8 +711,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e6587c7",
-   "metadata": {},
+   "id": "cee503b9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{\\beta}) = - \\sum_{i=1}^n \\left(y_i\\log{p(y_i \\vert x_i,\\boldsymbol{\\beta})}+(1-y_i)\\log{1-p(y_i \\vert x_i,\\boldsymbol{\\beta})}\\right),\n",
@@ -621,16 +723,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39bb5ba4",
-   "metadata": {},
+   "id": "19b29e02",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we had defined the logistic (sigmoid) function"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "fcb1f3d9",
-   "metadata": {},
+   "id": "19507159",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(y_i =1\\vert x_i,\\boldsymbol{\\beta})=\\frac{\\exp{(\\beta_0+\\beta_1 x_i)}}{1+\\exp{(\\beta_0+\\beta_1 x_i)}},\n",
@@ -639,16 +745,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20fc130a",
-   "metadata": {},
+   "id": "a15191e4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "66c7c0e9",
-   "metadata": {},
+   "id": "c9df7a22",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(y_i =0\\vert x_i,\\boldsymbol{\\beta})=1-p(y_i =1\\vert x_i,\\boldsymbol{\\beta}).\n",
@@ -657,8 +767,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e757c738",
-   "metadata": {},
+   "id": "0cae75ec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The parameters $\\boldsymbol{\\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. \n",
     "\n",
@@ -668,8 +780,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d048e79e",
-   "metadata": {},
+   "id": "36b0506b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "a_i^l = y_i = \\frac{\\exp{(z_i^l)}}{1+\\exp{(z_i^l)}},\n",
@@ -678,16 +792,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b97827e7",
-   "metadata": {},
+   "id": "0c729c48",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c11528eb",
-   "metadata": {},
+   "id": "060813af",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "z_i^l = \\sum_{j}w_{ij}^l a_j^{l-1}+b_i^l,\n",
@@ -696,8 +814,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94839c96",
-   "metadata": {},
+   "id": "f2a5059b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where the superscript $l-1$ indicates that these are the outputs from layer $l-1$.\n",
     "Our cost function at the final layer $l=L$ is now"
@@ -705,8 +825,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "694596c9",
-   "metadata": {},
+   "id": "6763074d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathcal{C}(\\boldsymbol{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(1-t_i)\\log{(1-a_i^L)}\\right),\n",
@@ -715,16 +837,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b4c8232e",
-   "metadata": {},
+   "id": "f498b6b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have defined the targets $t_i$. The derivatives of the cost function with respect to the output $a_i^L$ are then easily calculated and we get"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "9d611a08",
-   "metadata": {},
+   "id": "fedce928",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial \\mathcal{C}(\\boldsymbol{W})}{\\partial a_i^L} = \\frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.\n",
@@ -733,16 +859,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb7847ef",
-   "metadata": {},
+   "id": "429c11ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In case we use another activation function than the logistic one, we need to evaluate other derivatives."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "cd5be179",
-   "metadata": {},
+   "id": "ddde8370",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The Softmax function\n",
     "In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation $z_i^l$, that is we need"
@@ -750,8 +880,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96b7fe79",
-   "metadata": {},
+   "id": "637bd194",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial f(z_i^l)}{\\partial w_{jk}^l} =\n",
@@ -761,16 +893,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1040c590",
-   "metadata": {},
+   "id": "0792109c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "For the Softmax function we have"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3162bd5e",
-   "metadata": {},
+   "id": "10f14691",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(z_i^l) = \\frac{\\exp{(z_i^l)}}{\\sum_{m=1}^K\\exp{(z_m^l)}}.\n",
@@ -779,16 +915,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b7f2b7b8",
-   "metadata": {},
+   "id": "186529b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Its derivative with respect to $z_j^l$ gives"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "735fd9c0",
-   "metadata": {},
+   "id": "68afc0da",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial f(z_i^l)}{\\partial z_j^l}= f(z_i^l)\\left(\\delta_{ij}-f(z_j^l)\\right),\n",
@@ -797,16 +937,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3cbbb04",
-   "metadata": {},
+   "id": "cf48ea60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which in case of the simply binary model reduces to  having $i=j$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6462edbb",
-   "metadata": {},
+   "id": "861a3bbe",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Developing a code for doing neural networks with back propagation\n",
     "\n",
@@ -827,8 +971,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7915dc1d",
-   "metadata": {},
+   "id": "c8007ce7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Collect and pre-process data\n",
     "\n",
@@ -875,8 +1021,11 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "eb736d79",
-   "metadata": {},
+   "id": "29678f97",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "%matplotlib inline\n",
@@ -927,8 +1076,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01fcb50b",
-   "metadata": {},
+   "id": "3ba6d7d6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Train and test datasets\n",
     "\n",
@@ -946,8 +1097,11 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "e6b7f2e3",
-   "metadata": {},
+   "id": "7df51dd1",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn.model_selection import train_test_split\n",
@@ -981,8 +1135,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ca032f8",
-   "metadata": {},
+   "id": "249898fd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Define model and architecture\n",
     "\n",
@@ -1023,8 +1179,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6e4e1e18",
-   "metadata": {},
+   "id": "2d30ddd3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Layers\n",
     "\n",
@@ -1061,8 +1219,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab0ee6d8",
-   "metadata": {},
+   "id": "ce9f14e4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Weights and biases\n",
     "\n",
@@ -1080,8 +1240,11 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "15ad1599",
-   "metadata": {},
+   "id": "c3f75b32",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# building our neural network\n",
@@ -1103,8 +1266,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3efd576a",
-   "metadata": {},
+   "id": "4ebf4f68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Feed-forward pass\n",
     "\n",
@@ -1129,8 +1294,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "715c5d46",
-   "metadata": {},
+   "id": "c6760d1f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Matrix multiplications\n",
     "\n",
@@ -1164,8 +1331,11 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "ecaa833e",
-   "metadata": {},
+   "id": "98f3a5d5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# setup the feed-forward pass, subscript h = hidden layer\n",
@@ -1207,8 +1377,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0319e65",
-   "metadata": {},
+   "id": "19cd49ec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Choose cost function and optimizer\n",
     "\n",
@@ -1236,8 +1408,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98c6696e",
-   "metadata": {},
+   "id": "b0342f54",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Optimizing the cost function\n",
     "\n",
@@ -1272,8 +1446,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5d1145a",
-   "metadata": {},
+   "id": "7219731b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Regularization\n",
     "\n",
@@ -1304,8 +1480,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b73247fd",
-   "metadata": {},
+   "id": "248590b9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Matrix  multiplication\n",
     "\n",
@@ -1343,8 +1521,11 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "3d61438f",
-   "metadata": {},
+   "id": "1810a36c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# to categorical turns our integer vector into a onehot representation\n",
@@ -1419,8 +1600,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a20a495",
-   "metadata": {},
+   "id": "e094a404",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Improving performance\n",
     "\n",
@@ -1438,8 +1621,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "717b63a1",
-   "metadata": {},
+   "id": "1fb3aab5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Full object-oriented implementation\n",
     "\n",
@@ -1450,8 +1635,11 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "9d6c9929",
-   "metadata": {},
+   "id": "20b3c187",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "class NeuralNetwork:\n",
@@ -1557,8 +1745,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e70667c5",
-   "metadata": {},
+   "id": "f85564ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Evaluate model performance on test data\n",
     "\n",
@@ -1574,8 +1764,11 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "083dfe41",
-   "metadata": {},
+   "id": "9be7082e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "epochs = 100\n",
@@ -1598,8 +1791,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bffeadd3",
-   "metadata": {},
+   "id": "255b5b3d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Adjust hyperparameters\n",
     "\n",
@@ -1610,8 +1805,11 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "6513ac74",
-   "metadata": {},
+   "id": "fc014642",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "eta_vals = np.logspace(-5, 1, 7)\n",
@@ -1638,8 +1836,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a6e305f6",
-   "metadata": {},
+   "id": "96089af8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Visualization"
    ]
@@ -1647,8 +1847,11 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "d920e285",
-   "metadata": {},
+   "id": "04c4d29a",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# visual representation of grid search\n",
@@ -1688,8 +1891,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0f1aaadd",
-   "metadata": {},
+   "id": "472a5060",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## scikit-learn implementation\n",
     "\n",
@@ -1709,8 +1914,11 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "156764f3",
-   "metadata": {},
+   "id": "42e40777",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn.neural_network import MLPClassifier\n",
@@ -1733,8 +1941,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e5fec48",
-   "metadata": {},
+   "id": "57fc5d93",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Visualization"
    ]
@@ -1742,8 +1952,11 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "ace47e70",
-   "metadata": {},
+   "id": "90477fe7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# optional\n",
@@ -1784,8 +1997,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d327f9b",
-   "metadata": {},
+   "id": "29af8aff",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Building neural networks in Tensorflow and Keras\n",
     "\n",
@@ -1800,8 +2015,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2280cbce",
-   "metadata": {},
+   "id": "a70cf999",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Tensorflow\n",
     "\n",
@@ -1833,8 +2050,11 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "dff81198",
-   "metadata": {},
+   "id": "812c98fe",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "pip3 install tensorflow"
@@ -1842,8 +2062,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9bf9cac",
-   "metadata": {},
+   "id": "694c0bd7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and/or if you use **anaconda**, just write (or install from the graphical user interface)\n",
     "(current release of CPU-only TensorFlow)"
@@ -1852,8 +2074,11 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "1ccb8dba",
-   "metadata": {},
+   "id": "1ecd18cc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "conda create -n tf tensorflow\n",
@@ -1862,8 +2087,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efc3f4e2",
-   "metadata": {},
+   "id": "584ab0ab",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "To install the current release of GPU TensorFlow"
    ]
@@ -1871,8 +2098,11 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "01556b01",
-   "metadata": {},
+   "id": "a811e23d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "conda create -n tf-gpu tensorflow-gpu\n",
@@ -1881,8 +2111,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b900f015",
-   "metadata": {},
+   "id": "ab99008f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using Keras\n",
     "\n",
@@ -1894,8 +2126,11 @@
   {
    "cell_type": "code",
    "execution_count": 15,
-   "id": "3fd1f12f",
-   "metadata": {},
+   "id": "fe547415",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "conda install keras"
@@ -1903,8 +2138,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20ec35c5",
-   "metadata": {},
+   "id": "ed1e0fc6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "You can look up the [instructions here](https://keras.io/) for more information.\n",
     "\n",
@@ -1913,8 +2150,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "249e56f7",
-   "metadata": {},
+   "id": "6aebcb51",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Collect and pre-process data\n",
     "\n",
@@ -1924,8 +2163,11 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "0ff66efc",
-   "metadata": {},
+   "id": "a4a7d68d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# import necessary packages\n",
@@ -1976,8 +2218,11 @@
   {
    "cell_type": "code",
    "execution_count": 17,
-   "id": "2806c62b",
-   "metadata": {},
+   "id": "21335418",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from tensorflow.keras.layers import Input\n",
@@ -2002,8 +2247,11 @@
   {
    "cell_type": "code",
    "execution_count": 18,
-   "id": "3bf4c3f6",
-   "metadata": {},
+   "id": "e81d58de",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\n",
@@ -2020,7 +2268,7 @@
     "    model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=regularizers.l2(lmbd)))\n",
     "    model.add(Dense(n_categories, activation='softmax'))\n",
     "    \n",
-    "    sgd = optimizers.SGD(lr=eta)\n",
+    "    sgd = optimizers.SGD(learning_rate=eta)\n",
     "    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n",
     "    \n",
     "    return model"
@@ -2029,8 +2277,11 @@
   {
    "cell_type": "code",
    "execution_count": 19,
-   "id": "81a46485",
-   "metadata": {},
+   "id": "b91287cc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
@@ -2053,8 +2304,11 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "6e619c14",
-   "metadata": {},
+   "id": "d108674e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# optional\n",
@@ -2092,8 +2346,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c303d97b",
-   "metadata": {},
+   "id": "1198d799",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The Breast Cancer Data, now with Keras"
    ]
@@ -2101,8 +2357,11 @@
   {
    "cell_type": "code",
    "execution_count": 21,
-   "id": "03a57bfd",
-   "metadata": {},
+   "id": "eb1eb4fb",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\n",
@@ -2215,7 +2474,7 @@
     "        else:                       #Subsequent layers are capable of automatic shape inferencing\n",
     "            model.add(Dense(n_neuron,activation='relu',kernel_regularizer=regularizers.l2(lamda)))\n",
     "    model.add(Dense(2,activation='softmax'))  #2 outputs - ordered and disordered (softmax for prob)\n",
-    "    sgd=optimizers.SGD(lr=eta)\n",
+    "    sgd=optimizers.SGD(learning_rate=eta)\n",
     "    model.compile(loss='categorical_crossentropy',optimizer=sgd,metrics=['accuracy'])\n",
     "    return model\n",
     "\n",
@@ -2275,8 +2534,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9ad1085",
-   "metadata": {},
+   "id": "92834502",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Building a neural network code\n",
     "\n",
@@ -2292,8 +2553,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf4f3c14",
-   "metadata": {},
+   "id": "deb24cc1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Learning rate methods\n",
     "\n",
@@ -2312,8 +2575,11 @@
   {
    "cell_type": "code",
    "execution_count": 22,
-   "id": "467ea7a2",
-   "metadata": {},
+   "id": "d3619281",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2450,8 +2716,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6af64d5a",
-   "metadata": {},
+   "id": "f37fd7bc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Usage of the above learning rate schedulers\n",
     "\n",
@@ -2464,8 +2732,11 @@
   {
    "cell_type": "code",
    "execution_count": 23,
-   "id": "290e0d00",
-   "metadata": {},
+   "id": "5db34b9b",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "momentum_scheduler = Momentum(eta=1e-3, momentum=0.9)\n",
@@ -2474,8 +2745,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1f43cc5",
-   "metadata": {},
+   "id": "8b25a24d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Here is a small example for how a segment of code using schedulers\n",
     "could look. Switching out the schedulers is simple."
@@ -2484,8 +2757,11 @@
   {
    "cell_type": "code",
    "execution_count": 24,
-   "id": "0def5cec",
-   "metadata": {},
+   "id": "2d5f2887",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "weights = np.ones((3,3))\n",
@@ -2503,8 +2779,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b27dcd7",
-   "metadata": {},
+   "id": "9070c2d3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Cost functions\n",
     "\n",
@@ -2517,8 +2795,11 @@
   {
    "cell_type": "code",
    "execution_count": 25,
-   "id": "4217839c",
-   "metadata": {},
+   "id": "c360c736",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2552,8 +2833,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ef5f9fe9",
-   "metadata": {},
+   "id": "42c7ec61",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Below we give a short example of how these cost function may be used\n",
     "to obtain results if you wish to test them out on your own using\n",
@@ -2563,8 +2846,11 @@
   {
    "cell_type": "code",
    "execution_count": 26,
-   "id": "305e1479",
-   "metadata": {},
+   "id": "cd9cb3a5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from autograd import grad\n",
@@ -2581,8 +2867,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1499b193",
-   "metadata": {},
+   "id": "796aab4a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Activation functions\n",
     "\n",
@@ -2595,8 +2883,11 @@
   {
    "cell_type": "code",
    "execution_count": 27,
-   "id": "e7b59b25",
-   "metadata": {},
+   "id": "5ea4891d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -2650,8 +2941,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57599619",
-   "metadata": {},
+   "id": "2ff3c57c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Below follows a short demonstration of how to use an activation\n",
     "function. The derivative of the activation function will be important\n",
@@ -2663,8 +2956,11 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "id": "5ee68acd",
-   "metadata": {},
+   "id": "34289210",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "z = np.array([[4, 5, 6]]).T\n",
@@ -2681,8 +2977,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d3295d9",
-   "metadata": {},
+   "id": "0839f98b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### The Neural Network\n",
     "\n",
@@ -2703,8 +3001,11 @@
   {
    "cell_type": "code",
    "execution_count": 29,
-   "id": "c4cfc50a",
-   "metadata": {},
+   "id": "0fdc2707",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import math\n",
@@ -3172,8 +3473,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e6e81c1",
-   "metadata": {},
+   "id": "17bc192e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Before we make a model, we will quickly generate a dataset we can use\n",
     "for our linear regression problem as shown below"
@@ -3182,8 +3485,11 @@
   {
    "cell_type": "code",
    "execution_count": 30,
-   "id": "0d4f1ff8",
-   "metadata": {},
+   "id": "f3f5d088",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -3223,8 +3529,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8f1940f",
-   "metadata": {},
+   "id": "53c3b4c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Now that we have our dataset ready for the regression, we can create\n",
     "our regressor. Note that with the seed parameter, we can make sure our\n",
@@ -3237,8 +3545,11 @@
   {
    "cell_type": "code",
    "execution_count": 31,
-   "id": "ff6bd29b",
-   "metadata": {},
+   "id": "890d682f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -3249,8 +3560,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7b906df",
-   "metadata": {},
+   "id": "dc4da852",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We then fit our model with our training data using the scheduler of our choice."
    ]
@@ -3258,8 +3571,11 @@
   {
    "cell_type": "code",
    "execution_count": 32,
-   "id": "db7a5bf2",
-   "metadata": {},
+   "id": "1e98a3f8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -3270,8 +3586,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "508c351b",
-   "metadata": {},
+   "id": "68c5d793",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Due to the progress bar we can see the MSE (train_error) throughout\n",
     "the FFNN's training. Note that the fit() function has some optional\n",
@@ -3284,8 +3602,11 @@
   {
    "cell_type": "code",
    "execution_count": 33,
-   "id": "6b0562b2",
-   "metadata": {},
+   "id": "e735086e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "linear_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -3295,8 +3616,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f03172d9",
-   "metadata": {},
+   "id": "360468f6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We see that given more epochs to train on, the regressor reaches a lower MSE.\n",
     "\n",
@@ -3308,8 +3631,11 @@
   {
    "cell_type": "code",
    "execution_count": 34,
-   "id": "26d1d1c3",
-   "metadata": {},
+   "id": "c5937c59",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn.datasets import load_breast_cancer\n",
@@ -3331,8 +3657,11 @@
   {
    "cell_type": "code",
    "execution_count": 35,
-   "id": "6a78c633",
-   "metadata": {},
+   "id": "2e06b929",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -3343,8 +3672,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5feaced2",
-   "metadata": {},
+   "id": "94140fb1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We will now make use of our validation data by passing it into our fit function as a keyword argument"
    ]
@@ -3352,8 +3683,11 @@
   {
    "cell_type": "code",
    "execution_count": 36,
-   "id": "6a9b1538",
-   "metadata": {},
+   "id": "da82b266",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "logistic_regression.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -3364,8 +3698,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90c7f8f3",
-   "metadata": {},
+   "id": "19e8d4c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Finally, we will create a neural network with 2 hidden layers with activation functions."
    ]
@@ -3373,8 +3709,11 @@
   {
    "cell_type": "code",
    "execution_count": 37,
-   "id": "58954140",
-   "metadata": {},
+   "id": "4744accd",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "input_nodes = X_train.shape[1]\n",
@@ -3390,8 +3729,11 @@
   {
    "cell_type": "code",
    "execution_count": 38,
-   "id": "89536ca9",
-   "metadata": {},
+   "id": "f5b5b198",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "neural_network.reset_weights() # reset weights such that previous runs or reruns don't affect the weights\n",
@@ -3402,8 +3744,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "803f4791",
-   "metadata": {},
+   "id": "1f5fc0a0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "### Multiclass classification\n",
     "\n",
@@ -3415,8 +3759,11 @@
   {
    "cell_type": "code",
    "execution_count": 39,
-   "id": "50405951",
-   "metadata": {},
+   "id": "4308d82f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn.datasets import load_digits\n",
@@ -3449,8 +3796,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d906edf4",
-   "metadata": {},
+   "id": "96fc3508",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Testing the XOR gate and other gates\n",
     "\n",
@@ -3460,8 +3809,11 @@
   {
    "cell_type": "code",
    "execution_count": 40,
-   "id": "414ee306",
-   "metadata": {},
+   "id": "5aa9a2a4",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "X = np.array([ [0, 0], [0, 1], [1, 0],[1, 1]],dtype=np.float64)\n",
@@ -3480,18 +3832,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "982d1747",
-   "metadata": {},
+   "id": "d57346ae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Not bad, but the results depend strongly on the learning reate. Try different learning rates."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "616eae3e",
-   "metadata": {},
+   "id": "0219b252",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "## Solving ODEs with Deep Learning\n",
+    "## Solving differential equations  with Deep Learning\n",
     "\n",
     "The Universal Approximation Theorem states that a neural network can\n",
     "approximate any function at a single hidden layer along with one input\n",
@@ -3513,10 +3869,12 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43fb869c",
-   "metadata": {},
+   "id": "80032cfc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
-    "## Ordinary Differential Equations\n",
+    "## Ordinary Differential Equations first\n",
     "\n",
     "An ordinary differential equation (ODE) is an equation involving functions having one variable.\n",
     "\n",
@@ -3525,8 +3883,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4855aef1",
-   "metadata": {},
+   "id": "3c5546df",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"ode\"></div>\n",
@@ -3540,8 +3900,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d31c26fc",
-   "metadata": {},
+   "id": "e4f540a5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(x)$ is the function to find, and $g^{(n)}(x)$ is the $n$-th derivative of $g(x)$.\n",
     "\n",
@@ -3554,8 +3916,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08d629ec",
-   "metadata": {},
+   "id": "75ec2cfe",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "\n",
@@ -3564,8 +3928,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2cfd7bd",
-   "metadata": {},
+   "id": "a71e7eb8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto1\"></div>\n",
@@ -3580,8 +3946,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4cd106f",
-   "metadata": {},
+   "id": "9b06d2bf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $h_1(x)$ is a function that makes $g_t(x)$ satisfy a given set\n",
     "of conditions, $N(x,P)$ a neural network with weights and biases\n",
@@ -3599,8 +3967,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74da655f",
-   "metadata": {},
+   "id": "0aea2f3e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Minimization process\n",
     "\n",
@@ -3614,8 +3984,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efe0ec18",
-   "metadata": {},
+   "id": "a21c6a43",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(x, P\\right) = \\big(f\\left(x, \\, g(x), \\, g'(x), \\, g''(x), \\, \\dots \\, , \\, g^{(n)}(x)\\right)\\big)^2\n",
@@ -3624,8 +3996,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9c1643a",
-   "metadata": {},
+   "id": "ff939582",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If $N$ inputs are given as a vector $\\boldsymbol{x}$ with elements $x_i$ for $i = 1,\\dots,N$,\n",
     "the cost function becomes"
@@ -3633,8 +4007,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b900e26",
-   "metadata": {},
+   "id": "9f63085a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"cost\"></div>\n",
@@ -3648,8 +4024,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82e8e341",
-   "metadata": {},
+   "id": "2875658a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The neural net should then find the parameters $P$ that minimizes the cost function in\n",
     "([3](#cost)) for a set of $N$ training samples $x_i$."
@@ -3657,8 +4035,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b89f2f97",
-   "metadata": {},
+   "id": "8a63e4c6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Minimizing the cost function using gradient descent and automatic differentiation\n",
     "\n",
@@ -3671,8 +4051,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc38c37f",
-   "metadata": {},
+   "id": "2d5b4c88",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Exponential decay\n",
     "\n",
@@ -3681,8 +4063,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3c5f0410",
-   "metadata": {},
+   "id": "daab1d5e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solve_expdec\"></div>\n",
@@ -3696,8 +4080,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4531d4a4",
-   "metadata": {},
+   "id": "fc2cedc3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $g(0) = g_0$ for some chosen initial value $g_0$.\n",
     "\n",
@@ -3706,8 +4092,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d580caea",
-   "metadata": {},
+   "id": "da284bc1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"_auto2\"></div>\n",
@@ -3722,16 +4110,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f384ec5",
-   "metadata": {},
+   "id": "04c2531a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of ([4](#solve_expdec))."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e650af49",
-   "metadata": {},
+   "id": "62a110db",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The function to solve for\n",
     "\n",
@@ -3740,8 +4132,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68e3a73b",
-   "metadata": {},
+   "id": "7b5b722c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solveode\"></div>\n",
@@ -3755,8 +4149,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61f7dce9",
-   "metadata": {},
+   "id": "02446b0e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(0) = g_0$ with $\\gamma$ and $g_0$ being some chosen values.\n",
     "\n",
@@ -3765,8 +4161,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47e985ed",
-   "metadata": {},
+   "id": "205c8e89",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "To begin with, a trial solution $g_t(t)$ must be chosen. A general trial solution for ordinary differential equations could be"
@@ -3774,8 +4172,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5787755",
-   "metadata": {},
+   "id": "9e46aee1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x, P) = h_1(x) + h_2(x, N(x, P))\n",
@@ -3784,16 +4184,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efd0d663",
-   "metadata": {},
+   "id": "cb0d1f30",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $h_1(x)$ ensuring that $g_t(x)$ satisfies some conditions and $h_2(x,N(x, P))$ an expression involving $x$ and the output from the neural network $N(x,P)$ with $P $ being the collection of the weights and biases for each layer. For now, it is assumed that the network consists of one input layer, one hidden layer, and one output layer."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "de4cfa12",
-   "metadata": {},
+   "id": "8485bdd3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setup of Network\n",
     "\n",
@@ -3810,8 +4214,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4de8eeb1",
-   "metadata": {},
+   "id": "730e057b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"trial\"></div>\n",
@@ -3825,8 +4231,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3076a5d",
-   "metadata": {},
+   "id": "db8907ef",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Reformulating the problem\n",
     "\n",
@@ -3842,8 +4250,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00459420",
-   "metadata": {},
+   "id": "ce4a7022",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x, P) = g_0 + x \\cdot N(x, P)\n",
@@ -3852,16 +4262,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "493318e4",
-   "metadata": {},
+   "id": "b17ab00d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "has been chosen such that it already solves the condition $g(0) = g_0$. What remains, is to find $P$ such that"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b1cd6594",
-   "metadata": {},
+   "id": "f4af75e0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"nnmin\"></div>\n",
@@ -3875,16 +4289,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf2aa493",
-   "metadata": {},
+   "id": "4ea72b19",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "is fulfilled as *best as possible*."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5eda172b",
-   "metadata": {},
+   "id": "428cf327",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More technicalities\n",
     "\n",
@@ -3897,8 +4315,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2bfc8161",
-   "metadata": {},
+   "id": "1b4c9872",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P}\\Big\\{ \\big(g_t'(x, P) - ( -\\gamma g_t(x, P) \\big)^2 \\Big\\}\n",
@@ -3907,8 +4327,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9af6a125",
-   "metadata": {},
+   "id": "f12896dd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "(the notation $\\min_{P}\\{ f(x, P) \\}$ means that we desire to find $P$ that yields the minimum of $f(x, P)$)\n",
     "\n",
@@ -3917,8 +4339,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bea03f10",
-   "metadata": {},
+   "id": "70e2187e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P_{\\text{hidden} }, \\ P_{\\text{output} }}\\Big\\{ \\big(g_t'(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) - ( -\\gamma g_t(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) \\big)^2 \\Big\\}\n",
@@ -3927,16 +4351,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "352fb11e",
-   "metadata": {},
+   "id": "e0136d5f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for an input value $x$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "98d5219e",
-   "metadata": {},
+   "id": "ff915c59",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More details\n",
     "\n",
@@ -3945,8 +4373,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "83d7b299",
-   "metadata": {},
+   "id": "ca46667e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"min\"></div>\n",
@@ -3960,16 +4390,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ba53d11",
-   "metadata": {},
+   "id": "3efa1dc6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Letting $\\boldsymbol{x}$ be a vector with elements $x_i$ and $C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i  \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2$ denote the cost function, the minimization problem that our network must solve, becomes"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3953e778",
-   "metadata": {},
+   "id": "a3d800e8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\min_{P} C(\\boldsymbol{x}, P)\n",
@@ -3978,8 +4412,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "706a1978",
-   "metadata": {},
+   "id": "8fb679f5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In terms of $P_{\\text{hidden} }$ and $P_{\\text{output} }$, this could also be expressed as\n",
     "\n",
@@ -3990,8 +4426,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8ff57d1a",
-   "metadata": {},
+   "id": "08b2a19b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## A possible implementation of a neural network\n",
     "\n",
@@ -4004,8 +4442,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb487d3d",
-   "metadata": {},
+   "id": "082074c8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Technicalities\n",
     "\n",
@@ -4014,8 +4454,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d6ac6a6",
-   "metadata": {},
+   "id": "b69f9148",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4034,8 +4476,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fee86c29",
-   "metadata": {},
+   "id": "9feeefde",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities I\n",
     "\n",
@@ -4044,8 +4488,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "317dd762",
-   "metadata": {},
+   "id": "cde763a7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4065,8 +4511,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4641c716",
-   "metadata": {},
+   "id": "3c83e5dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities II\n",
     "\n",
@@ -4079,8 +4527,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a28fd5d3",
-   "metadata": {},
+   "id": "4566531c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "f(z) = \\frac{1}{1 + \\exp{(-z)}}\n",
@@ -4089,8 +4539,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2c6ce13",
-   "metadata": {},
+   "id": "e316d1e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "It is possible to use other activations functions for the hidden layer also.\n",
     "\n",
@@ -4111,8 +4563,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5bf0304c",
-   "metadata": {},
+   "id": "41ac9a1c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities III\n",
     "\n",
@@ -4121,8 +4575,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4ee906f",
-   "metadata": {},
+   "id": "b0a8a3c2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4140,8 +4596,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "454cd32f",
-   "metadata": {},
+   "id": "67447b23",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Final technicalities IV\n",
     "\n",
@@ -4150,8 +4608,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "49b52638",
-   "metadata": {},
+   "id": "12d3e1ee",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{z}_{1}^{\\text{output}} =\n",
@@ -4167,16 +4627,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75d1e0dc",
-   "metadata": {},
+   "id": "562a122c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In this case we seek a continuous range of values since we are approximating a function. This means that after computing $\\boldsymbol{z}_{1}^{\\text{output}}$ the neural network has finished its feed forward step, and $\\boldsymbol{z}_{1}^{\\text{output}}$ is the final output of the network."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "243508b9",
-   "metadata": {},
+   "id": "78789a96",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Back propagation\n",
     "\n",
@@ -4187,8 +4651,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cfaa5264",
-   "metadata": {},
+   "id": "76b734fb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i  \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2\n",
@@ -4197,8 +4663,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "188a58e4",
-   "metadata": {},
+   "id": "e2911f97",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In order to minimize the cost function, an optimization method must be chosen.\n",
     "\n",
@@ -4207,8 +4675,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f3c7251",
-   "metadata": {},
+   "id": "5e0c281c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Gradient descent\n",
     "\n",
@@ -4222,8 +4692,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b48662af",
-   "metadata": {},
+   "id": "077e3318",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\omega}_{\\text{new} } = \\boldsymbol{\\omega} - \\lambda \\nabla_{\\boldsymbol{\\omega}} C(\\boldsymbol{x}, \\boldsymbol{\\omega})\n",
@@ -4232,8 +4704,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46cc1b9b",
-   "metadata": {},
+   "id": "b6e9387d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for a number of iterations or until $ \\big|\\big| \\boldsymbol{\\omega}_{\\text{new} } - \\boldsymbol{\\omega} \\big|\\big|$ becomes smaller than some given tolerance.\n",
     "\n",
@@ -4252,8 +4726,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "018877f6",
-   "metadata": {},
+   "id": "3fa21e60",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4265,8 +4741,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "35e348bd",
-   "metadata": {},
+   "id": "e05e6028",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The code for solving the ODE"
    ]
@@ -4274,8 +4752,11 @@
   {
    "cell_type": "code",
    "execution_count": 41,
-   "id": "dafe8d25",
-   "metadata": {},
+   "id": "eb77d1cf",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -4426,8 +4907,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65e4f300",
-   "metadata": {},
+   "id": "bbd6562b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The network with one input layer, specified number of hidden layers, and one output layer\n",
     "\n",
@@ -4439,8 +4922,11 @@
   {
    "cell_type": "code",
    "execution_count": 42,
-   "id": "5ef5f766",
-   "metadata": {},
+   "id": "24ba1afd",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -4455,8 +4941,8 @@
     "# but with number of hidden layers specified by the user.\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consists of\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
     "                                        # parameters to all the hidden\n",
     "                                        # layers AND the output layer.\n",
     "\n",
@@ -4605,8 +5091,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7ad45ef",
-   "metadata": {},
+   "id": "3974040a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Population growth\n",
     "\n",
@@ -4616,8 +5104,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d1376bc",
-   "metadata": {},
+   "id": "a9d203ea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"log\"></div>\n",
@@ -4631,8 +5121,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f039785",
-   "metadata": {},
+   "id": "ede35f92",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(t)$ is the population density at time $t$, $\\alpha > 0$ the growth rate and $A > 0$ is the maximum population number in the environment.\n",
     "Also, at $t = 0$ the population has the size $g(0) = g_0$, where $g_0$ is some chosen constant.\n",
@@ -4645,8 +5137,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8dfcfb5e",
-   "metadata": {},
+   "id": "a9720dfc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the problem\n",
     "\n",
@@ -4656,8 +5150,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cb5e674",
-   "metadata": {},
+   "id": "5ef6b555",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"solveode_population\"></div>\n",
@@ -4671,8 +5167,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "56581c9f",
-   "metadata": {},
+   "id": "bd5c646e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $g(0) = g_0$.\n",
     "\n",
@@ -4681,8 +5179,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ebf7032a",
-   "metadata": {},
+   "id": "cdc5561b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "\n",
@@ -4706,8 +5206,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a943c5c6",
-   "metadata": {},
+   "id": "cebde164",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The program using Autograd\n",
     "\n",
@@ -4717,8 +5219,11 @@
   {
    "cell_type": "code",
    "execution_count": 43,
-   "id": "a3620769",
-   "metadata": {},
+   "id": "c71a9592",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -4737,9 +5242,12 @@
     "    g0 = 1.2\n",
     "    return alpha, A, g0\n",
     "\n",
-    "def deep_neural_network(P, x):\n",
+    "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(P) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -4756,7 +5264,7 @@
     "\n",
     "    for l in range(N_hidden):\n",
     "        # From the list of parameters P; find the correct weigths and bias for this layer\n",
-    "        w_hidden = P[l]\n",
+    "        w_hidden = deep_params[l]\n",
     "\n",
     "        # Add a row of ones to include bias\n",
     "        x_prev = np.concatenate((np.ones((1,num_values)), x_prev ), axis = 0)\n",
@@ -4770,7 +5278,7 @@
     "    ## Output layer:\n",
     "\n",
     "    # Get the weights and bias for this layer\n",
-    "    w_output = P[-1]\n",
+    "    w_output = deep_params[-1]\n",
     "\n",
     "    # Include bias:\n",
     "    x_prev = np.concatenate((np.ones((1,num_values)), x_prev), axis = 0)\n",
@@ -4781,6 +5289,8 @@
     "    return x_output\n",
     "\n",
     "\n",
+    "\n",
+    "\n",
     "def cost_function_deep(P, x):\n",
     "\n",
     "    # Evaluate the trial function with the current parameters P\n",
@@ -4888,8 +5398,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a21afc2",
-   "metadata": {},
+   "id": "bd70d6cc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Using forward Euler to solve the ODE\n",
     "\n",
@@ -4906,8 +5418,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a8ad46c",
-   "metadata": {},
+   "id": "ee3bdd02",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4919,8 +5433,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b83336b",
-   "metadata": {},
+   "id": "d81b6054",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "along with the condition that $g(0) = g_0$.\n",
     "\n",
@@ -4931,8 +5447,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea68eaac",
-   "metadata": {},
+   "id": "0d7a2272",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -4945,16 +5463,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c8a2f92c",
-   "metadata": {},
+   "id": "ca29846f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Now, if $g_i = g(t_i)$ then"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "4f1a2187",
-   "metadata": {},
+   "id": "1a51d849",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"odenum\"></div>\n",
@@ -4973,8 +5495,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb87fc93",
-   "metadata": {},
+   "id": "700a9bac",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for $i \\geq 1$ and $g_0 = g(t_0) = g(0) = g_0$.\n",
     "\n",
@@ -4985,8 +5509,11 @@
   {
    "cell_type": "code",
    "execution_count": 44,
-   "id": "f8c976e7",
-   "metadata": {},
+   "id": "482cf93c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# Assume that all function definitions from the example program using Autograd\n",
@@ -5058,8 +5585,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23756e15",
-   "metadata": {},
+   "id": "4ed3cefd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Solving the one dimensional Poisson equation\n",
     "\n",
@@ -5068,8 +5597,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a68185f",
-   "metadata": {},
+   "id": "d0bdfcdb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"poisson\"></div>\n",
@@ -5083,8 +5614,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc784286",
-   "metadata": {},
+   "id": "656240e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $f(x)$ is a given function for $x \\in (0,1)$.\n",
     "\n",
@@ -5093,8 +5626,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e0f7d593",
-   "metadata": {},
+   "id": "fb310d7c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -5106,8 +5641,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4cacfaeb",
-   "metadata": {},
+   "id": "e6b102dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This equation can be solved numerically using programs where e.g Autograd and TensorFlow are used.\n",
     "The results from the networks can then be compared to the analytical solution.\n",
@@ -5116,8 +5653,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69ba705a",
-   "metadata": {},
+   "id": "797d4bb8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The specific equation to solve for\n",
     "\n",
@@ -5126,8 +5665,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "995cfbc9",
-   "metadata": {},
+   "id": "da2e90b8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "-g''(x) = f(x),\\qquad x \\in (0,1)\n",
@@ -5136,16 +5677,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "769f9670",
-   "metadata": {},
+   "id": "318f8f3a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $f(x)$ is a given function, along with the chosen conditions"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "855cddbb",
-   "metadata": {},
+   "id": "c5e8ac9e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"cond\"></div>\n",
@@ -5159,8 +5704,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7006cb54",
-   "metadata": {},
+   "id": "220ceeb4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In this example, we consider the case when $f(x) = (3x + x^2)\\exp(x)$.\n",
     "\n",
@@ -5169,8 +5716,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5216ca22",
-   "metadata": {},
+   "id": "ec8b38dc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g_t(x) = x \\cdot (1-x) \\cdot N(P,x)\n",
@@ -5179,16 +5728,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b77670be",
-   "metadata": {},
+   "id": "0ed927a9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The analytical solution for this problem is"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "bf2bed23",
-   "metadata": {},
+   "id": "3a51ddcc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "g(x) = x(1 - x)\\exp(x)\n",
@@ -5197,8 +5750,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a22ccb78",
-   "metadata": {},
+   "id": "d5392b8d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Solving the equation using Autograd"
    ]
@@ -5206,8 +5761,11 @@
   {
    "cell_type": "code",
    "execution_count": 45,
-   "id": "7b3b5f5a",
-   "metadata": {},
+   "id": "95059f71",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -5220,7 +5778,10 @@
     "\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -5261,6 +5822,7 @@
     "\n",
     "    return x_output\n",
     "\n",
+    "\n",
     "def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
     "    # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
     "\n",
@@ -5364,8 +5926,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6668b7ef",
-   "metadata": {},
+   "id": "7c568bf3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Comparing with a numerical scheme\n",
     "\n",
@@ -5384,8 +5948,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec1adda2",
-   "metadata": {},
+   "id": "eab0bb68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"approx\"></div>\n",
@@ -5399,16 +5965,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33486af4",
-   "metadata": {},
+   "id": "c0ada0c0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If $x_i = i \\Delta x = x_{i-1} + \\Delta x$ and $g_i = g(x_i)$ for $i = 1,\\dots N_x - 2$ with $N_x$ being the number of values for $x$, ([15](#approx)) becomes"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "42c3ef84",
-   "metadata": {},
+   "id": "b483eace",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -5420,16 +5990,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f454dbea",
-   "metadata": {},
+   "id": "30d45122",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Since we know from our problem that"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "7411a707",
-   "metadata": {},
+   "id": "52c68e05",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -5441,8 +6015,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c47c3822",
-   "metadata": {},
+   "id": "1657934d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "along with the conditions $g(0) = g(1) = 0$,\n",
     "the following scheme can be used to find an approximate solution for $g(x)$ numerically:"
@@ -5450,8 +6026,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1cca824c",
-   "metadata": {},
+   "id": "9fc46a1b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"odesys\"></div>\n",
@@ -5468,8 +6046,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82ecd5a1",
-   "metadata": {},
+   "id": "cd79f75c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for $i = 1, \\dots, N_x - 2$ where $g_0 = g_{N_x - 1} = 0$ and $f(x_i) = (3x_i + x_i^2)\\exp(x_i)$, which is given for our specific problem.\n",
     "\n",
@@ -5478,8 +6058,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39f5fe07",
-   "metadata": {},
+   "id": "501ac880",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{aligned}\n",
@@ -5513,16 +6095,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ac54c35",
-   "metadata": {},
+   "id": "8551615b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which makes it possible to solve for the vector $\\boldsymbol{g}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "79ad3ebc",
-   "metadata": {},
+   "id": "dbd6d2a1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the code\n",
     "\n",
@@ -5532,8 +6118,11 @@
   {
    "cell_type": "code",
    "execution_count": 46,
-   "id": "be03bf2d",
-   "metadata": {},
+   "id": "c71a3063",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -5546,7 +6135,10 @@
     "\n",
     "def deep_neural_network(deep_params, x):\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    # deep_params is a list, len() should be used\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consists of\n",
+    "                                        # parameters to all the hidden\n",
+    "                                        # layers AND the output layer.\n",
     "\n",
     "    # Assumes input x being an one-dimensional array\n",
     "    num_values = np.size(x)\n",
@@ -5587,6 +6179,7 @@
     "\n",
     "    return x_output\n",
     "\n",
+    "\n",
     "def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
     "    # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
     "\n",
@@ -5730,8 +6323,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "faa0daa4",
-   "metadata": {},
+   "id": "da58cdec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Partial Differential Equations\n",
     "\n",
@@ -5745,8 +6340,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb7b7ff6",
-   "metadata": {},
+   "id": "df991968",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"PDE\"></div>\n",
@@ -5760,16 +6357,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71da1640",
-   "metadata": {},
+   "id": "59ef3099",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $f$ is an expression involving all kinds of possible mixed derivatives of $g(x_1,\\dots,x_N)$ up to an order $n$. In order for the solution to be unique, some additional conditions must also be given."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c77e6225",
-   "metadata": {},
+   "id": "a580ae0f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Type of problem\n",
     "\n",
@@ -5781,8 +6382,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98f82ea2",
-   "metadata": {},
+   "id": "a56f3fe1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -5793,8 +6396,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc33501c",
-   "metadata": {},
+   "id": "69586714",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $h_1(x_1,\\dots,x_N)$ is a function that ensures $g_t(x_1,\\dots,x_N)$ satisfies some given conditions.\n",
     "The neural network $N(x_1,\\dots,x_N,P)$ has weights and biases described by $P$ and $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$ is an expression using the output from the neural network in some way.\n",
@@ -5804,8 +6409,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "818e8900",
-   "metadata": {},
+   "id": "d8374dce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Network requirements\n",
     "\n",
@@ -5822,8 +6429,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "526d5428",
-   "metadata": {},
+   "id": "f3fe961e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(x_1, \\dots, x_N, P\\right) = \\left(  f\\left(x_1, \\, \\dots \\, , x_N, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1}, \\dots , \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_N}, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(x_1,\\dots,x_N) }{\\partial x_N^n} \\right) \\right)^2\n",
@@ -5832,8 +6441,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "279b9296",
-   "metadata": {},
+   "id": "4e453aa1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More details\n",
     "\n",
@@ -5842,8 +6453,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcb8ce40",
-   "metadata": {},
+   "id": "e1ebf5bd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(\\boldsymbol{x}, P\\right) = f\\left( \\left( \\boldsymbol{x}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}) }{\\partial x_N^n} \\right) \\right)^2\n",
@@ -5852,16 +6465,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6549ea7b",
-   "metadata": {},
+   "id": "b8c35553",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If we also have $M$ different sets of values for $x_1, \\dots, x_N$, that is $\\boldsymbol{x}_i = \\big(x_1^{(i)}, \\dots, x_N^{(i)}\\big)$ for $i = 1,\\dots,M$ being the rows in matrix $X$, the cost function can be generalized into"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "0956062e",
-   "metadata": {},
+   "id": "22a123d5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C\\left(X, P \\right) = \\sum_{i=1}^M f\\left( \\left( \\boldsymbol{x}_i, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}_i) }{\\partial x_N^n} \\right) \\right)^2.\n",
@@ -5870,8 +6487,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8fca0166",
-   "metadata": {},
+   "id": "b15eedf5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: The diffusion equation\n",
     "\n",
@@ -5880,8 +6499,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58ad6f25",
-   "metadata": {},
+   "id": "1a92cc8c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial g(x,t)}{\\partial t} = \\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
@@ -5890,16 +6511,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6e5728e",
-   "metadata": {},
+   "id": "e4862313",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where a possible choice of conditions are"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6921faa1",
-   "metadata": {},
+   "id": "5c186d68",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -5912,16 +6537,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80e632ef",
-   "metadata": {},
+   "id": "57d4f000",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $u(x)$ being some given function."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a2711421",
-   "metadata": {},
+   "id": "7c2cdc6b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Defining the problem\n",
     "\n",
@@ -5930,8 +6559,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "981da4af",
-   "metadata": {},
+   "id": "bde064ea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"diffonedim\"></div>\n",
@@ -5945,16 +6576,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1b8c16d",
-   "metadata": {},
+   "id": "7a558c97",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b8ed6509",
-   "metadata": {},
+   "id": "534a4844",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -5967,8 +6602,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "200050ac",
-   "metadata": {},
+   "id": "a07e0730",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $u(x) = \\sin(\\pi x)$.\n",
     "\n",
@@ -5979,8 +6616,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5dca99d2",
-   "metadata": {},
+   "id": "74b72286",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the network using Autograd\n",
     "\n",
@@ -5996,8 +6635,11 @@
   {
    "cell_type": "code",
    "execution_count": 47,
-   "id": "85f4b843",
-   "metadata": {},
+   "id": "4a0c57e9",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "def sigmoid(z):\n",
@@ -6011,7 +6653,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -6048,8 +6690,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9dd68ff8",
-   "metadata": {},
+   "id": "350b1d3d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the network using Autograd; The trial solution\n",
     "\n",
@@ -6076,8 +6720,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65f68c5a",
-   "metadata": {},
+   "id": "9fd438b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Why the jacobian?\n",
     "\n",
@@ -6103,8 +6749,11 @@
   {
    "cell_type": "code",
    "execution_count": 48,
-   "id": "91612f4f",
-   "metadata": {},
+   "id": "d1c81690",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# Set up the trial function:\n",
@@ -6147,8 +6796,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff9df4ba",
-   "metadata": {},
+   "id": "ca22d9ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Setting up the network using Autograd; The full program\n",
     "\n",
@@ -6171,8 +6822,11 @@
   {
    "cell_type": "code",
    "execution_count": 49,
-   "id": "e6451b9e",
-   "metadata": {},
+   "id": "5a9146bc",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -6195,7 +6849,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -6338,7 +6992,7 @@
     "    T,X = np.meshgrid(t,x)\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))\n",
     "    s = ax.plot_surface(T,X,g_dnn_ag,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -6346,14 +7000,14 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Analytical solution')\n",
     "    s = ax.plot_surface(T,X,G_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
     "    ax.set_ylabel('Position $x$');\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Difference')\n",
     "    s = ax.plot_surface(T,X,diff_ag,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -6402,8 +7056,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7f867cf2",
-   "metadata": {},
+   "id": "e59d2116",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example: Solving the wave equation with Neural Networks\n",
     "\n",
@@ -6412,8 +7068,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ded83be1",
-   "metadata": {},
+   "id": "e2ffdbaf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial^2 g(x,t)}{\\partial t^2} = c^2\\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
@@ -6422,8 +7080,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0aba0c9",
-   "metadata": {},
+   "id": "37b2cc03",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with $c$ being the specified wave speed.\n",
     "\n",
@@ -6432,8 +7092,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28a48fe7",
-   "metadata": {},
+   "id": "524df5d3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*}\n",
@@ -6447,16 +7109,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61ded78d",
-   "metadata": {},
+   "id": "d175b25f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $\\frac{\\partial g(x,t)}{\\partial t} \\Big |_{t = 0}$ means the derivative of $g(x,t)$ with respect to $t$ is evaluated at $t = 0$, and $u(x)$ and $v(x)$ being given functions."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "990695ea",
-   "metadata": {},
+   "id": "11b3289e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The problem to solve for\n",
     "\n",
@@ -6465,8 +7131,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58841089",
-   "metadata": {},
+   "id": "e469d65e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"wave\"></div>\n",
@@ -6480,8 +7148,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "303eb900",
-   "metadata": {},
+   "id": "5f773fa8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $c$ is the given wave speed.\n",
     "The chosen conditions for this equation are"
@@ -6489,8 +7159,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce5c5167",
-   "metadata": {},
+   "id": "2952f7b4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- Equation labels as ordinary links -->\n",
     "<div id=\"condwave\"></div>\n",
@@ -6507,16 +7179,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "609a7556",
-   "metadata": {},
+   "id": "99057b48",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In this example, let $c = 1$ and $u(x) = \\sin(\\pi x)$ and $v(x) = -\\pi\\sin(\\pi x)$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5edb8797",
-   "metadata": {},
+   "id": "7debdfea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The trial solution\n",
     "Setting up the network is done in similar matter as for the example of solving the diffusion equation.\n",
@@ -6539,8 +7215,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6be7518",
-   "metadata": {},
+   "id": "2d5d5c44",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The analytical solution\n",
     "\n",
@@ -6553,8 +7231,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "368bb540",
-   "metadata": {},
+   "id": "f97806ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Solving the wave equation - the full program using Autograd"
    ]
@@ -6562,8 +7242,11 @@
   {
    "cell_type": "code",
    "execution_count": 50,
-   "id": "65085f11",
-   "metadata": {},
+   "id": "9337b7c7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
@@ -6620,7 +7303,7 @@
     "    num_points = np.size(x,1)\n",
     "\n",
     "    # N_hidden is the number of hidden layers\n",
-    "    N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
+    "    N_hidden = len(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
     "\n",
     "    # Assume that the input layer does nothing to the input x\n",
     "    x_input = x\n",
@@ -6725,7 +7408,7 @@
     "    T,X = np.meshgrid(t,x)\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))\n",
     "    s = ax.plot_surface(T,X,res,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -6733,7 +7416,7 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Analytical solution')\n",
     "    s = ax.plot_surface(T,X,res_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -6741,7 +7424,7 @@
     "\n",
     "\n",
     "    fig = plt.figure(figsize=(10,10))\n",
-    "    ax = fig.gca(projection='3d')\n",
+    "    ax = fig.add_suplot(projection='3d')\n",
     "    ax.set_title('Difference')\n",
     "    s = ax.plot_surface(T,X,diff,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
     "    ax.set_xlabel('Time $t$')\n",
@@ -6790,8 +7473,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "41011c90",
-   "metadata": {},
+   "id": "6071d006",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resources on differential equations and deep learning\n",
     "\n",
@@ -6805,25 +7490,7 @@
    ]
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.9.15"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 5
 }
diff --git a/doc/pub/week43/html/week43-bs.html b/doc/pub/week43/html/week43-bs.html
index be20cd0b1..75f394fcb 100644
--- a/doc/pub/week43/html/week43-bs.html
+++ b/doc/pub/week43/html/week43-bs.html
@@ -488,8 +488,8 @@ MathJax.Hub.Config({
 <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
 <ul>
   <li> Building our own Feed-forward Neural Network with intro to Tensorflow</li>
-  <li> Solving differential equations with Neural Networks
-<!-- * <a href="https://youtu.be/" target="_self">Video of lecture to be posted asap</a> -->
+  <li> Solving differential equations with Neural Networks</li>
+  <li> "Video of lecture at <a href="https://youtu.be/vkBNTn-MLqs" target="_self"><tt>https://youtu.be/vkBNTn-MLqs</tt></a>
 <!-- * <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesOct21.pdf" target="_self">Whiteboard notes</a> --></li>
 </ul>
 </div>
diff --git a/doc/pub/week43/html/week43-reveal.html b/doc/pub/week43/html/week43-reveal.html
index 61513cb07..aae851132 100644
--- a/doc/pub/week43/html/week43-reveal.html
+++ b/doc/pub/week43/html/week43-reveal.html
@@ -204,8 +204,9 @@ MathJax.Hub.Config({
 
 <p><li> Building our own Feed-forward Neural Network with intro to Tensorflow</li>
 
-<p><li> Solving differential equations with Neural Networks
-<!-- * <a href="https://youtu.be/" target="_blank">Video of lecture to be posted asap</a> -->
+<p><li> Solving differential equations with Neural Networks</li>
+
+<p><li> "Video of lecture at <a href="https://youtu.be/vkBNTn-MLqs" target="_blank"><tt>https://youtu.be/vkBNTn-MLqs</tt></a>
 <!-- * <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesOct21.pdf" target="_blank">Whiteboard notes</a> --></li>
 </ul>
 </div>
diff --git a/doc/pub/week43/html/week43-solarized.html b/doc/pub/week43/html/week43-solarized.html
index 959c48e25..c74a76ad7 100644
--- a/doc/pub/week43/html/week43-solarized.html
+++ b/doc/pub/week43/html/week43-solarized.html
@@ -384,8 +384,8 @@ MathJax.Hub.Config({
 <p>
 <ul>
   <li> Building our own Feed-forward Neural Network with intro to Tensorflow</li>
-  <li> Solving differential equations with Neural Networks
-<!-- * <a href="https://youtu.be/" target="_blank">Video of lecture to be posted asap</a> -->
+  <li> Solving differential equations with Neural Networks</li>
+  <li> "Video of lecture at <a href="https://youtu.be/vkBNTn-MLqs" target="_blank"><tt>https://youtu.be/vkBNTn-MLqs</tt></a>
 <!-- * <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesOct21.pdf" target="_blank">Whiteboard notes</a> --></li>
 </ul>
 </div>
diff --git a/doc/pub/week43/html/week43.html b/doc/pub/week43/html/week43.html
index bc83851c2..be0d57012 100644
--- a/doc/pub/week43/html/week43.html
+++ b/doc/pub/week43/html/week43.html
@@ -461,8 +461,8 @@ MathJax.Hub.Config({
 <p>
 <ul>
   <li> Building our own Feed-forward Neural Network with intro to Tensorflow</li>
-  <li> Solving differential equations with Neural Networks
-<!-- * <a href="https://youtu.be/" target="_blank">Video of lecture to be posted asap</a> -->
+  <li> Solving differential equations with Neural Networks</li>
+  <li> "Video of lecture at <a href="https://youtu.be/vkBNTn-MLqs" target="_blank"><tt>https://youtu.be/vkBNTn-MLqs</tt></a>
 <!-- * <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesOct21.pdf" target="_blank">Whiteboard notes</a> --></li>
 </ul>
 </div>
diff --git a/doc/pub/week43/ipynb/ipynb-week43-src.tar.gz b/doc/pub/week43/ipynb/ipynb-week43-src.tar.gz
index 7860fbb0f20f854b1bc83a4d7e6e589110ceabb8..1842b323b2c1383152d46582ed330984566227ff 100644
GIT binary patch
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diff --git a/doc/pub/week43/ipynb/week43.ipynb b/doc/pub/week43/ipynb/week43.ipynb
index 202263be5..3a2029a79 100644
--- a/doc/pub/week43/ipynb/week43.ipynb
+++ b/doc/pub/week43/ipynb/week43.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "677a195d",
+   "id": "6528e21e",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e943e8f0",
+   "id": "3ee1b36e",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22cdced0",
+   "id": "ce7aadd0",
    "metadata": {
     "editable": true
    },
@@ -39,13 +39,14 @@
     "  * Building our own Feed-forward Neural Network with intro to Tensorflow\n",
     "\n",
     "  * Solving differential equations with Neural Networks\n",
-    "<!-- * [Video of lecture to be posted asap](https://youtu.be/) -->\n",
+    "\n",
+    "  * \"Video of lecture at <https://youtu.be/vkBNTn-MLqs>\n",
     "<!-- * [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesOct21.pdf) -->"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a57ef6df",
+   "id": "3b148f15",
    "metadata": {
     "editable": true
    },
@@ -62,7 +63,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c4a134ee",
+   "id": "de5149e1",
    "metadata": {
     "editable": true
    },
@@ -78,7 +79,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd73045e",
+   "id": "4dfacc15",
    "metadata": {
     "editable": true
    },
@@ -89,7 +90,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "372f4aa4",
+   "id": "07178d65",
    "metadata": {
     "editable": true
    },
@@ -103,7 +104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05efbc6f",
+   "id": "b4b2da11",
    "metadata": {
     "editable": true
    },
@@ -116,7 +117,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d04b0948",
+   "id": "c264977f",
    "metadata": {
     "editable": true
    },
@@ -133,7 +134,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b9d41f5c",
+   "id": "9e588fe4",
    "metadata": {
     "editable": true
    },
@@ -143,7 +144,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68606991",
+   "id": "fd47ec8c",
    "metadata": {
     "editable": true
    },
@@ -170,7 +171,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a564a394",
+   "id": "97fdb112",
    "metadata": {
     "editable": true
    },
@@ -193,7 +194,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43ab4381",
+   "id": "98139ea4",
    "metadata": {
     "editable": true
    },
@@ -205,7 +206,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f578cee4",
+   "id": "6eab3a16",
    "metadata": {
     "editable": true
    },
@@ -217,7 +218,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbc05943",
+   "id": "3bd14855",
    "metadata": {
     "editable": true
    },
@@ -227,7 +228,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6ad3c28f",
+   "id": "e1ec5ba9",
    "metadata": {
     "editable": true
    },
@@ -239,7 +240,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "135513b5",
+   "id": "4a2edd2d",
    "metadata": {
     "editable": true
    },
@@ -253,7 +254,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f643ecdf",
+   "id": "8e4eb5d7",
    "metadata": {
     "editable": true
    },
@@ -265,7 +266,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "077ef1c2",
+   "id": "1757a0c5",
    "metadata": {
     "editable": true
    },
@@ -277,7 +278,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50cf7472",
+   "id": "5c1d75f4",
    "metadata": {
     "editable": true
    },
@@ -287,7 +288,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a10f406c",
+   "id": "ddb26b01",
    "metadata": {
     "editable": true
    },
@@ -299,7 +300,7 @@
   },
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@@ -311,7 +312,7 @@
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@@ -321,7 +322,7 @@
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@@ -333,7 +334,7 @@
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@@ -345,7 +346,7 @@
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@@ -368,7 +369,7 @@
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@@ -380,7 +381,7 @@
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@@ -392,7 +393,7 @@
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@@ -414,7 +415,7 @@
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@@ -545,7 +546,7 @@
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@@ -555,7 +556,7 @@
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@@ -567,7 +568,7 @@
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@@ -590,7 +591,7 @@
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@@ -603,7 +604,7 @@
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@@ -628,7 +629,7 @@
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@@ -641,7 +642,7 @@
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@@ -653,7 +654,7 @@
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@@ -665,7 +666,7 @@
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@@ -675,7 +676,7 @@
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@@ -687,7 +688,7 @@
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@@ -699,7 +700,7 @@
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@@ -711,7 +712,7 @@
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@@ -723,7 +724,7 @@
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@@ -733,7 +734,7 @@
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@@ -745,7 +746,7 @@
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@@ -755,7 +756,7 @@
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@@ -767,7 +768,7 @@
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@@ -780,7 +781,7 @@
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@@ -792,7 +793,7 @@
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@@ -802,7 +803,7 @@
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@@ -814,7 +815,7 @@
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@@ -825,7 +826,7 @@
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@@ -837,7 +838,7 @@
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@@ -847,7 +848,7 @@
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@@ -859,7 +860,7 @@
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@@ -869,7 +870,7 @@
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@@ -880,7 +881,7 @@
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@@ -893,7 +894,7 @@
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@@ -903,7 +904,7 @@
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@@ -915,7 +916,7 @@
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@@ -925,7 +926,7 @@
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@@ -937,7 +938,7 @@
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@@ -947,7 +948,7 @@
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@@ -971,7 +972,7 @@
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@@ -1021,7 +1022,7 @@
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@@ -1076,7 +1077,7 @@
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@@ -1097,7 +1098,7 @@
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@@ -1135,7 +1136,7 @@
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@@ -1179,7 +1180,7 @@
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@@ -1219,7 +1220,7 @@
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@@ -1240,7 +1241,7 @@
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@@ -1266,7 +1267,7 @@
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@@ -1294,7 +1295,7 @@
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@@ -1331,7 +1332,7 @@
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@@ -1377,7 +1378,7 @@
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@@ -1408,7 +1409,7 @@
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@@ -1446,7 +1447,7 @@
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@@ -1480,7 +1481,7 @@
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@@ -1521,7 +1522,7 @@
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@@ -1600,7 +1601,7 @@
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@@ -1621,7 +1622,7 @@
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@@ -1635,7 +1636,7 @@
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@@ -1745,7 +1746,7 @@
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@@ -1764,7 +1765,7 @@
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@@ -1791,7 +1792,7 @@
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@@ -1805,7 +1806,7 @@
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@@ -1836,7 +1837,7 @@
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@@ -1847,7 +1848,7 @@
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@@ -1891,7 +1892,7 @@
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@@ -1914,7 +1915,7 @@
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@@ -1941,7 +1942,7 @@
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@@ -1952,7 +1953,7 @@
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@@ -1997,7 +1998,7 @@
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@@ -2015,7 +2016,7 @@
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@@ -2050,7 +2051,7 @@
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@@ -2062,7 +2063,7 @@
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@@ -2074,7 +2075,7 @@
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@@ -2087,7 +2088,7 @@
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@@ -2098,7 +2099,7 @@
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@@ -2111,7 +2112,7 @@
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@@ -2126,7 +2127,7 @@
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@@ -2138,7 +2139,7 @@
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@@ -2150,7 +2151,7 @@
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@@ -2163,7 +2164,7 @@
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@@ -2218,7 +2219,7 @@
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@@ -2247,7 +2248,7 @@
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@@ -2277,7 +2278,7 @@
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@@ -2304,7 +2305,7 @@
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@@ -2346,7 +2347,7 @@
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@@ -2357,7 +2358,7 @@
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@@ -2534,7 +2535,7 @@
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@@ -2553,7 +2554,7 @@
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@@ -2575,7 +2576,7 @@
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@@ -2716,7 +2717,7 @@
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@@ -2732,7 +2733,7 @@
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@@ -2745,7 +2746,7 @@
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@@ -2757,7 +2758,7 @@
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@@ -2779,7 +2780,7 @@
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@@ -2795,7 +2796,7 @@
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@@ -2833,7 +2834,7 @@
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@@ -2846,7 +2847,7 @@
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@@ -2867,7 +2868,7 @@
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@@ -2883,7 +2884,7 @@
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@@ -2941,7 +2942,7 @@
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@@ -2956,7 +2957,7 @@
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@@ -2977,7 +2978,7 @@
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@@ -3001,7 +3002,7 @@
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@@ -3473,7 +3474,7 @@
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@@ -3485,7 +3486,7 @@
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@@ -3529,7 +3530,7 @@
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@@ -3545,7 +3546,7 @@
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@@ -3560,7 +3561,7 @@
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@@ -3571,7 +3572,7 @@
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@@ -3586,7 +3587,7 @@
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@@ -3602,7 +3603,7 @@
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@@ -3616,7 +3617,7 @@
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@@ -3631,7 +3632,7 @@
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@@ -3657,7 +3658,7 @@
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@@ -3672,7 +3673,7 @@
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@@ -3683,7 +3684,7 @@
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@@ -3698,7 +3699,7 @@
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@@ -3709,7 +3710,7 @@
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@@ -3729,7 +3730,7 @@
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@@ -3744,7 +3745,7 @@
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@@ -3759,7 +3760,7 @@
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@@ -3796,7 +3797,7 @@
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@@ -3809,7 +3810,7 @@
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@@ -3832,7 +3833,7 @@
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@@ -3842,7 +3843,7 @@
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@@ -3869,7 +3870,7 @@
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@@ -3883,7 +3884,7 @@
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@@ -3900,7 +3901,7 @@
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@@ -3916,7 +3917,7 @@
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@@ -3928,7 +3929,7 @@
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@@ -3946,7 +3947,7 @@
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@@ -3967,7 +3968,7 @@
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@@ -3984,7 +3985,7 @@
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@@ -3996,7 +3997,7 @@
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@@ -4007,7 +4008,7 @@
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@@ -4024,7 +4025,7 @@
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@@ -4035,7 +4036,7 @@
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@@ -4051,7 +4052,7 @@
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@@ -4063,7 +4064,7 @@
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@@ -4080,7 +4081,7 @@
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@@ -4092,7 +4093,7 @@
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@@ -4110,7 +4111,7 @@
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@@ -4120,7 +4121,7 @@
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@@ -4132,7 +4133,7 @@
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@@ -4149,7 +4150,7 @@
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@@ -4161,7 +4162,7 @@
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@@ -4172,7 +4173,7 @@
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@@ -4184,7 +4185,7 @@
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@@ -4194,7 +4195,7 @@
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@@ -4214,7 +4215,7 @@
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@@ -4231,7 +4232,7 @@
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@@ -4250,7 +4251,7 @@
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@@ -4262,7 +4263,7 @@
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@@ -4272,7 +4273,7 @@
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@@ -4289,7 +4290,7 @@
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@@ -4299,7 +4300,7 @@
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@@ -4315,7 +4316,7 @@
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@@ -4327,7 +4328,7 @@
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@@ -4339,7 +4340,7 @@
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@@ -4351,7 +4352,7 @@
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@@ -4361,7 +4362,7 @@
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@@ -4373,7 +4374,7 @@
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@@ -4390,7 +4391,7 @@
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@@ -4400,7 +4401,7 @@
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@@ -4412,7 +4413,7 @@
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@@ -4426,7 +4427,7 @@
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@@ -4442,7 +4443,7 @@
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@@ -4454,7 +4455,7 @@
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@@ -4476,7 +4477,7 @@
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@@ -4488,7 +4489,7 @@
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@@ -4511,7 +4512,7 @@
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@@ -4527,7 +4528,7 @@
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@@ -4539,7 +4540,7 @@
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@@ -4563,7 +4564,7 @@
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@@ -4575,7 +4576,7 @@
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@@ -4596,7 +4597,7 @@
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@@ -4608,7 +4609,7 @@
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@@ -4627,7 +4628,7 @@
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@@ -4637,7 +4638,7 @@
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@@ -4651,7 +4652,7 @@
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@@ -4663,7 +4664,7 @@
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@@ -4675,7 +4676,7 @@
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@@ -4692,7 +4693,7 @@
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@@ -4704,7 +4705,7 @@
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@@ -4726,7 +4727,7 @@
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@@ -4741,7 +4742,7 @@
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@@ -4752,7 +4753,7 @@
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@@ -4907,7 +4908,7 @@
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    },
@@ -4922,7 +4923,7 @@
   {
    "cell_type": "code",
    "execution_count": 42,
-   "id": "24ba1afd",
+   "id": "2481727a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5091,7 +5092,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3974040a",
+   "id": "94e67eb6",
    "metadata": {
     "editable": true
    },
@@ -5104,7 +5105,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9d203ea",
+   "id": "3c847d14",
    "metadata": {
     "editable": true
    },
@@ -5121,7 +5122,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ede35f92",
+   "id": "88c997db",
    "metadata": {
     "editable": true
    },
@@ -5137,7 +5138,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a9720dfc",
+   "id": "3ee360d6",
    "metadata": {
     "editable": true
    },
@@ -5150,7 +5151,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ef6b555",
+   "id": "915df9b1",
    "metadata": {
     "editable": true
    },
@@ -5167,7 +5168,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bd5c646e",
+   "id": "3cce06b5",
    "metadata": {
     "editable": true
    },
@@ -5179,7 +5180,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cdc5561b",
+   "id": "164a26c3",
    "metadata": {
     "editable": true
    },
@@ -5206,7 +5207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cebde164",
+   "id": "a588ddab",
    "metadata": {
     "editable": true
    },
@@ -5219,7 +5220,7 @@
   {
    "cell_type": "code",
    "execution_count": 43,
-   "id": "c71a9592",
+   "id": "76252b3a",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5398,7 +5399,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bd70d6cc",
+   "id": "2e9f770a",
    "metadata": {
     "editable": true
    },
@@ -5418,7 +5419,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee3bdd02",
+   "id": "6613bf81",
    "metadata": {
     "editable": true
    },
@@ -5433,7 +5434,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d81b6054",
+   "id": "4f2611c5",
    "metadata": {
     "editable": true
    },
@@ -5447,7 +5448,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0d7a2272",
+   "id": "fbbfb78c",
    "metadata": {
     "editable": true
    },
@@ -5463,7 +5464,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca29846f",
+   "id": "fede632e",
    "metadata": {
     "editable": true
    },
@@ -5473,7 +5474,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a51d849",
+   "id": "63169a3e",
    "metadata": {
     "editable": true
    },
@@ -5495,7 +5496,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "700a9bac",
+   "id": "1638bb66",
    "metadata": {
     "editable": true
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@@ -5509,7 +5510,7 @@
   {
    "cell_type": "code",
    "execution_count": 44,
-   "id": "482cf93c",
+   "id": "805cdc28",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5585,7 +5586,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4ed3cefd",
+   "id": "b958d38c",
    "metadata": {
     "editable": true
    },
@@ -5597,7 +5598,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0bdfcdb",
+   "id": "1208716b",
    "metadata": {
     "editable": true
    },
@@ -5614,7 +5615,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "656240e7",
+   "id": "9cd38ea9",
    "metadata": {
     "editable": true
    },
@@ -5626,7 +5627,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb310d7c",
+   "id": "9694bb51",
    "metadata": {
     "editable": true
    },
@@ -5641,7 +5642,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6b102dc",
+   "id": "6e07281b",
    "metadata": {
     "editable": true
    },
@@ -5653,7 +5654,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "797d4bb8",
+   "id": "db57a833",
    "metadata": {
     "editable": true
    },
@@ -5665,7 +5666,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da2e90b8",
+   "id": "ebdeaa75",
    "metadata": {
     "editable": true
    },
@@ -5677,7 +5678,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "318f8f3a",
+   "id": "5f930649",
    "metadata": {
     "editable": true
    },
@@ -5687,7 +5688,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5e8ac9e",
+   "id": "f7e8ffc6",
    "metadata": {
     "editable": true
    },
@@ -5704,7 +5705,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "220ceeb4",
+   "id": "8cfec0e6",
    "metadata": {
     "editable": true
    },
@@ -5716,7 +5717,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec8b38dc",
+   "id": "1fc6e392",
    "metadata": {
     "editable": true
    },
@@ -5728,7 +5729,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ed927a9",
+   "id": "8aba4caa",
    "metadata": {
     "editable": true
    },
@@ -5738,7 +5739,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a51ddcc",
+   "id": "fd018426",
    "metadata": {
     "editable": true
    },
@@ -5750,7 +5751,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5392b8d",
+   "id": "44764933",
    "metadata": {
     "editable": true
    },
@@ -5761,7 +5762,7 @@
   {
    "cell_type": "code",
    "execution_count": 45,
-   "id": "95059f71",
+   "id": "76170788",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5926,7 +5927,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c568bf3",
+   "id": "afe64d3c",
    "metadata": {
     "editable": true
    },
@@ -5948,7 +5949,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eab0bb68",
+   "id": "b579efba",
    "metadata": {
     "editable": true
    },
@@ -5965,7 +5966,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0ada0c0",
+   "id": "1f9afc2e",
    "metadata": {
     "editable": true
    },
@@ -5975,7 +5976,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b483eace",
+   "id": "cdc8be09",
    "metadata": {
     "editable": true
    },
@@ -5990,7 +5991,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "30d45122",
+   "id": "5955fec0",
    "metadata": {
     "editable": true
    },
@@ -6000,7 +6001,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52c68e05",
+   "id": "ce2797bd",
    "metadata": {
     "editable": true
    },
@@ -6015,7 +6016,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1657934d",
+   "id": "dd635489",
    "metadata": {
     "editable": true
    },
@@ -6026,7 +6027,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9fc46a1b",
+   "id": "2eddadc9",
    "metadata": {
     "editable": true
    },
@@ -6046,7 +6047,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd79f75c",
+   "id": "65a61481",
    "metadata": {
     "editable": true
    },
@@ -6058,7 +6059,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "501ac880",
+   "id": "7013915a",
    "metadata": {
     "editable": true
    },
@@ -6095,7 +6096,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8551615b",
+   "id": "6b5d013b",
    "metadata": {
     "editable": true
    },
@@ -6105,7 +6106,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbd6d2a1",
+   "id": "3877834e",
    "metadata": {
     "editable": true
    },
@@ -6118,7 +6119,7 @@
   {
    "cell_type": "code",
    "execution_count": 46,
-   "id": "c71a3063",
+   "id": "7e63f565",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -6323,7 +6324,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da58cdec",
+   "id": "2592748f",
    "metadata": {
     "editable": true
    },
@@ -6340,7 +6341,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df991968",
+   "id": "f76a2424",
    "metadata": {
     "editable": true
    },
@@ -6357,7 +6358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59ef3099",
+   "id": "06bb4068",
    "metadata": {
     "editable": true
    },
@@ -6367,7 +6368,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a580ae0f",
+   "id": "cf449250",
    "metadata": {
     "editable": true
    },
@@ -6382,7 +6383,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a56f3fe1",
+   "id": "72fe7bb2",
    "metadata": {
     "editable": true
    },
@@ -6396,7 +6397,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69586714",
+   "id": "97d43e59",
    "metadata": {
     "editable": true
    },
@@ -6409,7 +6410,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8374dce",
+   "id": "26ed608f",
    "metadata": {
     "editable": true
    },
@@ -6429,7 +6430,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3fe961e",
+   "id": "ae2b2d38",
    "metadata": {
     "editable": true
    },
@@ -6441,7 +6442,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e453aa1",
+   "id": "0bc085b8",
    "metadata": {
     "editable": true
    },
@@ -6453,7 +6454,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e1ebf5bd",
+   "id": "1634a37d",
    "metadata": {
     "editable": true
    },
@@ -6465,7 +6466,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b8c35553",
+   "id": "4700b147",
    "metadata": {
     "editable": true
    },
@@ -6475,7 +6476,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22a123d5",
+   "id": "07da99c0",
    "metadata": {
     "editable": true
    },
@@ -6487,7 +6488,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b15eedf5",
+   "id": "7d3e9d8a",
    "metadata": {
     "editable": true
    },
@@ -6499,7 +6500,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a92cc8c",
+   "id": "77e9e06c",
    "metadata": {
     "editable": true
    },
@@ -6511,7 +6512,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4862313",
+   "id": "ab19ecd2",
    "metadata": {
     "editable": true
    },
@@ -6521,7 +6522,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c186d68",
+   "id": "31ff9094",
    "metadata": {
     "editable": true
    },
@@ -6537,7 +6538,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57d4f000",
+   "id": "3896b229",
    "metadata": {
     "editable": true
    },
@@ -6547,7 +6548,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c2cdc6b",
+   "id": "40d97099",
    "metadata": {
     "editable": true
    },
@@ -6559,7 +6560,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bde064ea",
+   "id": "32cda23a",
    "metadata": {
     "editable": true
    },
@@ -6576,7 +6577,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a558c97",
+   "id": "140ba57b",
    "metadata": {
     "editable": true
    },
@@ -6586,7 +6587,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "534a4844",
+   "id": "68834674",
    "metadata": {
     "editable": true
    },
@@ -6602,7 +6603,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a07e0730",
+   "id": "198be6e0",
    "metadata": {
     "editable": true
    },
@@ -6616,7 +6617,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74b72286",
+   "id": "e56f85f9",
    "metadata": {
     "editable": true
    },
@@ -6635,7 +6636,7 @@
   {
    "cell_type": "code",
    "execution_count": 47,
-   "id": "4a0c57e9",
+   "id": "4ee57304",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -6690,7 +6691,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "350b1d3d",
+   "id": "0088cd21",
    "metadata": {
     "editable": true
    },
@@ -6720,7 +6721,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9fd438b5",
+   "id": "c422d21e",
    "metadata": {
     "editable": true
    },
@@ -6749,7 +6750,7 @@
   {
    "cell_type": "code",
    "execution_count": 48,
-   "id": "d1c81690",
+   "id": "86acdd1c",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -6796,7 +6797,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca22d9ce",
+   "id": "6097ee56",
    "metadata": {
     "editable": true
    },
@@ -6822,7 +6823,7 @@
   {
    "cell_type": "code",
    "execution_count": 49,
-   "id": "5a9146bc",
+   "id": "8cf456d6",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -7056,7 +7057,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e59d2116",
+   "id": "1f09e18d",
    "metadata": {
     "editable": true
    },
@@ -7068,7 +7069,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e2ffdbaf",
+   "id": "2f8d1764",
    "metadata": {
     "editable": true
    },
@@ -7080,7 +7081,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37b2cc03",
+   "id": "2e187f3c",
    "metadata": {
     "editable": true
    },
@@ -7092,7 +7093,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "524df5d3",
+   "id": "b9710ff1",
    "metadata": {
     "editable": true
    },
@@ -7109,7 +7110,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d175b25f",
+   "id": "474b116e",
    "metadata": {
     "editable": true
    },
@@ -7119,7 +7120,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11b3289e",
+   "id": "f50a379c",
    "metadata": {
     "editable": true
    },
@@ -7131,7 +7132,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e469d65e",
+   "id": "b9be7c57",
    "metadata": {
     "editable": true
    },
@@ -7148,7 +7149,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f773fa8",
+   "id": "e9a7c309",
    "metadata": {
     "editable": true
    },
@@ -7159,7 +7160,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2952f7b4",
+   "id": "82102f94",
    "metadata": {
     "editable": true
    },
@@ -7179,7 +7180,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99057b48",
+   "id": "33008606",
    "metadata": {
     "editable": true
    },
@@ -7189,7 +7190,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7debdfea",
+   "id": "a4efa0b7",
    "metadata": {
     "editable": true
    },
@@ -7215,7 +7216,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d5d5c44",
+   "id": "2a1267ce",
    "metadata": {
     "editable": true
    },
@@ -7231,7 +7232,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f97806ce",
+   "id": "0aa8903b",
    "metadata": {
     "editable": true
    },
@@ -7242,7 +7243,7 @@
   {
    "cell_type": "code",
    "execution_count": 50,
-   "id": "9337b7c7",
+   "id": "40349a4d",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -7473,7 +7474,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6071d006",
+   "id": "9e31fdb4",
    "metadata": {
     "editable": true
    },
diff --git a/doc/src/week43/week43.do.txt b/doc/src/week43/week43.do.txt
index d0d35f649..b65ea9b44 100644
--- a/doc/src/week43/week43.do.txt
+++ b/doc/src/week43/week43.do.txt
@@ -8,7 +8,7 @@ DATE: October 21, 2024
 !bblock Material for the lecture on Monday October 21, 2024
   * Building our own Feed-forward Neural Network with intro to Tensorflow
   * Solving differential equations with Neural Networks
-#  * "Video of lecture to be posted asap":"https://youtu.be/"
+  * "Video of lecture at URL:"https://youtu.be/vkBNTn-MLqs"
 #  * "Whiteboard notes":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesOct21.pdf"  
 !eblock