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+<meta name="description" content="Week 42 Solving differential equations and Convolutional (CNN)">
+
+<title>Week 42 Solving differential equations and Convolutional (CNN)</title>
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+
+/* Adds an invisible element before each target to offset for the navigation
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+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Plan for week 42', 2, None, 'plan-for-week-42'),
+              ('Using Automatic differentiation',
+               2,
+               None,
+               'using-automatic-differentiation'),
+              ('Solving ODEs with Deep Learning',
+               2,
+               None,
+               'solving-odes-with-deep-learning'),
+              ('Ordinary Differential Equations',
+               2,
+               None,
+               'ordinary-differential-equations'),
+              ('The trial solution', 2, None, 'the-trial-solution'),
+              ('Minimization process', 2, None, 'minimization-process'),
+              ('Minimizing the cost function using gradient descent and '
+               'automatic differentiation',
+               2,
+               None,
+               'minimizing-the-cost-function-using-gradient-descent-and-automatic-differentiation'),
+              ('Example: Exponential decay',
+               2,
+               None,
+               'example-exponential-decay'),
+              ('The function to solve for',
+               2,
+               None,
+               'the-function-to-solve-for'),
+              ('The trial solution', 2, None, 'the-trial-solution'),
+              ('Setup of Network', 2, None, 'setup-of-network'),
+              ('Reformulating the problem',
+               2,
+               None,
+               'reformulating-the-problem'),
+              ('More technicalities', 2, None, 'more-technicalities'),
+              ('More details', 2, None, 'more-details'),
+              ('A possible implementation of a neural network',
+               2,
+               None,
+               'a-possible-implementation-of-a-neural-network'),
+              ('Technicalities', 2, None, 'technicalities'),
+              ('Final technicalities I', 2, None, 'final-technicalities-i'),
+              ('Final technicalities II', 2, None, 'final-technicalities-ii'),
+              ('Final technicalities III', 2, None, 'final-technicalities-iii'),
+              ('Final technicalities IV', 2, None, 'final-technicalities-iv'),
+              ('Back propagation', 2, None, 'back-propagation'),
+              ('Gradient descent', 2, None, 'gradient-descent'),
+              ('The code for solving the ODE',
+               2,
+               None,
+               'the-code-for-solving-the-ode'),
+              ('The network with one input layer, specified number of hidden '
+               'layers, and one output layer',
+               2,
+               None,
+               'the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer'),
+              ('Example: Population growth',
+               2,
+               None,
+               'example-population-growth'),
+              ('Setting up the problem', 2, None, 'setting-up-the-problem'),
+              ('The trial solution', 2, None, 'the-trial-solution'),
+              ('The program using Autograd',
+               2,
+               None,
+               'the-program-using-autograd'),
+              ('Using forward Euler to solve the ODE',
+               2,
+               None,
+               'using-forward-euler-to-solve-the-ode'),
+              ('Example: Solving the one dimensional Poisson equation',
+               2,
+               None,
+               'example-solving-the-one-dimensional-poisson-equation'),
+              ('The specific equation to solve for',
+               2,
+               None,
+               'the-specific-equation-to-solve-for'),
+              ('Solving the equation using Autograd',
+               2,
+               None,
+               'solving-the-equation-using-autograd'),
+              ('Comparing with a numerical scheme',
+               2,
+               None,
+               'comparing-with-a-numerical-scheme'),
+              ('Setting up the code', 2, None, 'setting-up-the-code'),
+              ('Partial Differential Equations',
+               2,
+               None,
+               'partial-differential-equations'),
+              ('Type of problem', 2, None, 'type-of-problem'),
+              ('Network requirements', 2, None, 'network-requirements'),
+              ('More details', 2, None, 'more-details'),
+              ('Example: The diffusion equation',
+               2,
+               None,
+               'example-the-diffusion-equation'),
+              ('Defining the problem', 2, None, 'defining-the-problem'),
+              ('Setting up the network using Autograd',
+               2,
+               None,
+               'setting-up-the-network-using-autograd'),
+              ('Setting up the network using Autograd; The trial solution',
+               2,
+               None,
+               'setting-up-the-network-using-autograd-the-trial-solution'),
+              ('Why the jacobian?', 2, None, 'why-the-jacobian'),
+              ('Setting up the network using Autograd; The full program',
+               2,
+               None,
+               'setting-up-the-network-using-autograd-the-full-program'),
+              ('Example: Solving the wave equation with Neural Networks',
+               2,
+               None,
+               'example-solving-the-wave-equation-with-neural-networks'),
+              ('The problem to solve for', 2, None, 'the-problem-to-solve-for'),
+              ('The trial solution', 2, None, 'the-trial-solution'),
+              ('The analytical solution', 2, None, 'the-analytical-solution'),
+              ('Solving the wave equation - the full program using Autograd',
+               2,
+               None,
+               'solving-the-wave-equation-the-full-program-using-autograd'),
+              ('Resources on differential equations and deep learning',
+               2,
+               None,
+               'resources-on-differential-equations-and-deep-learning'),
+              ('Convolutional Neural Networks (recognizing images)',
+               2,
+               None,
+               'convolutional-neural-networks-recognizing-images'),
+              ('What is the Difference', 2, None, 'what-is-the-difference'),
+              ('Neural Networks vs CNNs', 2, None, 'neural-networks-vs-cnns'),
+              ('Why CNNS for images, sound files, medical images from CT scans '
+               'etc?',
+               2,
+               None,
+               'why-cnns-for-images-sound-files-medical-images-from-ct-scans-etc'),
+              ('Regular NNs don’t scale well to full images',
+               2,
+               None,
+               'regular-nns-don-t-scale-well-to-full-images'),
+              ('3D volumes of neurons', 2, None, '3d-volumes-of-neurons'),
+              ('Layers used to build CNNs',
+               2,
+               None,
+               'layers-used-to-build-cnns'),
+              ('Transforming images', 2, None, 'transforming-images'),
+              ('CNNs in brief', 2, None, 'cnns-in-brief'),
+              ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+              ('Convolution Examples: Polynomial multiplication',
+               2,
+               None,
+               'convolution-examples-polynomial-multiplication'),
+              ('Efficient Polynomial Multiplication',
+               2,
+               None,
+               'efficient-polynomial-multiplication'),
+              ('A more efficient way of coding the above Convolution',
+               2,
+               None,
+               'a-more-efficient-way-of-coding-the-above-convolution'),
+              ('Convolution Examples: Principle of Superposition and Periodic '
+               'Forces (Fourier Transforms)',
+               2,
+               None,
+               'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
+              ('Principle of Superposition',
+               2,
+               None,
+               'principle-of-superposition'),
+              ('Simple Code Example', 2, None, 'simple-code-example'),
+              ('Wrapping up Fourier transforms',
+               2,
+               None,
+               'wrapping-up-fourier-transforms'),
+              ('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
+              ('Final words on Fourier Transforms',
+               2,
+               None,
+               'final-words-on-fourier-transforms'),
+              ('Two-dimensional Objects', 2, None, 'two-dimensional-objects'),
+              ('Cross-Correlation', 2, None, 'cross-correlation'),
+              ('More on Dimensionalities', 2, None, 'more-on-dimensionalities'),
+              ('Further Dimensionality Remarks',
+               2,
+               None,
+               'further-dimensionality-remarks'),
+              ('CNNs in more detail, building convolutional neural networks in '
+               'Tensorflow and Keras',
+               2,
+               None,
+               'cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras'),
+              ('Setting it up', 2, None, 'setting-it-up'),
+              ('The MNIST dataset again', 2, None, 'the-mnist-dataset-again'),
+              ('Strong correlations', 2, None, 'strong-correlations'),
+              ('Layers of a CNN', 2, None, 'layers-of-a-cnn'),
+              ('Systematic reduction', 2, None, 'systematic-reduction'),
+              ('Prerequisites: Collect and pre-process data',
+               2,
+               None,
+               'prerequisites-collect-and-pre-process-data'),
+              ('Importing Keras and Tensorflow',
+               2,
+               None,
+               'importing-keras-and-tensorflow'),
+              ('Running with Keras', 2, None, 'running-with-keras'),
+              ('Final part', 2, None, 'final-part'),
+              ('Final visualization', 2, None, 'final-visualization'),
+              ('The CIFAR01 data set', 2, None, 'the-cifar01-data-set'),
+              ('Verifying the data set', 2, None, 'verifying-the-data-set'),
+              ('Set up  the model', 2, None, 'set-up-the-model'),
+              ('Add Dense layers on top', 2, None, 'add-dense-layers-on-top'),
+              ('Compile and train the model',
+               2,
+               None,
+               'compile-and-train-the-model'),
+              ('Finally, evaluate the model',
+               2,
+               None,
+               'finally-evaluate-the-model')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
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+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
+    <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
+      <span class="icon-bar"></span>
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+    <a class="navbar-brand" href="week42-bs.html">Week 42 Solving differential equations and Convolutional (CNN)</a>
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+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week42-bs001.html#plan-for-week-42" style="font-size: 80%;">Plan for week 42</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs002.html#using-automatic-differentiation" style="font-size: 80%;">Using Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs003.html#solving-odes-with-deep-learning" style="font-size: 80%;">Solving ODEs with Deep Learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs004.html#ordinary-differential-equations" style="font-size: 80%;">Ordinary Differential Equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs047.html#the-trial-solution" style="font-size: 80%;">The trial solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs006.html#minimization-process" style="font-size: 80%;">Minimization process</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs007.html#minimizing-the-cost-function-using-gradient-descent-and-automatic-differentiation" style="font-size: 80%;">Minimizing the cost function using gradient descent and automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs008.html#example-exponential-decay" style="font-size: 80%;">Example: Exponential decay</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs009.html#the-function-to-solve-for" style="font-size: 80%;">The function to solve for</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs047.html#the-trial-solution" style="font-size: 80%;">The trial solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs011.html#setup-of-network" style="font-size: 80%;">Setup of Network</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs012.html#reformulating-the-problem" style="font-size: 80%;">Reformulating the problem</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs013.html#more-technicalities" style="font-size: 80%;">More technicalities</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs038.html#more-details" style="font-size: 80%;">More details</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs015.html#a-possible-implementation-of-a-neural-network" style="font-size: 80%;">A possible implementation of a neural network</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs016.html#technicalities" style="font-size: 80%;">Technicalities</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs017.html#final-technicalities-i" style="font-size: 80%;">Final technicalities I</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs018.html#final-technicalities-ii" style="font-size: 80%;">Final technicalities II</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs019.html#final-technicalities-iii" style="font-size: 80%;">Final technicalities III</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs020.html#final-technicalities-iv" style="font-size: 80%;">Final technicalities IV</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs021.html#back-propagation" style="font-size: 80%;">Back propagation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs022.html#gradient-descent" style="font-size: 80%;">Gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs023.html#the-code-for-solving-the-ode" style="font-size: 80%;">The code for solving the ODE</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs024.html#the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer" style="font-size: 80%;">The network with one input layer, specified number of hidden layers, and one output layer</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs025.html#example-population-growth" style="font-size: 80%;">Example: Population growth</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs026.html#setting-up-the-problem" style="font-size: 80%;">Setting up the problem</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs047.html#the-trial-solution" style="font-size: 80%;">The trial solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs028.html#the-program-using-autograd" style="font-size: 80%;">The program using Autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs029.html#using-forward-euler-to-solve-the-ode" style="font-size: 80%;">Using forward Euler to solve the ODE</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs030.html#example-solving-the-one-dimensional-poisson-equation" style="font-size: 80%;">Example: Solving the one dimensional Poisson equation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs031.html#the-specific-equation-to-solve-for" style="font-size: 80%;">The specific equation to solve for</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs032.html#solving-the-equation-using-autograd" style="font-size: 80%;">Solving the equation using Autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs033.html#comparing-with-a-numerical-scheme" style="font-size: 80%;">Comparing with a numerical scheme</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs034.html#setting-up-the-code" style="font-size: 80%;">Setting up the code</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs035.html#partial-differential-equations" style="font-size: 80%;">Partial Differential Equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs036.html#type-of-problem" style="font-size: 80%;">Type of problem</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs037.html#network-requirements" style="font-size: 80%;">Network requirements</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs038.html#more-details" style="font-size: 80%;">More details</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs039.html#example-the-diffusion-equation" style="font-size: 80%;">Example: The diffusion equation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs040.html#defining-the-problem" style="font-size: 80%;">Defining the problem</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs041.html#setting-up-the-network-using-autograd" style="font-size: 80%;">Setting up the network using Autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs042.html#setting-up-the-network-using-autograd-the-trial-solution" style="font-size: 80%;">Setting up the network using Autograd; The trial solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs043.html#why-the-jacobian" style="font-size: 80%;">Why the jacobian?</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs044.html#setting-up-the-network-using-autograd-the-full-program" style="font-size: 80%;">Setting up the network using Autograd; The full program</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs045.html#example-solving-the-wave-equation-with-neural-networks" style="font-size: 80%;">Example: Solving the wave equation with Neural Networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs046.html#the-problem-to-solve-for" style="font-size: 80%;">The problem to solve for</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs047.html#the-trial-solution" style="font-size: 80%;">The trial solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs048.html#the-analytical-solution" style="font-size: 80%;">The analytical solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs049.html#solving-the-wave-equation-the-full-program-using-autograd" style="font-size: 80%;">Solving the wave equation - the full program using Autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs050.html#resources-on-differential-equations-and-deep-learning" style="font-size: 80%;">Resources on differential equations and deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs051.html#convolutional-neural-networks-recognizing-images" style="font-size: 80%;">Convolutional Neural Networks (recognizing images)</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs052.html#what-is-the-difference" style="font-size: 80%;">What is the Difference</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs053.html#neural-networks-vs-cnns" style="font-size: 80%;">Neural Networks vs CNNs</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs054.html#why-cnns-for-images-sound-files-medical-images-from-ct-scans-etc" style="font-size: 80%;">Why CNNS for images, sound files, medical images from CT scans etc?</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs055.html#regular-nns-don-t-scale-well-to-full-images" style="font-size: 80%;">Regular NNs don’t scale well to full images</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs056.html#3d-volumes-of-neurons" style="font-size: 80%;">3D volumes of neurons</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs057.html#layers-used-to-build-cnns" style="font-size: 80%;">Layers used to build CNNs</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs058.html#transforming-images" style="font-size: 80%;">Transforming images</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs059.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs060.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs062.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs063.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs064.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs065.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs066.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs067.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs068.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs069.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs070.html#two-dimensional-objects" style="font-size: 80%;">Two-dimensional Objects</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs071.html#cross-correlation" style="font-size: 80%;">Cross-Correlation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs072.html#more-on-dimensionalities" style="font-size: 80%;">More on Dimensionalities</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs073.html#further-dimensionality-remarks" style="font-size: 80%;">Further Dimensionality Remarks</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs074.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs075.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs076.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs077.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs078.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs079.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs080.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs081.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs082.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs083.html#final-part" style="font-size: 80%;">Final part</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs084.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs085.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs086.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs087.html#set-up-the-model" style="font-size: 80%;">Set up  the model</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs088.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
+     <!-- navigation toc: --> <li><a href="#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs090.html#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0089"></a>
+<!-- !split -->
+
+<h2 id="compile-and-train-the-model" class="anchor">Compile and train the model </h2>
+
+<p>
+
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>model<span style="color: #666666">.</span>compile(optimizer<span style="color: #666666">=</span><span style="color: #BA2121">&#39;adam&#39;</span>,
+              loss<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>keras<span style="color: #666666">.</span>losses<span style="color: #666666">.</span>SparseCategoricalCrossentropy(from_logits<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>),
+              metrics<span style="color: #666666">=</span>[<span style="color: #BA2121">&#39;accuracy&#39;</span>])
+​
+history <span style="color: #666666">=</span> model<span style="color: #666666">.</span>fit(train_images, train_labels, epochs<span style="color: #666666">=10</span>, 
+                    validation_data<span style="color: #666666">=</span>(test_images, test_labels))
+</pre></div>
+<p>
+<p>
+<!-- navigation buttons at the bottom of the page -->
+<ul class="pagination">
+<li><a href="._week42-bs088.html">&laquo;</a></li>
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diff --git a/doc/pub/week42/html/._week42-bs090.html b/doc/pub/week42/html/._week42-bs090.html
new file mode 100644
index 000000000..9d4668ce0
--- /dev/null
+++ b/doc/pub/week42/html/._week42-bs090.html
@@ -0,0 +1,463 @@
+<!--
+Automatically generated HTML file from DocOnce source
+(https://github.com/doconce/doconce/)
+-->
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
+<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
+<meta name="viewport" content="width=device-width, initial-scale=1.0" />
+<meta name="description" content="Week 42 Solving differential equations and Convolutional (CNN)">
+
+<title>Week 42 Solving differential equations and Convolutional (CNN)</title>
+
+<!-- Bootstrap style: bootstrap -->
+<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
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+-->
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+<style type="text/css">
+
+/* Add scrollbar to dropdown menus in bootstrap navigation bar */
+.dropdown-menu {
+   height: auto;
+   max-height: 400px;
+   overflow-x: hidden;
+}
+
+/* Adds an invisible element before each target to offset for the navigation
+   bar */
+.anchor::before {
+  content:"";
+  display:block;
+  height:50px;      /* fixed header height for style bootstrap */
+  margin:-50px 0 0; /* negative fixed header height */
+}
+</style>
+
+
+</head>
+
+<!-- tocinfo
+{'highest level': 2,
+ 'sections': [('Plan for week 42', 2, None, 'plan-for-week-42'),
+              ('Using Automatic differentiation',
+               2,
+               None,
+               'using-automatic-differentiation'),
+              ('Solving ODEs with Deep Learning',
+               2,
+               None,
+               'solving-odes-with-deep-learning'),
+              ('Ordinary Differential Equations',
+               2,
+               None,
+               'ordinary-differential-equations'),
+              ('The trial solution', 2, None, 'the-trial-solution'),
+              ('Minimization process', 2, None, 'minimization-process'),
+              ('Minimizing the cost function using gradient descent and '
+               'automatic differentiation',
+               2,
+               None,
+               'minimizing-the-cost-function-using-gradient-descent-and-automatic-differentiation'),
+              ('Example: Exponential decay',
+               2,
+               None,
+               'example-exponential-decay'),
+              ('The function to solve for',
+               2,
+               None,
+               'the-function-to-solve-for'),
+              ('The trial solution', 2, None, 'the-trial-solution'),
+              ('Setup of Network', 2, None, 'setup-of-network'),
+              ('Reformulating the problem',
+               2,
+               None,
+               'reformulating-the-problem'),
+              ('More technicalities', 2, None, 'more-technicalities'),
+              ('More details', 2, None, 'more-details'),
+              ('A possible implementation of a neural network',
+               2,
+               None,
+               'a-possible-implementation-of-a-neural-network'),
+              ('Technicalities', 2, None, 'technicalities'),
+              ('Final technicalities I', 2, None, 'final-technicalities-i'),
+              ('Final technicalities II', 2, None, 'final-technicalities-ii'),
+              ('Final technicalities III', 2, None, 'final-technicalities-iii'),
+              ('Final technicalities IV', 2, None, 'final-technicalities-iv'),
+              ('Back propagation', 2, None, 'back-propagation'),
+              ('Gradient descent', 2, None, 'gradient-descent'),
+              ('The code for solving the ODE',
+               2,
+               None,
+               'the-code-for-solving-the-ode'),
+              ('The network with one input layer, specified number of hidden '
+               'layers, and one output layer',
+               2,
+               None,
+               'the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer'),
+              ('Example: Population growth',
+               2,
+               None,
+               'example-population-growth'),
+              ('Setting up the problem', 2, None, 'setting-up-the-problem'),
+              ('The trial solution', 2, None, 'the-trial-solution'),
+              ('The program using Autograd',
+               2,
+               None,
+               'the-program-using-autograd'),
+              ('Using forward Euler to solve the ODE',
+               2,
+               None,
+               'using-forward-euler-to-solve-the-ode'),
+              ('Example: Solving the one dimensional Poisson equation',
+               2,
+               None,
+               'example-solving-the-one-dimensional-poisson-equation'),
+              ('The specific equation to solve for',
+               2,
+               None,
+               'the-specific-equation-to-solve-for'),
+              ('Solving the equation using Autograd',
+               2,
+               None,
+               'solving-the-equation-using-autograd'),
+              ('Comparing with a numerical scheme',
+               2,
+               None,
+               'comparing-with-a-numerical-scheme'),
+              ('Setting up the code', 2, None, 'setting-up-the-code'),
+              ('Partial Differential Equations',
+               2,
+               None,
+               'partial-differential-equations'),
+              ('Type of problem', 2, None, 'type-of-problem'),
+              ('Network requirements', 2, None, 'network-requirements'),
+              ('More details', 2, None, 'more-details'),
+              ('Example: The diffusion equation',
+               2,
+               None,
+               'example-the-diffusion-equation'),
+              ('Defining the problem', 2, None, 'defining-the-problem'),
+              ('Setting up the network using Autograd',
+               2,
+               None,
+               'setting-up-the-network-using-autograd'),
+              ('Setting up the network using Autograd; The trial solution',
+               2,
+               None,
+               'setting-up-the-network-using-autograd-the-trial-solution'),
+              ('Why the jacobian?', 2, None, 'why-the-jacobian'),
+              ('Setting up the network using Autograd; The full program',
+               2,
+               None,
+               'setting-up-the-network-using-autograd-the-full-program'),
+              ('Example: Solving the wave equation with Neural Networks',
+               2,
+               None,
+               'example-solving-the-wave-equation-with-neural-networks'),
+              ('The problem to solve for', 2, None, 'the-problem-to-solve-for'),
+              ('The trial solution', 2, None, 'the-trial-solution'),
+              ('The analytical solution', 2, None, 'the-analytical-solution'),
+              ('Solving the wave equation - the full program using Autograd',
+               2,
+               None,
+               'solving-the-wave-equation-the-full-program-using-autograd'),
+              ('Resources on differential equations and deep learning',
+               2,
+               None,
+               'resources-on-differential-equations-and-deep-learning'),
+              ('Convolutional Neural Networks (recognizing images)',
+               2,
+               None,
+               'convolutional-neural-networks-recognizing-images'),
+              ('What is the Difference', 2, None, 'what-is-the-difference'),
+              ('Neural Networks vs CNNs', 2, None, 'neural-networks-vs-cnns'),
+              ('Why CNNS for images, sound files, medical images from CT scans '
+               'etc?',
+               2,
+               None,
+               'why-cnns-for-images-sound-files-medical-images-from-ct-scans-etc'),
+              ('Regular NNs don’t scale well to full images',
+               2,
+               None,
+               'regular-nns-don-t-scale-well-to-full-images'),
+              ('3D volumes of neurons', 2, None, '3d-volumes-of-neurons'),
+              ('Layers used to build CNNs',
+               2,
+               None,
+               'layers-used-to-build-cnns'),
+              ('Transforming images', 2, None, 'transforming-images'),
+              ('CNNs in brief', 2, None, 'cnns-in-brief'),
+              ('Mathematics of CNNs', 2, None, 'mathematics-of-cnns'),
+              ('Convolution Examples: Polynomial multiplication',
+               2,
+               None,
+               'convolution-examples-polynomial-multiplication'),
+              ('Efficient Polynomial Multiplication',
+               2,
+               None,
+               'efficient-polynomial-multiplication'),
+              ('A more efficient way of coding the above Convolution',
+               2,
+               None,
+               'a-more-efficient-way-of-coding-the-above-convolution'),
+              ('Convolution Examples: Principle of Superposition and Periodic '
+               'Forces (Fourier Transforms)',
+               2,
+               None,
+               'convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms'),
+              ('Principle of Superposition',
+               2,
+               None,
+               'principle-of-superposition'),
+              ('Simple Code Example', 2, None, 'simple-code-example'),
+              ('Wrapping up Fourier transforms',
+               2,
+               None,
+               'wrapping-up-fourier-transforms'),
+              ('Finding the Coefficients', 2, None, 'finding-the-coefficients'),
+              ('Final words on Fourier Transforms',
+               2,
+               None,
+               'final-words-on-fourier-transforms'),
+              ('Two-dimensional Objects', 2, None, 'two-dimensional-objects'),
+              ('Cross-Correlation', 2, None, 'cross-correlation'),
+              ('More on Dimensionalities', 2, None, 'more-on-dimensionalities'),
+              ('Further Dimensionality Remarks',
+               2,
+               None,
+               'further-dimensionality-remarks'),
+              ('CNNs in more detail, building convolutional neural networks in '
+               'Tensorflow and Keras',
+               2,
+               None,
+               'cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras'),
+              ('Setting it up', 2, None, 'setting-it-up'),
+              ('The MNIST dataset again', 2, None, 'the-mnist-dataset-again'),
+              ('Strong correlations', 2, None, 'strong-correlations'),
+              ('Layers of a CNN', 2, None, 'layers-of-a-cnn'),
+              ('Systematic reduction', 2, None, 'systematic-reduction'),
+              ('Prerequisites: Collect and pre-process data',
+               2,
+               None,
+               'prerequisites-collect-and-pre-process-data'),
+              ('Importing Keras and Tensorflow',
+               2,
+               None,
+               'importing-keras-and-tensorflow'),
+              ('Running with Keras', 2, None, 'running-with-keras'),
+              ('Final part', 2, None, 'final-part'),
+              ('Final visualization', 2, None, 'final-visualization'),
+              ('The CIFAR01 data set', 2, None, 'the-cifar01-data-set'),
+              ('Verifying the data set', 2, None, 'verifying-the-data-set'),
+              ('Set up  the model', 2, None, 'set-up-the-model'),
+              ('Add Dense layers on top', 2, None, 'add-dense-layers-on-top'),
+              ('Compile and train the model',
+               2,
+               None,
+               'compile-and-train-the-model'),
+              ('Finally, evaluate the model',
+               2,
+               None,
+               'finally-evaluate-the-model')]}
+end of tocinfo -->
+
+<body>
+
+
+
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+  TeX: {
+     equationNumbers: {  autoNumber: "none"  },
+     extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
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+});
+</script>
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+    
+<!-- Bootstrap navigation bar -->
+<div class="navbar navbar-default navbar-fixed-top">
+  <div class="navbar-header">
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+    <a class="navbar-brand" href="week42-bs.html">Week 42 Solving differential equations and Convolutional (CNN)</a>
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+  <div class="navbar-collapse collapse navbar-responsive-collapse">
+    <ul class="nav navbar-nav navbar-right">
+      <li class="dropdown">
+        <a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
+        <ul class="dropdown-menu">
+     <!-- navigation toc: --> <li><a href="._week42-bs001.html#plan-for-week-42" style="font-size: 80%;">Plan for week 42</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs002.html#using-automatic-differentiation" style="font-size: 80%;">Using Automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs003.html#solving-odes-with-deep-learning" style="font-size: 80%;">Solving ODEs with Deep Learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs004.html#ordinary-differential-equations" style="font-size: 80%;">Ordinary Differential Equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs047.html#the-trial-solution" style="font-size: 80%;">The trial solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs006.html#minimization-process" style="font-size: 80%;">Minimization process</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs007.html#minimizing-the-cost-function-using-gradient-descent-and-automatic-differentiation" style="font-size: 80%;">Minimizing the cost function using gradient descent and automatic differentiation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs008.html#example-exponential-decay" style="font-size: 80%;">Example: Exponential decay</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs009.html#the-function-to-solve-for" style="font-size: 80%;">The function to solve for</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs047.html#the-trial-solution" style="font-size: 80%;">The trial solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs011.html#setup-of-network" style="font-size: 80%;">Setup of Network</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs012.html#reformulating-the-problem" style="font-size: 80%;">Reformulating the problem</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs013.html#more-technicalities" style="font-size: 80%;">More technicalities</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs038.html#more-details" style="font-size: 80%;">More details</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs015.html#a-possible-implementation-of-a-neural-network" style="font-size: 80%;">A possible implementation of a neural network</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs016.html#technicalities" style="font-size: 80%;">Technicalities</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs017.html#final-technicalities-i" style="font-size: 80%;">Final technicalities I</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs018.html#final-technicalities-ii" style="font-size: 80%;">Final technicalities II</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs019.html#final-technicalities-iii" style="font-size: 80%;">Final technicalities III</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs020.html#final-technicalities-iv" style="font-size: 80%;">Final technicalities IV</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs021.html#back-propagation" style="font-size: 80%;">Back propagation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs022.html#gradient-descent" style="font-size: 80%;">Gradient descent</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs023.html#the-code-for-solving-the-ode" style="font-size: 80%;">The code for solving the ODE</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs024.html#the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer" style="font-size: 80%;">The network with one input layer, specified number of hidden layers, and one output layer</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs025.html#example-population-growth" style="font-size: 80%;">Example: Population growth</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs026.html#setting-up-the-problem" style="font-size: 80%;">Setting up the problem</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs047.html#the-trial-solution" style="font-size: 80%;">The trial solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs028.html#the-program-using-autograd" style="font-size: 80%;">The program using Autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs029.html#using-forward-euler-to-solve-the-ode" style="font-size: 80%;">Using forward Euler to solve the ODE</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs030.html#example-solving-the-one-dimensional-poisson-equation" style="font-size: 80%;">Example: Solving the one dimensional Poisson equation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs031.html#the-specific-equation-to-solve-for" style="font-size: 80%;">The specific equation to solve for</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs032.html#solving-the-equation-using-autograd" style="font-size: 80%;">Solving the equation using Autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs033.html#comparing-with-a-numerical-scheme" style="font-size: 80%;">Comparing with a numerical scheme</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs034.html#setting-up-the-code" style="font-size: 80%;">Setting up the code</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs035.html#partial-differential-equations" style="font-size: 80%;">Partial Differential Equations</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs036.html#type-of-problem" style="font-size: 80%;">Type of problem</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs037.html#network-requirements" style="font-size: 80%;">Network requirements</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs038.html#more-details" style="font-size: 80%;">More details</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs039.html#example-the-diffusion-equation" style="font-size: 80%;">Example: The diffusion equation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs040.html#defining-the-problem" style="font-size: 80%;">Defining the problem</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs041.html#setting-up-the-network-using-autograd" style="font-size: 80%;">Setting up the network using Autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs042.html#setting-up-the-network-using-autograd-the-trial-solution" style="font-size: 80%;">Setting up the network using Autograd; The trial solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs043.html#why-the-jacobian" style="font-size: 80%;">Why the jacobian?</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs044.html#setting-up-the-network-using-autograd-the-full-program" style="font-size: 80%;">Setting up the network using Autograd; The full program</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs045.html#example-solving-the-wave-equation-with-neural-networks" style="font-size: 80%;">Example: Solving the wave equation with Neural Networks</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs046.html#the-problem-to-solve-for" style="font-size: 80%;">The problem to solve for</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs047.html#the-trial-solution" style="font-size: 80%;">The trial solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs048.html#the-analytical-solution" style="font-size: 80%;">The analytical solution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs049.html#solving-the-wave-equation-the-full-program-using-autograd" style="font-size: 80%;">Solving the wave equation - the full program using Autograd</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs050.html#resources-on-differential-equations-and-deep-learning" style="font-size: 80%;">Resources on differential equations and deep learning</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs051.html#convolutional-neural-networks-recognizing-images" style="font-size: 80%;">Convolutional Neural Networks (recognizing images)</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs052.html#what-is-the-difference" style="font-size: 80%;">What is the Difference</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs053.html#neural-networks-vs-cnns" style="font-size: 80%;">Neural Networks vs CNNs</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs054.html#why-cnns-for-images-sound-files-medical-images-from-ct-scans-etc" style="font-size: 80%;">Why CNNS for images, sound files, medical images from CT scans etc?</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs055.html#regular-nns-don-t-scale-well-to-full-images" style="font-size: 80%;">Regular NNs don’t scale well to full images</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs056.html#3d-volumes-of-neurons" style="font-size: 80%;">3D volumes of neurons</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs057.html#layers-used-to-build-cnns" style="font-size: 80%;">Layers used to build CNNs</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs058.html#transforming-images" style="font-size: 80%;">Transforming images</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs059.html#cnns-in-brief" style="font-size: 80%;">CNNs in brief</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs060.html#mathematics-of-cnns" style="font-size: 80%;">Mathematics of CNNs</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs061.html#convolution-examples-polynomial-multiplication" style="font-size: 80%;">Convolution Examples: Polynomial multiplication</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs062.html#efficient-polynomial-multiplication" style="font-size: 80%;">Efficient Polynomial Multiplication</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs063.html#a-more-efficient-way-of-coding-the-above-convolution" style="font-size: 80%;">A more efficient way of coding the above Convolution</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs064.html#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" style="font-size: 80%;">Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs065.html#principle-of-superposition" style="font-size: 80%;">Principle of Superposition</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs066.html#simple-code-example" style="font-size: 80%;">Simple Code Example</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs067.html#wrapping-up-fourier-transforms" style="font-size: 80%;">Wrapping up Fourier transforms</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs068.html#finding-the-coefficients" style="font-size: 80%;">Finding the Coefficients</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs069.html#final-words-on-fourier-transforms" style="font-size: 80%;">Final words on Fourier Transforms</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs070.html#two-dimensional-objects" style="font-size: 80%;">Two-dimensional Objects</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs071.html#cross-correlation" style="font-size: 80%;">Cross-Correlation</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs072.html#more-on-dimensionalities" style="font-size: 80%;">More on Dimensionalities</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs073.html#further-dimensionality-remarks" style="font-size: 80%;">Further Dimensionality Remarks</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs074.html#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs075.html#setting-it-up" style="font-size: 80%;">Setting it up</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs076.html#the-mnist-dataset-again" style="font-size: 80%;">The MNIST dataset again</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs077.html#strong-correlations" style="font-size: 80%;">Strong correlations</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs078.html#layers-of-a-cnn" style="font-size: 80%;">Layers of a CNN</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs079.html#systematic-reduction" style="font-size: 80%;">Systematic reduction</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs080.html#prerequisites-collect-and-pre-process-data" style="font-size: 80%;">Prerequisites: Collect and pre-process data</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs081.html#importing-keras-and-tensorflow" style="font-size: 80%;">Importing Keras and Tensorflow</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs082.html#running-with-keras" style="font-size: 80%;">Running with Keras</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs083.html#final-part" style="font-size: 80%;">Final part</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs084.html#final-visualization" style="font-size: 80%;">Final visualization</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs085.html#the-cifar01-data-set" style="font-size: 80%;">The CIFAR01 data set</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs086.html#verifying-the-data-set" style="font-size: 80%;">Verifying the data set</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs087.html#set-up-the-model" style="font-size: 80%;">Set up  the model</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs088.html#add-dense-layers-on-top" style="font-size: 80%;">Add Dense layers on top</a></li>
+     <!-- navigation toc: --> <li><a href="._week42-bs089.html#compile-and-train-the-model" style="font-size: 80%;">Compile and train the model</a></li>
+     <!-- navigation toc: --> <li><a href="#finally-evaluate-the-model" style="font-size: 80%;">Finally, evaluate the model</a></li>
+
+        </ul>
+      </li>
+    </ul>
+  </div>
+</div>
+</div> <!-- end of navigation bar -->
+
+<div class="container">
+
+<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
+
+<a name="part0090"></a>
+<!-- !split -->
+
+<h2 id="finally-evaluate-the-model" class="anchor">Finally, evaluate the model </h2>
+
+<p>
+
+<!-- code=python (!bc pycod) typeset with pygments style "default" -->
+<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%;"><span></span>plt<span style="color: #666666">.</span>plot(history<span style="color: #666666">.</span>history[<span style="color: #BA2121">&#39;accuracy&#39;</span>], label<span style="color: #666666">=</span><span style="color: #BA2121">&#39;accuracy&#39;</span>)
+plt<span style="color: #666666">.</span>plot(history<span style="color: #666666">.</span>history[<span style="color: #BA2121">&#39;val_accuracy&#39;</span>], label <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;val_accuracy&#39;</span>)
+plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&#39;Epoch&#39;</span>)
+plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&#39;Accuracy&#39;</span>)
+plt<span style="color: #666666">.</span>ylim([<span style="color: #666666">0.5</span>, <span style="color: #666666">1</span>])
+plt<span style="color: #666666">.</span>legend(loc<span style="color: #666666">=</span><span style="color: #BA2121">&#39;lower right&#39;</span>)
+
+test_loss, test_acc <span style="color: #666666">=</span> model<span style="color: #666666">.</span>evaluate(test_images,  test_labels, verbose<span style="color: #666666">=2</span>)
+
+<span style="color: #008000">print</span>(test_acc)
+</pre></div>
+<p>
+
+<p>
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