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Morten Hjorth-Jensen
2023-11-13 06:15:13 +01:00
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doc/LectureNotes/Project2.ipynb
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"# Project 2 on Machine Learning, deadline November 13 (Midnight)\n",
"# Project 2 on Machine Learning, deadline November 17 (Midnight)\n",
"**[Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html)**, Department of Physics, University of Oslo, Norway\n",
"\n",
"Date: **Oct 9, 2023**\n",
"Date: **Nov 13, 2023**\n",
"\n",
"Copyright 1999-2023, [Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html). Released under CC Attribution-NonCommercial 4.0 license"
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doc/LectureNotes/Project3.ipynb
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"# Project 3 on Machine Learning, deadline December 18 (midnight), 2023\n",
"**[Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html)**, Department of Physics, University of Oslo, Norway\n",
"\n",
"Date: **Nov 12, 2023**\n",
"Date: **Nov 13, 2023**\n",
"\n",
"Copyright 1999-2023, [Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html). Released under CC Attribution-NonCommercial 4.0 license"
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"3. Or other sources.\n",
"\n",
"The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:\n",
"1. Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among **linear regression (including Ridge and Lasso)**, **Logistic Regression**, **Neural Networks**, **Convolution Neural Networks**, **Recurrent Neural Networks**, and **Decision Trees, Random Forests, Bagging and Boosting**. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into **convolutional neural networks** or **recurrent neural networks**, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attention to supervised learning. \n",
"1. Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among **linear regression (including Ridge and Lasso)**, **Logistic Regression**, **Neural Networks**, **Convolution Neural Networks**, **Recurrent Neural Networks**, and **Decision Trees, Random Forests, Bagging and Boosting**.\n",
"\n",
"Feel also free to use support vector machines, $k$-means and principal components analysis, although the latter have not been covered during the lectures. This material can be found in the lecture notes.\n",
"\n",
"You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into **convolutional neural networks** or **recurrent neural networks**, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attention to supervised learning. \n",
"\n",
"For Boosting, feel also free to write your own codes.\n",
"\n",
"1. For project 3, you should feel free to use your own codes from projects 1 and 2, eventually write your own for Decision trees/random forests/bagging/boosting' or use the available functionality of **Scikit-Learn**, **Tensorflow**, etc. \n",
"1. For project 3, you should feel free to use your own codes from projects 1 and 2, eventually write your own for Decision trees/random forests/bagging/boosting' or use the available functionality of **Scikit-Learn**, **Tensorflow**, PyTorch etc. \n",
"\n",
"2. The estimates you used and tested in projects 1 and 2 should also be included, that is the $R2$-score, **MSE**, confusion matrix, accuracy score, information gain, ROC and Cumulative gains curves and other, cross-validation and/or bootstrap if these are relevant.\n",
"\n",
@@ -72,12 +76,12 @@
"\n",
"We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.\n",
"\n",
"This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides [from week 43](https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week42.html) and/or the textbook by [Yadav et al](https://www.springer.com/gp/book/9789401798150)."
"This is a field with large scientific interest, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides [from week 43](https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week42.html) and/or the textbook by [Yadav et al](https://www.springer.com/gp/book/9789401798150)."
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"equation in one dimension using a standard explicit scheme and neural\n",
"networks to solve the same equations.\n",
"\n",
"For the explicit scheme, you can study for example chapter 10 of the lecture notes in [Computational Physics](https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf) or alternative sources. For the solution of ordinary and partial differential equations using neural networks, the lectures by [Kristine Baluka Hein and included in the lectures of week 43](https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week43.html) at this course are highly recommended.\n",
"For the explicit scheme, you can study for example chapter 10 of the lecture notes in [Computational Physics, FYS3150/4150](https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf) or alternative sources from courses like [MAT-MEK4270](https://www.uio.no/studier/emner/matnat/math/MAT-MEK4270/index.html). For the solution of ordinary and partial differential equations using neural networks, the lectures by [included in the lectures of week 43](https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week43.html) at this course are highly recommended.\n",
"\n",
"For the machine learning part you can use your own code from project 2 or the functionality of for example **Tensorflow/Keras**.."
"For the machine learning part you can use your own code from project 2 or the functionality of for example **Tensorflow/Keras**, **PyTorch** or other libraries such [Physics informed machine learning](https://maziarraissi.github.io/PINNs/)."
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"### Alternative differential equations\n",
"\n",
"Note that you can replace the one-dimensional diffusion equation discussed below with other sets of either ordinary differential equations or partial differential equations.\n",
"Please discuss such a change with us at the lab."
]
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"### Part d)\n",
"### Part d) Neural network complexity\n",
"\n",
"Finally, present a critical assessment of the methods you have studied\n",
"and discuss the potential for the solving differential equations and\n",
"eigenvalue problems with machine learning methods."
"Here we study the stability of the results of the results as functions of the number of hidden nodes, layers and activation functions for the hidden layers.\n",
"Increase the number of hidden nodes and layers in order to see if this improves your results. Try also different activation functions for the hidden layers, such as the **tanh**, **ReLU**, and other activation functions. \n",
"Discuss your results."
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"### Part e)\n",
"\n",
"Finally, present a critical assessment of the methods you have studied\n",
"and discuss the potential for the solving differential equations with machine learning methods."
]
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</li>
<li class="toctree-l1">
<a class="reference internal" href="project2.html">
Project 2 on Machine Learning, deadline November 13 (Midnight)
Project 2 on Machine Learning, deadline November 17 (Midnight)
</a>
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@@ -496,6 +496,11 @@ const thebe_selector_output = ".output, .cell_output"
Solving partial differential equations with neural networks
</a>
<ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#alternative-differential-equations">
Alternative differential equations
</a>
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<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#part-a-setting-up-the-problem">
Part a), setting up the problem
@@ -511,9 +516,14 @@ const thebe_selector_output = ".output, .cell_output"
Part c) Neural networks
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#part-d-neural-network-complexity">
Part d) Neural network complexity
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#id2">
Part d)
Part e)
</a>
</li>
</ul>
@@ -607,6 +617,11 @@ const thebe_selector_output = ".output, .cell_output"
Solving partial differential equations with neural networks
</a>
<ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#alternative-differential-equations">
Alternative differential equations
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#part-a-setting-up-the-problem">
Part a), setting up the problem
@@ -622,9 +637,14 @@ const thebe_selector_output = ".output, .cell_output"
Part c) Neural networks
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#part-d-neural-network-complexity">
Part d) Neural network complexity
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#id2">
Part d)
Part e)
</a>
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@@ -660,7 +680,7 @@ doconce format html Project3.do.txt -->
<!-- dom:TITLE: Project 3 on Machine Learning, deadline December 18 (midnight), 2023 --><div class="tex2jax_ignore mathjax_ignore section" id="project-3-on-machine-learning-deadline-december-18-midnight-2023">
<h1>Project 3 on Machine Learning, deadline December 18 (midnight), 2023<a class="headerlink" href="#project-3-on-machine-learning-deadline-december-18-midnight-2023" title="Permalink to this headline"></a></h1>
<p><strong><a class="reference external" href="http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html">Data Analysis and Machine Learning FYS-STK3155/FYS4155</a></strong>, Department of Physics, University of Oslo, Norway</p>
<p>Date: <strong>Nov 12, 2023</strong></p>
<p>Date: <strong>Nov 13, 2023</strong></p>
<p>Copyright 1999-2023, <a class="reference external" href="http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html">Data Analysis and Machine Learning FYS-STK3155/FYS4155</a>. Released under CC Attribution-NonCommercial 4.0 license</p>
</div>
<div class="tex2jax_ignore mathjax_ignore section" id="paths-for-project-3">
@@ -675,11 +695,13 @@ doconce format html Project3.do.txt -->
</ol>
<p>The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:</p>
<ol class="simple">
<li><p>Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among <strong>linear regression (including Ridge and Lasso)</strong>, <strong>Logistic Regression</strong>, <strong>Neural Networks</strong>, <strong>Convolution Neural Networks</strong>, <strong>Recurrent Neural Networks</strong>, and <strong>Decision Trees, Random Forests, Bagging and Boosting</strong>. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into <strong>convolutional neural networks</strong> or <strong>recurrent neural networks</strong>, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attention to supervised learning.</p></li>
<li><p>Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among <strong>linear regression (including Ridge and Lasso)</strong>, <strong>Logistic Regression</strong>, <strong>Neural Networks</strong>, <strong>Convolution Neural Networks</strong>, <strong>Recurrent Neural Networks</strong>, and <strong>Decision Trees, Random Forests, Bagging and Boosting</strong>.</p></li>
</ol>
<p>Feel also free to use support vector machines, <span class="math notranslate nohighlight">\(k\)</span>-means and principal components analysis, although the latter have not been covered during the lectures. This material can be found in the lecture notes.</p>
<p>You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into <strong>convolutional neural networks</strong> or <strong>recurrent neural networks</strong>, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attention to supervised learning.</p>
<p>For Boosting, feel also free to write your own codes.</p>
<ol class="simple">
<li><p>For project 3, you should feel free to use your own codes from projects 1 and 2, eventually write your own for Decision trees/random forests/bagging/boosting’ or use the available functionality of <strong>Scikit-Learn</strong>, <strong>Tensorflow</strong>, etc.</p></li>
<li><p>For project 3, you should feel free to use your own codes from projects 1 and 2, eventually write your own for Decision trees/random forests/bagging/boosting’ or use the available functionality of <strong>Scikit-Learn</strong>, <strong>Tensorflow</strong>, PyTorch etc.</p></li>
<li><p>The estimates you used and tested in projects 1 and 2 should also be included, that is the <span class="math notranslate nohighlight">\(R2\)</span>-score, <strong>MSE</strong>, confusion matrix, accuracy score, information gain, ROC and Cumulative gains curves and other, cross-validation and/or bootstrap if these are relevant.</p></li>
<li><p>Similarly, feel free to explore various activations functions in deep learning and various approachs to stochastic gradient descent approaches.</p></li>
<li><p>If possible, you should link the data sets with exisiting research and analyses thereof. Scientific articles which have used Machine Learning algorithms to analyze the data are highly welcome. Perhaps you can improve previous analyses and even publish a new article?</p></li>
@@ -687,7 +709,7 @@ doconce format html Project3.do.txt -->
</ol>
<p>All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..</p>
<p>We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.</p>
<p>This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week42.html">from week 43</a> and/or the textbook by <a class="reference external" href="https://www.springer.com/gp/book/9789401798150">Yadav et al</a>.</p>
<p>This is a field with large scientific interest, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week42.html">from week 43</a> and/or the textbook by <a class="reference external" href="https://www.springer.com/gp/book/9789401798150">Yadav et al</a>.</p>
</div>
<div class="section" id="the-basic-structure-of-your-project">
<h2>The basic structure of your project<a class="headerlink" href="#the-basic-structure-of-your-project" title="Permalink to this headline"></a></h2>
@@ -720,8 +742,13 @@ background in the solution of partial differential equations using
finite difference schemes. We will study the solution of the diffusion
equation in one dimension using a standard explicit scheme and neural
networks to solve the same equations.</p>
<p>For the explicit scheme, you can study for example chapter 10 of the lecture notes in <a class="reference external" href="https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf">Computational Physics</a> or alternative sources. For the solution of ordinary and partial differential equations using neural networks, the lectures by <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week43.html">Kristine Baluka Hein and included in the lectures of week 43</a> at this course are highly recommended.</p>
<p>For the machine learning part you can use your own code from project 2 or the functionality of for example <strong>Tensorflow/Keras</strong>..</p>
<p>For the explicit scheme, you can study for example chapter 10 of the lecture notes in <a class="reference external" href="https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf">Computational Physics, FYS3150/4150</a> or alternative sources from courses like <a class="reference external" href="https://www.uio.no/studier/emner/matnat/math/MAT-MEK4270/index.html">MAT-MEK4270</a>. For the solution of ordinary and partial differential equations using neural networks, the lectures by <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week43.html">included in the lectures of week 43</a> at this course are highly recommended.</p>
<p>For the machine learning part you can use your own code from project 2 or the functionality of for example <strong>Tensorflow/Keras</strong>, <strong>PyTorch</strong> or other libraries such <a class="reference external" href="https://maziarraissi.github.io/PINNs/">Physics informed machine learning</a>.</p>
<div class="section" id="alternative-differential-equations">
<h3>Alternative differential equations<a class="headerlink" href="#alternative-differential-equations" title="Permalink to this headline"></a></h3>
<p>Note that you can replace the one-dimensional diffusion equation discussed below with other sets of either ordinary differential equations or partial differential equations.
Please discuss such a change with us at the lab.</p>
</div>
<div class="section" id="part-a-setting-up-the-problem">
<h3>Part a), setting up the problem<a class="headerlink" href="#part-a-setting-up-the-problem" title="Permalink to this headline"></a></h3>
<p>The physical problem can be that of the temperature gradient in a rod of length <span class="math notranslate nohighlight">\(L=1\)</span> at <span class="math notranslate nohighlight">\(x=0\)</span> and <span class="math notranslate nohighlight">\(x=1\)</span>.
@@ -788,11 +815,16 @@ part b). Discuss your results and compare them with the standard
explicit scheme. Include also the analytical solution and compare with
that.</p>
</div>
<div class="section" id="part-d-neural-network-complexity">
<h3>Part d) Neural network complexity<a class="headerlink" href="#part-d-neural-network-complexity" title="Permalink to this headline"></a></h3>
<p>Here we study the stability of the results of the results as functions of the number of hidden nodes, layers and activation functions for the hidden layers.
Increase the number of hidden nodes and layers in order to see if this improves your results. Try also different activation functions for the hidden layers, such as the <strong>tanh</strong>, <strong>ReLU</strong>, and other activation functions.
Discuss your results.</p>
</div>
<div class="section" id="id2">
<h3>Part d)<a class="headerlink" href="#id2" title="Permalink to this headline"></a></h3>
<h3>Part e)<a class="headerlink" href="#id2" title="Permalink to this headline"></a></h3>
<p>Finally, present a critical assessment of the methods you have studied
and discuss the potential for the solving differential equations and
eigenvalue problems with machine learning methods.</p>
and discuss the potential for the solving differential equations with machine learning methods.</p>
</div>
</div>
<div class="section" id="introduction-to-numerical-projects">
doc/LectureNotes/_build/html/_sources/Project3.ipynb
+74 -44
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@@ -2,7 +2,7 @@
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@@ -22,14 +22,14 @@
"# Project 3 on Machine Learning, deadline December 18 (midnight), 2023\n",
"**[Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html)**, Department of Physics, University of Oslo, Norway\n",
"\n",
"Date: **Nov 12, 2023**\n",
"Date: **Nov 13, 2023**\n",
"\n",
"Copyright 1999-2023, [Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html). Released under CC Attribution-NonCommercial 4.0 license"
]
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{
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@@ -39,7 +39,7 @@
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@@ -54,11 +54,15 @@
"3. Or other sources.\n",
"\n",
"The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:\n",
"1. Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among **linear regression (including Ridge and Lasso)**, **Logistic Regression**, **Neural Networks**, **Convolution Neural Networks**, **Recurrent Neural Networks**, and **Decision Trees, Random Forests, Bagging and Boosting**. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into **convolutional neural networks** or **recurrent neural networks**, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attention to supervised learning. \n",
"1. Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among **linear regression (including Ridge and Lasso)**, **Logistic Regression**, **Neural Networks**, **Convolution Neural Networks**, **Recurrent Neural Networks**, and **Decision Trees, Random Forests, Bagging and Boosting**.\n",
"\n",
"Feel also free to use support vector machines, $k$-means and principal components analysis, although the latter have not been covered during the lectures. This material can be found in the lecture notes.\n",
"\n",
"You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into **convolutional neural networks** or **recurrent neural networks**, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attention to supervised learning. \n",
"\n",
"For Boosting, feel also free to write your own codes.\n",
"\n",
"1. For project 3, you should feel free to use your own codes from projects 1 and 2, eventually write your own for Decision trees/random forests/bagging/boosting' or use the available functionality of **Scikit-Learn**, **Tensorflow**, etc. \n",
"1. For project 3, you should feel free to use your own codes from projects 1 and 2, eventually write your own for Decision trees/random forests/bagging/boosting' or use the available functionality of **Scikit-Learn**, **Tensorflow**, PyTorch etc. \n",
"\n",
"2. The estimates you used and tested in projects 1 and 2 should also be included, that is the $R2$-score, **MSE**, confusion matrix, accuracy score, information gain, ROC and Cumulative gains curves and other, cross-validation and/or bootstrap if these are relevant.\n",
"\n",
@@ -72,12 +76,12 @@
"\n",
"We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.\n",
"\n",
"This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides [from week 43](https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week42.html) and/or the textbook by [Yadav et al](https://www.springer.com/gp/book/9789401798150)."
"This is a field with large scientific interest, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides [from week 43](https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week42.html) and/or the textbook by [Yadav et al](https://www.springer.com/gp/book/9789401798150)."
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@@ -89,7 +93,7 @@
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@@ -101,7 +105,7 @@
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@@ -113,7 +117,7 @@
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@@ -125,7 +129,7 @@
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@@ -137,7 +141,7 @@
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@@ -149,7 +153,7 @@
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@@ -162,14 +166,27 @@
"equation in one dimension using a standard explicit scheme and neural\n",
"networks to solve the same equations.\n",
"\n",
"For the explicit scheme, you can study for example chapter 10 of the lecture notes in [Computational Physics](https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf) or alternative sources. For the solution of ordinary and partial differential equations using neural networks, the lectures by [Kristine Baluka Hein and included in the lectures of week 43](https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week43.html) at this course are highly recommended.\n",
"For the explicit scheme, you can study for example chapter 10 of the lecture notes in [Computational Physics, FYS3150/4150](https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf) or alternative sources from courses like [MAT-MEK4270](https://www.uio.no/studier/emner/matnat/math/MAT-MEK4270/index.html). For the solution of ordinary and partial differential equations using neural networks, the lectures by [included in the lectures of week 43](https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week43.html) at this course are highly recommended.\n",
"\n",
"For the machine learning part you can use your own code from project 2 or the functionality of for example **Tensorflow/Keras**.."
"For the machine learning part you can use your own code from project 2 or the functionality of for example **Tensorflow/Keras**, **PyTorch** or other libraries such [Physics informed machine learning](https://maziarraissi.github.io/PINNs/)."
]
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{
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"id": "c97df4f9",
"metadata": {
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"source": [
"### Alternative differential equations\n",
"\n",
"Note that you can replace the one-dimensional diffusion equation discussed below with other sets of either ordinary differential equations or partial differential equations.\n",
"Please discuss such a change with us at the lab."
]
},
{
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@@ -183,7 +200,7 @@
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@@ -195,7 +212,7 @@
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@@ -205,7 +222,7 @@
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@@ -217,7 +234,7 @@
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@@ -227,7 +244,7 @@
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@@ -239,7 +256,7 @@
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@@ -250,7 +267,7 @@
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@@ -262,7 +279,7 @@
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@@ -272,7 +289,7 @@
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@@ -284,7 +301,7 @@
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@@ -297,7 +314,7 @@
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@@ -309,7 +326,7 @@
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@@ -319,7 +336,7 @@
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@@ -397,21 +414,34 @@
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"### Part d)\n",
"### Part d) Neural network complexity\n",
"\n",
"Finally, present a critical assessment of the methods you have studied\n",
"and discuss the potential for the solving differential equations and\n",
"eigenvalue problems with machine learning methods."
"Here we study the stability of the results of the results as functions of the number of hidden nodes, layers and activation functions for the hidden layers.\n",
"Increase the number of hidden nodes and layers in order to see if this improves your results. Try also different activation functions for the hidden layers, such as the **tanh**, **ReLU**, and other activation functions. \n",
"Discuss your results."
]
},
{
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"metadata": {
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"### Part e)\n",
"\n",
"Finally, present a critical assessment of the methods you have studied\n",
"and discuss the potential for the solving differential equations with machine learning methods."
]
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"# Project 2 on Machine Learning, deadline November 13 (Midnight)\n",
"# Project 2 on Machine Learning, deadline November 17 (Midnight)\n",
"**[Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html)**, Department of Physics, University of Oslo, Norway\n",
"\n",
"Date: **Oct 9, 2023**\n",
"Date: **Nov 13, 2023**\n",
"\n",
"Copyright 1999-2023, [Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html). Released under CC Attribution-NonCommercial 4.0 license"
]
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Project 2 on Machine Learning, deadline November 13 (Midnight)
Project 2 on Machine Learning, deadline November 17 (Midnight)
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Project 2 on Machine Learning, deadline November 17 (Midnight)
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Week 45, Recurrent Neural Networks
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Week 46: Decision Trees, Ensemble methods and Random Forests
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Project 2 on Machine Learning, deadline November 13 (Midnight)
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<h1>Project 2 on Machine Learning, deadline November 17 (Midnight)</h1>
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<!-- dom:TITLE: Project 2 on Machine Learning, deadline November 13 (Midnight) --><div class="tex2jax_ignore mathjax_ignore section" id="project-2-on-machine-learning-deadline-november-13-midnight">
<h1>Project 2 on Machine Learning, deadline November 13 (Midnight)<a class="headerlink" href="#project-2-on-machine-learning-deadline-november-13-midnight" title="Permalink to this headline"></a></h1>
<!-- dom:TITLE: Project 2 on Machine Learning, deadline November 17 (Midnight) --><div class="tex2jax_ignore mathjax_ignore section" id="project-2-on-machine-learning-deadline-november-17-midnight">
<h1>Project 2 on Machine Learning, deadline November 17 (Midnight)<a class="headerlink" href="#project-2-on-machine-learning-deadline-november-17-midnight" title="Permalink to this headline"></a></h1>
<p><strong><a class="reference external" href="http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html">Data Analysis and Machine Learning FYS-STK3155/FYS4155</a></strong>, Department of Physics, University of Oslo, Norway</p>
<p>Date: <strong>Oct 9, 2023</strong></p>
<p>Date: <strong>Nov 13, 2023</strong></p>
<p>Copyright 1999-2023, <a class="reference external" href="http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html">Data Analysis and Machine Learning FYS-STK3155/FYS4155</a>. Released under CC Attribution-NonCommercial 4.0 license</p>
<div class="section" id="classification-and-regression-from-linear-and-logistic-regression-to-neural-networks">
<h2>Classification and Regression, from linear and logistic regression to neural networks<a class="headerlink" href="#classification-and-regression-from-linear-and-logistic-regression-to-neural-networks" title="Permalink to this headline"></a></h2>
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<a class="reference internal" href="project2.html">
Project 2 on Machine Learning, deadline November 13 (Midnight)
Project 2 on Machine Learning, deadline November 17 (Midnight)
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"# Project 3 on Machine Learning, deadline December 18 (midnight), 2023\n",
"**[Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html)**, Department of Physics, University of Oslo, Norway\n",
"\n",
"Date: **Nov 12, 2023**\n",
"Date: **Nov 13, 2023**\n",
"\n",
"Copyright 1999-2023, [Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html). Released under CC Attribution-NonCommercial 4.0 license"
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"3. Or other sources.\n",
"\n",
"The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:\n",
"1. Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among **linear regression (including Ridge and Lasso)**, **Logistic Regression**, **Neural Networks**, **Convolution Neural Networks**, **Recurrent Neural Networks**, and **Decision Trees, Random Forests, Bagging and Boosting**. You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into **convolutional neural networks** or **recurrent neural networks**, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attention to supervised learning. \n",
"1. Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among **linear regression (including Ridge and Lasso)**, **Logistic Regression**, **Neural Networks**, **Convolution Neural Networks**, **Recurrent Neural Networks**, and **Decision Trees, Random Forests, Bagging and Boosting**.\n",
"\n",
"Feel also free to use support vector machines, $k$-means and principal components analysis, although the latter have not been covered during the lectures. This material can be found in the lecture notes.\n",
"\n",
"You could for example explore all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into **convolutional neural networks** or **recurrent neural networks**, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attention to supervised learning. \n",
"\n",
"For Boosting, feel also free to write your own codes.\n",
"\n",
"1. For project 3, you should feel free to use your own codes from projects 1 and 2, eventually write your own for Decision trees/random forests/bagging/boosting' or use the available functionality of **Scikit-Learn**, **Tensorflow**, etc. \n",
"1. For project 3, you should feel free to use your own codes from projects 1 and 2, eventually write your own for Decision trees/random forests/bagging/boosting' or use the available functionality of **Scikit-Learn**, **Tensorflow**, PyTorch etc. \n",
"\n",
"2. The estimates you used and tested in projects 1 and 2 should also be included, that is the $R2$-score, **MSE**, confusion matrix, accuracy score, information gain, ROC and Cumulative gains curves and other, cross-validation and/or bootstrap if these are relevant.\n",
"\n",
@@ -72,12 +76,12 @@
"\n",
"We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.\n",
"\n",
"This is a field with a large interest recently, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides [from week 43](https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week42.html) and/or the textbook by [Yadav et al](https://www.springer.com/gp/book/9789401798150)."
"This is a field with large scientific interest, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides [from week 43](https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week42.html) and/or the textbook by [Yadav et al](https://www.springer.com/gp/book/9789401798150)."
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"equation in one dimension using a standard explicit scheme and neural\n",
"networks to solve the same equations.\n",
"\n",
"For the explicit scheme, you can study for example chapter 10 of the lecture notes in [Computational Physics](https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf) or alternative sources. For the solution of ordinary and partial differential equations using neural networks, the lectures by [Kristine Baluka Hein and included in the lectures of week 43](https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week43.html) at this course are highly recommended.\n",
"For the explicit scheme, you can study for example chapter 10 of the lecture notes in [Computational Physics, FYS3150/4150](https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf) or alternative sources from courses like [MAT-MEK4270](https://www.uio.no/studier/emner/matnat/math/MAT-MEK4270/index.html). For the solution of ordinary and partial differential equations using neural networks, the lectures by [included in the lectures of week 43](https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week43.html) at this course are highly recommended.\n",
"\n",
"For the machine learning part you can use your own code from project 2 or the functionality of for example **Tensorflow/Keras**.."
"For the machine learning part you can use your own code from project 2 or the functionality of for example **Tensorflow/Keras**, **PyTorch** or other libraries such [Physics informed machine learning](https://maziarraissi.github.io/PINNs/)."
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"### Alternative differential equations\n",
"\n",
"Note that you can replace the one-dimensional diffusion equation discussed below with other sets of either ordinary differential equations or partial differential equations.\n",
"Please discuss such a change with us at the lab."
]
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"### Part d)\n",
"### Part d) Neural network complexity\n",
"\n",
"Finally, present a critical assessment of the methods you have studied\n",
"and discuss the potential for the solving differential equations and\n",
"eigenvalue problems with machine learning methods."
"Here we study the stability of the results of the results as functions of the number of hidden nodes, layers and activation functions for the hidden layers.\n",
"Increase the number of hidden nodes and layers in order to see if this improves your results. Try also different activation functions for the hidden layers, such as the **tanh**, **ReLU**, and other activation functions. \n",
"Discuss your results."
]
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"### Part e)\n",
"\n",
"Finally, present a critical assessment of the methods you have studied\n",
"and discuss the potential for the solving differential equations with machine learning methods."
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"# Project 2 on Machine Learning, deadline November 13 (Midnight)\n",
"# Project 2 on Machine Learning, deadline November 17 (Midnight)\n",
"**[Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html)**, Department of Physics, University of Oslo, Norway\n",
"\n",
"Date: **Oct 9, 2023**\n",
"Date: **Nov 13, 2023**\n",
"\n",
"Copyright 1999-2023, [Data Analysis and Machine Learning FYS-STK3155/FYS4155](http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html). Released under CC Attribution-NonCommercial 4.0 license"
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