From 4294dd652a5a1354d552caa172db94619cabf141 Mon Sep 17 00:00:00 2001
From: StefanTodoran <StefanTodoran@users.noreply.github.com>
Date: Mon, 25 Nov 2024 17:31:42 +0000
Subject: [PATCH] deploy: ec94fe20fea1d0a9554ed813956661bd171e537a

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diff --git a/Chapter4-DeepLearning/mlgeo_4.4_RNN.html b/Chapter4-DeepLearning/mlgeo_4.4_RNN.html
index 501ad31..445c086 100644
--- a/Chapter4-DeepLearning/mlgeo_4.4_RNN.html
+++ b/Chapter4-DeepLearning/mlgeo_4.4_RNN.html
@@ -651,6 +651,11 @@ <h1 class="site-logo" id="site-title">ML Geo Curriculum</h1>
     </div>
     <nav id="bd-toc-nav" aria-label="Page">
         <ul class="visible nav section-nav flex-column">
+ <li class="toc-h2 nav-item toc-entry">
+  <a class="reference internal nav-link" href="#design-a-vanilla-rnn">
+   Design a vanilla RNN
+  </a>
+ </li>
  <li class="toc-h2 nav-item toc-entry">
   <a class="reference internal nav-link" href="#forecast-of-several-steps-ahead-how-far-can-you-predict-the-future">
    Forecast of several steps ahead: how far can you predict the future?
@@ -687,6 +692,11 @@ <h2> Contents </h2>
                         </div>
                         <nav aria-label="Page">
                             <ul class="visible nav section-nav flex-column">
+ <li class="toc-h2 nav-item toc-entry">
+  <a class="reference internal nav-link" href="#design-a-vanilla-rnn">
+   Design a vanilla RNN
+  </a>
+ </li>
  <li class="toc-h2 nav-item toc-entry">
   <a class="reference internal nav-link" href="#forecast-of-several-steps-ahead-how-far-can-you-predict-the-future">
    Forecast of several steps ahead: how far can you predict the future?
@@ -716,8 +726,8 @@ <h2> Contents </h2>
                 
   <section class="tex2jax_ignore mathjax_ignore" id="recurrent-neural-networks-processing-sequences">
 <h1>4.4  Recurrent Neural Networks: Processing sequences<a class="headerlink" href="#recurrent-neural-networks-processing-sequences" title="Permalink to this headline">#</a></h1>
-<p>They are used for time series predictions. Regular dense networks can also do it, and CNNs can also work for very long time series.
-A recurrent neuron  receives an input <em>and</em> the output from the neuron at the previous time step. Because each neuron learns from the previous time step, it has <em>memory</em>; but these simple cells have relatively short memory (10 cells about).
+<p>They are used for time series <em><strong>forecast</strong></em>. Regular dense networks can also do it, and CNNs can also work for very long time series.</p>
+<p>A recurrent neuron  receives an input <em>and</em> the output from the neuron at the previous time step. Because each neuron learns from the previous time step, it has <em>memory</em>; but these simple cells have relatively short memory (10 cells about).
 RNNs take in a sequence and output a sequence.</p>
 <p><img alt="RNN" src="../_images/rnn.svg" /></p>
 <p>From D2DL: example of an RNN with a hidden state.
@@ -727,14 +737,18 @@ <h1>4.4  Recurrent Neural Networks: Processing sequences<a class="headerlink" hr
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
 <span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
-<span class="kn">import</span> <span class="nn">tensorflow</span> <span class="k">as</span> <span class="nn">tf</span>
-<span class="kn">from</span> <span class="nn">tensorflow</span> <span class="kn">import</span> <span class="n">keras</span>
+<span class="kn">import</span> <span class="nn">torch</span>
 </pre></div>
 </div>
 </div>
 </div>
+<p>In time series forecasting, the goal is to predict future values based on historical data. Two important concepts in this process are context data and prediction length.</p>
+<ol class="simple">
+<li><p><strong>Context Data</strong> refers to the historical data used by the forecasting model to make predictions. This data provides the context or background information needed to understand the patterns, trends, and seasonality in the time series. The length of the context data is often referred to as the look-back window or input window.</p></li>
+<li><p><strong>Prediction length</strong> refers to the number of future time steps the model aims to predict. This is also known as the <em><strong>forecast horizon</strong></em>. The number of future time steps the model predicts. For example, if the forecast horizon is 5, the model predicts the next 5 time steps.</p></li>
+</ol>
 <p><strong>Synthetic data</strong></p>
-<p>Let’s create a synthetic time series</p>
+<p>Let’s create a synthetic time series. We will overlap 2 frequencies with noise.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">generate_time_series</span><span class="p">(</span><span class="n">batch_size</span><span class="p">,</span><span class="n">n_steps</span><span class="p">):</span>
@@ -743,112 +757,244 @@ <h1>4.4  Recurrent Neural Networks: Processing sequences<a class="headerlink" hr
     <span class="n">y</span> <span class="o">=</span> <span class="mf">0.5</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span> <span class="p">(</span><span class="n">t</span><span class="o">-</span><span class="n">off1</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">f1</span><span class="o">*</span><span class="mi">10</span><span class="o">+</span><span class="mi">10</span><span class="p">)</span> <span class="p">)</span> <span class="c1"># first wave</span>
     <span class="n">y</span> <span class="o">+=</span> <span class="mf">0.5</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span> <span class="p">(</span><span class="n">t</span><span class="o">-</span><span class="n">off2</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">f2</span><span class="o">*</span><span class="mi">20</span><span class="o">+</span><span class="mi">20</span><span class="p">)</span> <span class="p">)</span> <span class="c1"># second wave</span>
     <span class="n">y</span> <span class="o">+=</span> <span class="mf">0.3</span><span class="o">*</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">batch_size</span><span class="p">,</span><span class="n">n_steps</span><span class="p">)</span><span class="o">-</span><span class="mf">0.5</span><span class="p">)</span> <span class="c1"># noise</span>
-    <span class="k">return</span> <span class="n">y</span><span class="p">[</span><span class="o">...</span><span class="p">,</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> 
-<span class="c1"># here we added a dimension to the output time series because most ML algorithms can be multidimensional, but here we are just doing a single time series.</span>
-
-<span class="c1"># we generate 10k time series of 51 points.</span>
-<span class="n">n_steps</span><span class="o">=</span><span class="mi">50</span>
-<span class="n">y</span> <span class="o">=</span> <span class="n">generate_time_series</span><span class="p">(</span><span class="mi">10000</span><span class="p">,</span><span class="n">n_steps</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">y</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>  
 </pre></div>
 </div>
 </div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="mi">5000</span><span class="p">,:]);</span><span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># we generate 10k time series of context+prediction_horizon points.</span>
+<span class="n">context</span><span class="o">=</span><span class="mi">50</span>
+<span class="n">prediction_horizon</span><span class="o">=</span><span class="mi">10</span>
+<span class="n">data</span> <span class="o">=</span> <span class="n">generate_time_series</span><span class="p">(</span><span class="mi">10000</span><span class="p">,</span><span class="n">context</span><span class="o">+</span><span class="n">prediction_horizon</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
 </div>
-<p><strong>train-validation-test split</strong></p>
-<p>In forecasting problem, we do not want to shuffle the training and test set since we want to make sure test is a prediction from the past (training).</p>
-<p>The training data are time series of 50 points, the “label” or “model output” is the <strong>last value</strong> of the time series.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x_train</span><span class="p">,</span><span class="n">y_train</span> <span class="o">=</span> <span class="n">y</span><span class="p">[:</span><span class="mi">7000</span><span class="p">,:</span><span class="n">n_steps</span><span class="p">],</span><span class="n">y</span><span class="p">[:</span><span class="mi">7000</span><span class="p">,</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> 
-<span class="n">x_val</span><span class="p">,</span><span class="n">y_val</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="mi">7000</span><span class="p">:</span><span class="mi">9000</span><span class="p">,:</span><span class="n">n_steps</span><span class="p">],</span><span class="n">y</span><span class="p">[</span><span class="mi">7000</span><span class="p">:</span><span class="mi">9000</span><span class="p">,</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> 
-<span class="n">x_test</span><span class="p">,</span><span class="n">y_test</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="mi">9000</span><span class="p">:,:</span><span class="n">n_steps</span><span class="p">],</span><span class="n">y</span><span class="p">[</span><span class="mi">9000</span><span class="p">:,</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> 
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># plot some of the time series in a 2x3 grid</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span><span class="mi">4</span><span class="p">))</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">6</span><span class="p">):</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+    <span class="c1"># plot context data</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">context</span><span class="p">),</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">,:</span><span class="n">context</span><span class="p">],</span><span class="s1">&#39;b-&#39;</span><span class="p">,</span><span class="n">label</span><span class="o">=</span><span class="s1">&#39;context&#39;</span><span class="p">)</span>
+    <span class="c1"># plot prediction horizon</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">context</span><span class="p">,</span><span class="n">context</span><span class="o">+</span><span class="n">prediction_horizon</span><span class="p">),</span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="n">context</span><span class="p">:],</span><span class="s1">&#39;r-&#39;</span><span class="p">,</span><span class="n">label</span><span class="o">=</span><span class="s1">&#39;prediction&#39;</span><span class="p">)</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
 </pre></div>
 </div>
 </div>
 </div>
+<section id="design-a-vanilla-rnn">
+<h2>Design a vanilla RNN<a class="headerlink" href="#design-a-vanilla-rnn" title="Permalink to this headline">#</a></h2>
+<p>The RNN will take context</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n_steps</span><span class="p">),</span><span class="n">x_train</span><span class="p">[</span><span class="mi">5000</span><span class="p">,:],</span><span class="s1">&#39;b&#39;</span><span class="p">)</span>
-<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="mi">51</span><span class="p">,</span><span class="n">y_train</span><span class="p">[</span><span class="mi">5000</span><span class="p">],</span><span class="s1">&#39;r+&#39;</span><span class="p">)</span>
-<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">VanillaRNN</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">Module</span><span class="p">):</span>
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">input_size</span><span class="p">,</span> <span class="n">hidden_size</span><span class="p">,</span> <span class="n">output_size</span><span class="p">):</span>
+        <span class="nb">super</span><span class="p">(</span><span class="n">VanillaRNN</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">rnn</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">RNN</span><span class="p">(</span><span class="n">input_size</span><span class="p">,</span> <span class="n">hidden_size</span><span class="p">,</span> <span class="n">batch_first</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> <span class="c1"># RNN layer, batch_size is the first dimension</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">fc</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">hidden_size</span><span class="p">,</span> <span class="n">output_size</span><span class="p">)</span> <span class="c1"># Fully connected layer</span>
+    
+    <span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
+        <span class="n">out</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rnn</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="c1"># out: tensor of shape (batch_size, seq_length, hidden_size)</span>
+        <span class="n">out</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">fc</span><span class="p">(</span><span class="n">out</span><span class="p">[:,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="p">:])</span> <span class="c1"># out: tensor of shape (batch_size, output_size)</span>
+        <span class="k">return</span> <span class="n">out</span>
+
+<span class="k">def</span> <span class="nf">create_rnn_and_data</span><span class="p">(</span><span class="n">time_series</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">prediction_horizon</span><span class="p">):</span>
+    <span class="n">input_size</span> <span class="o">=</span> <span class="n">time_series</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+    <span class="n">hidden_size</span> <span class="o">=</span> <span class="mi">20</span>  <span class="c1"># You can adjust this value</span>
+    <span class="n">output_size</span> <span class="o">=</span> <span class="n">prediction_horizon</span>
+    
+    <span class="n">model</span> <span class="o">=</span> <span class="n">VanillaRNN</span><span class="p">(</span><span class="n">input_size</span><span class="p">,</span> <span class="n">hidden_size</span><span class="p">,</span> <span class="n">output_size</span><span class="p">)</span>
+    
+    <span class="c1"># Prepare the input and target data</span>
+    <span class="n">x</span> <span class="o">=</span> <span class="n">time_series</span><span class="p">[:,</span> <span class="p">:</span><span class="n">context</span><span class="p">,</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span> <span class="p">]</span> <span class="c1"># Add a dummy dimension for the input size</span>
+    <span class="n">y</span> <span class="o">=</span> <span class="n">time_series</span><span class="p">[:,</span> <span class="n">context</span><span class="p">:</span><span class="n">context</span> <span class="o">+</span> <span class="n">prediction_horizon</span><span class="p">]</span>
+    
+    <span class="k">return</span> <span class="n">model</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span>
 </pre></div>
 </div>
 </div>
 </div>
-<p>We can use the past values to predict the state, called <em>naive forecasting</em>:</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">y_pred</span><span class="o">=</span><span class="n">x_val</span><span class="p">[:,</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">model</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">create_rnn_and_data</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">context</span><span class="p">,</span> <span class="n">prediction_horizon</span><span class="p">)</span>
+
+<span class="c1"># Print model summary</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">model</span><span class="p">)</span>
 </pre></div>
 </div>
-<p>Or we can use a fully connected network and predict the value as a MLP regression:</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">model</span><span class="o">.</span><span class="n">keras</span><span class="o">.</span><span class="n">models</span><span class="o">.</span><span class="n">Sequential</span><span class="p">([</span><span class="n">keras</span><span class="o">.</span><span class="n">layers</span><span class="o">.</span><span class="n">Flatten</span><span class="p">(</span><span class="n">input_shape</span><span class="o">=</span><span class="p">[</span><span class="mi">50</span><span class="p">,</span><span class="mi">1</span><span class="p">]),</span>
-                              <span class="n">keras</span><span class="o">.</span><span class="n">layers</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">1</span><span class="p">)])</span>
+</div>
+</div>
+<p>Now prepare the training function</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">train</span><span class="p">(</span><span class="n">model</span><span class="p">,</span> <span class="n">x_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">x_val</span><span class="p">,</span> <span class="n">y_val</span><span class="p">,</span> <span class="n">n_epochs</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mf">0.001</span><span class="p">):</span>
+
+    <span class="sd">&#39;&#39;&#39;</span>
+<span class="sd">    Function to train the model.</span>
+
+<span class="sd">    Parameters:</span>
+<span class="sd">    model: torch.nn.Module</span>
+<span class="sd">        The model to train</span>
+<span class="sd">    x_train: np.ndarray</span>
+<span class="sd">        The input data for training (context)</span>
+<span class="sd">    y_train: np.ndarray</span>
+<span class="sd">        The target data for training (prediction horizon)</span>
+<span class="sd">    x_val: np.ndarray</span>
+<span class="sd">        The input data for validation (context)</span>
+<span class="sd">    y_val: np.ndarray</span>
+<span class="sd">        The target data for validation (prediction horizon)</span>
+<span class="sd">    n_epochs: int</span>
+<span class="sd">        The number of epochs</span>
+<span class="sd">    lr: float</span>
+<span class="sd">        The learning rate</span>
+
+<span class="sd">    Returns:</span>
+<span class="sd">    train_losses: list</span>
+<span class="sd">        The training losses for each epoch</span>
+<span class="sd">    val_losses: list</span>
+<span class="sd">        The validation losses for each epoch    </span>
+<span class="sd">    </span>
+<span class="sd">    </span>
+<span class="sd">    &#39;&#39;&#39;</span>
+
+    <span class="n">optimizer</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">optim</span><span class="o">.</span><span class="n">Adam</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">(),</span> <span class="n">lr</span><span class="o">=</span><span class="n">lr</span><span class="p">)</span>
+    <span class="n">loss_fn</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">MSELoss</span><span class="p">()</span>
+    <span class="n">train_losses</span> <span class="o">=</span> <span class="p">[]</span>
+    <span class="n">val_losses</span> <span class="o">=</span> <span class="p">[]</span>
+    
+    <span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_epochs</span><span class="p">):</span>
+        <span class="n">model</span><span class="o">.</span><span class="n">train</span><span class="p">()</span>
+        <span class="n">optimizer</span><span class="o">.</span><span class="n">zero_grad</span><span class="p">()</span>
+        <span class="n">y_pred</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">x_train</span><span class="p">)</span><span class="o">.</span><span class="n">float</span><span class="p">())</span>
+        <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Shape of outputs: </span><span class="si">{</span><span class="n">y_pred</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+        <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Shape of y_train: </span><span class="si">{</span><span class="n">y_train</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+
+        <span class="n">loss</span> <span class="o">=</span> <span class="n">loss_fn</span><span class="p">(</span><span class="n">y_pred</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">y_train</span><span class="p">)</span><span class="o">.</span><span class="n">float</span><span class="p">())</span>
+        <span class="n">train_losses</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">loss</span><span class="o">.</span><span class="n">item</span><span class="p">())</span>
+        <span class="n">loss</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
+        <span class="n">optimizer</span><span class="o">.</span><span class="n">step</span><span class="p">()</span>
+        
+        <span class="k">if</span> <span class="n">epoch</span> <span class="o">%</span> <span class="mi">10</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">model</span><span class="o">.</span><span class="n">eval</span><span class="p">()</span>
+            <span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">():</span>
+                <span class="n">y_val_pred</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">x_val</span><span class="p">)</span><span class="o">.</span><span class="n">float</span><span class="p">())</span>
+                <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Shape of val_outputs: </span><span class="si">{</span><span class="n">y_val_pred</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+                <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Shape of y_val: </span><span class="si">{</span><span class="n">y_val</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+  
+                <span class="n">val_loss</span> <span class="o">=</span> <span class="n">loss_fn</span><span class="p">(</span><span class="n">y_val_pred</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">y_val</span><span class="p">)</span><span class="o">.</span><span class="n">float</span><span class="p">())</span>
+                <span class="n">val_losses</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">val_loss</span><span class="o">.</span><span class="n">item</span><span class="p">())</span>
+            <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Epoch </span><span class="si">{</span><span class="n">epoch</span><span class="si">}</span><span class="s1">, Loss </span><span class="si">{</span><span class="n">loss</span><span class="o">.</span><span class="n">item</span><span class="p">()</span><span class="si">:</span><span class="s1">.6f</span><span class="si">}</span><span class="s1">, Val loss </span><span class="si">{</span><span class="n">val_loss</span><span class="o">.</span><span class="n">item</span><span class="p">()</span><span class="si">:</span><span class="s1">.6f</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
+    
+    <span class="k">return</span> <span class="n">train_losses</span><span class="p">,</span> <span class="n">val_losses</span>
 </pre></div>
 </div>
-<p>They don’t do too bad in this problem. The simple block is a <code class="docutils literal notranslate"><span class="pre">simpleRNN</span></code>. The simplest recurrent neuron is a <code class="docutils literal notranslate"><span class="pre">SimpleRNN(1,input_shape=[None,1])</span></code> that takes any input scalar since it can process any number of time steps. The default activation function is <code class="docutils literal notranslate"><span class="pre">tanh</span></code>. To return a time series, and not its final output, you need to set <code class="docutils literal notranslate"><span class="pre">return_sequences=True</span></code>. It turns out that the simplest and single recurrent neuron won’t work. So we stack several simpleRNNs.</p>
+</div>
+</div>
+<p>Train the VanillaRNN by first splitting the data between training and validation data</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">model</span><span class="o">=</span><span class="n">keras</span><span class="o">.</span><span class="n">models</span><span class="o">.</span><span class="n">Sequential</span><span class="p">([</span>
-    <span class="n">keras</span><span class="o">.</span><span class="n">layers</span><span class="o">.</span><span class="n">SimpleRNN</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span><span class="n">input_shape</span><span class="o">=</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span><span class="n">return_sequences</span><span class="o">=</span><span class="kc">True</span><span class="p">),</span>
-    <span class="n">keras</span><span class="o">.</span><span class="n">layers</span><span class="o">.</span><span class="n">SimpleRNN</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span><span class="n">return_sequences</span><span class="o">=</span><span class="kc">True</span><span class="p">),</span>
-    <span class="n">keras</span><span class="o">.</span><span class="n">layers</span><span class="o">.</span><span class="n">SimpleRNN</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
-    <span class="p">])</span>
-<span class="n">model</span><span class="o">.</span><span class="n">summary</span><span class="p">()</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">y</span><span class="o">.</span><span class="n">shape</span>
 </pre></div>
 </div>
 </div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">model</span><span class="o">.</span><span class="n">compile</span><span class="p">(</span><span class="n">optimizer</span><span class="o">=</span><span class="s1">&#39;adam&#39;</span><span class="p">,</span><span class="n">loss</span><span class="o">=</span><span class="s1">&#39;mse&#39;</span><span class="p">,</span><span class="n">metrics</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;mse&#39;</span><span class="p">])</span>
-<span class="n">history</span><span class="o">=</span><span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">x_train</span><span class="p">,</span><span class="n">y_train</span><span class="p">,</span><span class="n">validation_data</span><span class="o">=</span><span class="p">(</span><span class="n">x_val</span><span class="p">,</span><span class="n">y_val</span><span class="p">),</span> <span class="n">epochs</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="mi">128</span><span class="p">)</span> 
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">prediction_horizon</span><span class="p">,</span> <span class="n">context</span>
 </pre></div>
 </div>
 </div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">history</span><span class="o">.</span><span class="n">history</span><span class="p">)</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span><span class="mi">5</span><span class="p">))</span>
-<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
-<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;epochs&#39;</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">data</span><span class="o">.</span><span class="n">shape</span>
 </pre></div>
 </div>
 </div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">model</span><span class="o">=</span><span class="n">keras</span><span class="o">.</span><span class="n">models</span><span class="o">.</span><span class="n">Sequential</span><span class="p">([</span>
-    <span class="n">keras</span><span class="o">.</span><span class="n">layers</span><span class="o">.</span><span class="n">SimpleRNN</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span><span class="n">input_shape</span><span class="o">=</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span><span class="n">return_sequences</span><span class="o">=</span><span class="kc">True</span><span class="p">),</span>
-    <span class="n">keras</span><span class="o">.</span><span class="n">layers</span><span class="o">.</span><span class="n">SimpleRNN</span><span class="p">(</span><span class="mi">20</span><span class="p">),</span>
-    <span class="n">keras</span><span class="o">.</span><span class="n">layers</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
-    <span class="p">])</span>
-<span class="n">model</span><span class="o">.</span><span class="n">summary</span><span class="p">()</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># split y into training and validation sets</span>
+<span class="n">n_train</span> <span class="o">=</span> <span class="mi">7000</span>
+<span class="n">x_train</span><span class="p">,</span> <span class="n">y_train</span> <span class="o">=</span> <span class="n">data</span><span class="p">[:</span><span class="n">n_train</span><span class="p">,</span> <span class="p">:</span><span class="n">context</span><span class="p">],</span> <span class="n">data</span><span class="p">[:</span><span class="n">n_train</span><span class="p">,</span> <span class="n">context</span><span class="p">:</span><span class="n">context</span> <span class="o">+</span> <span class="n">prediction_horizon</span><span class="p">]</span>
+<span class="n">x_val</span><span class="p">,</span> <span class="n">y_val</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">n_train</span><span class="p">:,</span> <span class="p">:</span><span class="n">context</span><span class="p">],</span> <span class="n">data</span><span class="p">[</span><span class="n">n_train</span><span class="p">:,</span> <span class="n">context</span><span class="p">:</span><span class="n">context</span> <span class="o">+</span> <span class="n">prediction_horizon</span><span class="p">]</span>
 </pre></div>
 </div>
 </div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">model</span><span class="o">.</span><span class="n">compile</span><span class="p">(</span><span class="n">optimizer</span><span class="o">=</span><span class="s1">&#39;adam&#39;</span><span class="p">,</span><span class="n">loss</span><span class="o">=</span><span class="s1">&#39;mse&#39;</span><span class="p">,</span><span class="n">metrics</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;mse&#39;</span><span class="p">])</span>
-<span class="n">history</span><span class="o">=</span><span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">x_train</span><span class="p">,</span><span class="n">y_train</span><span class="p">,</span><span class="n">validation_data</span><span class="o">=</span><span class="p">(</span><span class="n">x_val</span><span class="p">,</span><span class="n">y_val</span><span class="p">),</span> <span class="n">epochs</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="mi">128</span><span class="p">)</span> 
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x_train</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">y_train</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">x_val</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">y_val</span><span class="o">.</span><span class="n">shape</span>
+</pre></div>
+</div>
+</div>
+</div>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># remove the last dimnsion of y_train and y_val</span>
+<span class="n">y_train</span> <span class="o">=</span> <span class="n">y_train</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
+<span class="n">y_val</span> <span class="o">=</span> <span class="n">y_val</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
+</pre></div>
+</div>
+</div>
+</div>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">train_losses</span><span class="p">,</span> <span class="n">val_losses</span> <span class="o">=</span> <span class="n">train</span><span class="p">(</span><span class="n">model</span><span class="p">,</span> <span class="n">x_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">x_val</span><span class="p">,</span> <span class="n">y_val</span><span class="p">,</span> <span class="n">n_epochs</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mf">0.001</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">history</span><span class="o">.</span><span class="n">history</span><span class="p">)</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span><span class="mi">5</span><span class="p">))</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># plot the loss curves</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">train_losses</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;train&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">val_losses</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;val&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
 <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
-<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;epochs&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">yscale</span><span class="p">(</span><span class="s1">&#39;log&#39;</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">y_val</span><span class="o">.</span><span class="n">shape</span>
 </pre></div>
 </div>
 </div>
 </div>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># now show examples on the validation set with the ground truth and the prediction</span>
+<span class="c1"># add a dimension to x_val</span>
+<span class="c1"># x_val = x_val[...,np.newaxis]</span>
+<span class="n">model</span><span class="o">.</span><span class="n">eval</span><span class="p">()</span>
+<span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">():</span>
+    <span class="n">y_val_pred</span> <span class="o">=</span> <span class="n">model</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">x_val</span><span class="p">)</span><span class="o">.</span><span class="n">float</span><span class="p">())</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
+
+<span class="c1"># plot some of the time series in a 2x3 grid</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span><span class="mi">4</span><span class="p">))</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">6</span><span class="p">):</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">x_val</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="n">y_val</span><span class="p">[</span><span class="n">i</span><span class="p">]]),</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;GT&#39;</span><span class="p">)</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">x_val</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="n">y_val_pred</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span><span class="o">.</span><span class="n">T</span><span class="p">]),</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Prediction&#39;</span><span class="p">)</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
 <section id="forecast-of-several-steps-ahead-how-far-can-you-predict-the-future">
 <h2>Forecast of several steps ahead: how far can you predict the future?<a class="headerlink" href="#forecast-of-several-steps-ahead-how-far-can-you-predict-the-future" title="Permalink to this headline">#</a></h2>
 <p>We will try and predict 10 steps ahead. The early part of the forecast will be a lot better than the later part of the forecast as uncertainties increase.</p>
diff --git a/Chapter4-DeepLearning/mlgeo_4.6_AutoEncoder.html b/Chapter4-DeepLearning/mlgeo_4.6_AutoEncoder.html
index bbd930e..5829858 100644
--- a/Chapter4-DeepLearning/mlgeo_4.6_AutoEncoder.html
+++ b/Chapter4-DeepLearning/mlgeo_4.6_AutoEncoder.html
@@ -809,6 +809,48 @@ <h1>4.6 Auto-encoders<a class="headerlink" href="#auto-encoders" title="Permalin
 </pre></div>
 </div>
 </div>
+<div class="cell_output docutils container">
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz
+Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz to ./FashionMNIST/raw/train-images-idx3-ubyte.gz
+</pre></div>
+</div>
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|██████████| 26421880/26421880 [00:02&lt;00:00, 10417165.17it/s]
+</pre></div>
+</div>
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Extracting ./FashionMNIST/raw/train-images-idx3-ubyte.gz to ./FashionMNIST/raw
+
+Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz
+Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz to ./FashionMNIST/raw/train-labels-idx1-ubyte.gz
+</pre></div>
+</div>
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|██████████| 29515/29515 [00:00&lt;00:00, 175578.14it/s]
+</pre></div>
+</div>
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Extracting ./FashionMNIST/raw/train-labels-idx1-ubyte.gz to ./FashionMNIST/raw
+
+Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz
+Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz to ./FashionMNIST/raw/t10k-images-idx3-ubyte.gz
+</pre></div>
+</div>
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|██████████| 4422102/4422102 [00:01&lt;00:00, 3538808.13it/s]
+</pre></div>
+</div>
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Extracting ./FashionMNIST/raw/t10k-images-idx3-ubyte.gz to ./FashionMNIST/raw
+
+Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz
+Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz to ./FashionMNIST/raw/t10k-labels-idx1-ubyte.gz
+</pre></div>
+</div>
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|██████████| 5148/5148 [00:00&lt;00:00, 8317518.10it/s]
+</pre></div>
+</div>
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Extracting ./FashionMNIST/raw/t10k-labels-idx1-ubyte.gz to ./FashionMNIST/raw
+</pre></div>
+</div>
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
+</pre></div>
+</div>
+</div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -820,8 +862,7 @@ <h1>4.6 Auto-encoders<a class="headerlink" href="#auto-encoders" title="Permalin
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;torch.utils.data.dataset.Subset object at 0x2af90f8b0&gt;
-torch.Size([50, 1, 28, 28])
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>torch.Size([50, 1, 28, 28])
 </pre></div>
 </div>
 </div>
@@ -1005,11 +1046,11 @@ <h1>4.6 Auto-encoders<a class="headerlink" href="#auto-encoders" title="Permalin
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[Epoch 1] train loss: 0.596 - val loss: 0.594
-[Epoch 2] train loss: 0.596 - val loss: 0.593
-[Epoch 3] train loss: 0.595 - val loss: 0.593
-[Epoch 4] train loss: 0.595 - val loss: 0.593
-[Epoch 5] train loss: 0.595 - val loss: 0.593
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[Epoch 1] train loss: 0.617 - val loss: 0.603
+[Epoch 2] train loss: 0.599 - val loss: 0.599
+[Epoch 3] train loss: 0.596 - val loss: 0.597
+[Epoch 4] train loss: 0.595 - val loss: 0.597
+[Epoch 5] train loss: 0.595 - val loss: 0.596
 </pre></div>
 </div>
 </div>
@@ -1023,7 +1064,7 @@ <h1>4.6 Auto-encoders<a class="headerlink" href="#auto-encoders" title="Permalin
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x2d0523130&gt;]
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x3154edbb0&gt;]
 </pre></div>
 </div>
 <img alt="../_images/mlgeo_4.6_AutoEncoder_11_1.png" src="../_images/mlgeo_4.6_AutoEncoder_11_1.png" />
@@ -1141,11 +1182,11 @@ <h1>Convolutional autoencoder<a class="headerlink" href="#convolutional-autoenco
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[Epoch 1] train loss: 0.609 - val loss: 0.574
-[Epoch 2] train loss: 0.574 - val loss: 0.571
-[Epoch 3] train loss: 0.572 - val loss: 0.570
-[Epoch 4] train loss: 0.571 - val loss: 0.569
-[Epoch 5] train loss: 0.571 - val loss: 0.569
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[Epoch 1] train loss: 0.611 - val loss: 0.578
+[Epoch 2] train loss: 0.574 - val loss: 0.574
+[Epoch 3] train loss: 0.572 - val loss: 0.573
+[Epoch 4] train loss: 0.571 - val loss: 0.573
+[Epoch 5] train loss: 0.571 - val loss: 0.572
 </pre></div>
 </div>
 </div>
@@ -1176,7 +1217,7 @@ <h1>Denoising auto-encoder<a class="headerlink" href="#denoising-auto-encoder" t
 
         <span class="c1"># Encoder</span>
         <span class="bp">self</span><span class="o">.</span><span class="n">encoder</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Sequential</span><span class="p">(</span>
-            <span class="n">nn</span><span class="o">.</span><span class="n">DropOut</span><span class="p">(</span><span class="mf">0.2</span><span class="p">),</span> <span class="c1">#  Dropout layer to mimic noisy data</span>
+            <span class="n">nn</span><span class="o">.</span><span class="n">Dropout</span><span class="p">(</span><span class="mf">0.2</span><span class="p">),</span> <span class="c1">#  Dropout layer to mimic noisy data</span>
             <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="n">kernel_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span>
             <span class="n">nn</span><span class="o">.</span><span class="n">ReLU</span><span class="p">(),</span>
             <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">32</span><span class="p">,</span> <span class="n">kernel_size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="mi">1</span><span class="p">),</span>
@@ -1198,70 +1239,23 @@ <h1>Denoising auto-encoder<a class="headerlink" href="#denoising-auto-encoder" t
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Model: &quot;sequential_15&quot;
-_________________________________________________________________
-Layer (type)                 Output Shape              Param #   
-=================================================================
-encoder_cnn (Sequential)     (None, 3, 3, 64)          23296     
-_________________________________________________________________
-decoder_cnn (Sequential)     (None, 28, 28)            23233     
-=================================================================
-Total params: 46,529
-Trainable params: 46,529
-Non-trainable params: 0
-_________________________________________________________________
+</div>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Instantiate the model</span>
+<span class="n">model_denoised_CNNAE</span> <span class="o">=</span> <span class="n">DenoiseCNNAE</span><span class="p">()</span>
 </pre></div>
 </div>
 </div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">loss_val</span><span class="p">)</span> <span class="o">=</span> <span class="n">train</span><span class="p">(</span><span class="n">DenoiseCNNAE</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span><span class="n">loaded_train</span><span class="p">,</span> <span class="n">loaded_test</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">loss_val</span><span class="p">)</span> <span class="o">=</span> <span class="n">train</span><span class="p">(</span><span class="n">model_denoised_CNNAE</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span><span class="n">loaded_train</span><span class="p">,</span> <span class="n">loaded_test</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch 1/20
-1719/1719 [==============================] - 25s 14ms/step - loss: 0.2551 - val_loss: 0.2533
-Epoch 2/20
-1719/1719 [==============================] - 26s 15ms/step - loss: 0.2565 - val_loss: 0.2543
-Epoch 3/20
-1719/1719 [==============================] - 26s 15ms/step - loss: 0.2554 - val_loss: 0.2525
-Epoch 4/20
-1719/1719 [==============================] - 25s 14ms/step - loss: 0.2551 - val_loss: 0.2531
-Epoch 5/20
-1719/1719 [==============================] - 26s 15ms/step - loss: 0.2557 - val_loss: 0.2524
-Epoch 6/20
-1719/1719 [==============================] - 27s 16ms/step - loss: 0.2550 - val_loss: 0.2526
-Epoch 7/20
-1719/1719 [==============================] - 26s 15ms/step - loss: 0.2552 - val_loss: 0.2539
-Epoch 8/20
-1719/1719 [==============================] - 26s 15ms/step - loss: 0.2549 - val_loss: 0.2521
-Epoch 9/20
-1719/1719 [==============================] - 26s 15ms/step - loss: 0.2558 - val_loss: 0.2527
-Epoch 10/20
-1719/1719 [==============================] - 25s 15ms/step - loss: 0.2552 - val_loss: 0.2524
-Epoch 11/20
-1719/1719 [==============================] - 25s 15ms/step - loss: 0.2548 - val_loss: 0.2525
-Epoch 12/20
-1719/1719 [==============================] - 25s 15ms/step - loss: 0.2564 - val_loss: 0.2523
-Epoch 13/20
-1719/1719 [==============================] - 23s 13ms/step - loss: 0.2556 - val_loss: 0.2522
-Epoch 14/20
-1719/1719 [==============================] - 23s 13ms/step - loss: 0.2550 - val_loss: 0.2520
-Epoch 15/20
-1719/1719 [==============================] - 23s 13ms/step - loss: 0.2550 - val_loss: 0.2524
-Epoch 16/20
-1719/1719 [==============================] - 23s 13ms/step - loss: 0.2553 - val_loss: 0.2526
-Epoch 17/20
-1719/1719 [==============================] - 23s 13ms/step - loss: 0.2541 - val_loss: 0.2533
-Epoch 18/20
-1719/1719 [==============================] - 23s 14ms/step - loss: 0.2550 - val_loss: 0.2520
-Epoch 19/20
-1719/1719 [==============================] - 22s 13ms/step - loss: 0.2555 - val_loss: 0.2519
-Epoch 20/20
-1719/1719 [==============================] - 23s 13ms/step - loss: 0.2550 - val_loss: 0.2540
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[Epoch 1] train loss: 0.612 - val loss: 0.585
 </pre></div>
 </div>
 </div>
@@ -1273,7 +1267,7 @@ <h1>Denoising auto-encoder<a class="headerlink" href="#denoising-auto-encoder" t
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/mlgeo_4.6_AutoEncoder_24_0.png" src="../_images/mlgeo_4.6_AutoEncoder_24_0.png" />
+<img alt="../_images/mlgeo_4.6_AutoEncoder_25_0.png" src="../_images/mlgeo_4.6_AutoEncoder_25_0.png" />
 </div>
 </div>
 </section>
diff --git a/Chapter4-DeepLearning/mlgeo_4.7_PINN.html b/Chapter4-DeepLearning/mlgeo_4.7_PINN.html
index a6a35da..56c3af3 100644
--- a/Chapter4-DeepLearning/mlgeo_4.7_PINN.html
+++ b/Chapter4-DeepLearning/mlgeo_4.7_PINN.html
@@ -1100,29 +1100,49 @@ <h2>Create Synthetic Data<a class="headerlink" href="#create-synthetic-data" tit
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">net</span> <span class="o">=</span> <span class="n">Net</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span> <span class="n">loss2</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="mi">20000</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-5</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">DEVICE</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">net</span> <span class="o">=</span> <span class="n">Net</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span> <span class="n">loss2</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="mi">2000</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">DEVICE</span><span class="p">)</span>
 
 <span class="n">losses</span> <span class="o">=</span> <span class="n">net</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">T</span><span class="p">)</span>
 
 <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">losses</span><span class="p">)</span>
-<span class="n">plt</span><span class="o">.</span><span class="n">yscale</span><span class="p">(</span><span class="s1">&#39;log&#39;</span><span class="p">)</span>
+<span class="c1"># plt.yscale(&#39;log&#39;)</span>
 </pre></div>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch 0/20000, loss: 4713.87
-Epoch 2000/20000, loss: 2509.96
-Epoch 4000/20000, loss: 2140.79
-Epoch 6000/20000, loss: 724.98
-Epoch 8000/20000, loss: 87.96
-Epoch 10000/20000, loss: 1.94
-Epoch 12000/20000, loss: 0.40
-Epoch 14000/20000, loss: 0.35
-Epoch 16000/20000, loss: 0.34
-Epoch 18000/20000, loss: 0.33
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch 0/2000, loss: 4816.01
+Epoch 200/2000, loss: 2511.37
+Epoch 400/2000, loss: 2074.74
+Epoch 600/2000, loss: 613.42
+Epoch 800/2000, loss: 95.27
+Epoch 1000/2000, loss: 25.84
+Epoch 1200/2000, loss: 8.47
+Epoch 1400/2000, loss: 3.51
+Epoch 1600/2000, loss: 2.66
+Epoch 1800/2000, loss: 2.31
+</pre></div>
+</div>
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x16a576310&gt;]
 </pre></div>
 </div>
-<img alt="../_images/mlgeo_4.7_PINN_7_1.png" src="../_images/mlgeo_4.7_PINN_7_1.png" />
+<img alt="../_images/mlgeo_4.7_PINN_7_2.png" src="../_images/mlgeo_4.7_PINN_7_2.png" />
+</div>
+</div>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">prediction_temp_baseline</span> <span class="o">=</span> <span class="n">net</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">times</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">times</span><span class="p">,</span> <span class="n">prediction_temp_baseline</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="s1">&#39;o&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s1">&#39;Prediction&#39;</span><span class="p">,</span> <span class="s1">&#39;Training data&#39;</span><span class="p">])</span>
+</pre></div>
+</div>
+</div>
+<div class="cell_output docutils container">
+<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;matplotlib.legend.Legend at 0x16a5cf580&gt;
+</pre></div>
+</div>
+<img alt="../_images/mlgeo_4.7_PINN_8_1.png" src="../_images/mlgeo_4.7_PINN_8_1.png" />
 </div>
 </div>
 <div class="cell docutils container">
@@ -1146,32 +1166,32 @@ <h2>Create Synthetic Data<a class="headerlink" href="#create-synthetic-data" tit
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch 0/20000, loss: 11220.99
-Epoch 2000/20000, loss: 3922.64
-Epoch 4000/20000, loss: 2426.29
-Epoch 6000/20000, loss: 1615.85
-Epoch 8000/20000, loss: 1198.53
-Epoch 10000/20000, loss: 1020.56
-Epoch 12000/20000, loss: 923.80
-Epoch 14000/20000, loss: 848.24
-Epoch 16000/20000, loss: 783.72
-Epoch 18000/20000, loss: 719.29
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch 0/20000, loss: 11694.52
+Epoch 2000/20000, loss: 4116.99
+Epoch 4000/20000, loss: 2410.78
+Epoch 6000/20000, loss: 1415.76
+Epoch 8000/20000, loss: 904.16
+Epoch 10000/20000, loss: 697.12
+Epoch 12000/20000, loss: 616.28
+Epoch 14000/20000, loss: 566.81
+Epoch 16000/20000, loss: 523.32
+Epoch 18000/20000, loss: 484.77
 </pre></div>
 </div>
-<img alt="../_images/mlgeo_4.7_PINN_9_1.png" src="../_images/mlgeo_4.7_PINN_9_1.png" />
+<img alt="../_images/mlgeo_4.7_PINN_10_1.png" src="../_images/mlgeo_4.7_PINN_10_1.png" />
 </div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">predsreg</span> <span class="o">=</span> <span class="n">netreg</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">times</span><span class="p">)</span>
 
-<span class="n">preds</span> <span class="o">=</span> <span class="n">net</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">times</span><span class="p">)</span>
+<span class="n">prediction_temp_regularized</span> <span class="o">=</span> <span class="n">netreg</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">times</span><span class="p">)</span>
 <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">times</span><span class="p">,</span> <span class="n">temps</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
 <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="s1">&#39;o&#39;</span><span class="p">)</span>
-<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">times</span><span class="p">,</span> <span class="n">preds</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
-<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">times</span><span class="p">,</span> <span class="n">predsreg</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">times</span><span class="p">,</span> <span class="n">prediction_temp_regularized</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">times</span><span class="p">,</span> <span class="n">prediction_temp_baseline</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
 
-<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">labels</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;Equation&#39;</span><span class="p">,</span><span class="s1">&#39;Training data&#39;</span><span class="p">,</span> <span class="s1">&#39;Network&#39;</span><span class="p">,</span> <span class="s1">&#39;L2 Network&#39;</span><span class="p">])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">labels</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;Equation&#39;</span><span class="p">,</span><span class="s1">&#39;Training data&#39;</span><span class="p">,</span> <span class="s1">&#39;Regularized&#39;</span><span class="p">,</span> <span class="s1">&#39;Baseline&#39;</span><span class="p">])</span>
 <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Temperature (C)&#39;</span><span class="p">)</span>
 <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Time (s)&#39;</span><span class="p">)</span>
 </pre></div>
@@ -1181,7 +1201,7 @@ <h2>Create Synthetic Data<a class="headerlink" href="#create-synthetic-data" tit
 <div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0.5, 0, &#39;Time (s)&#39;)
 </pre></div>
 </div>
-<img alt="../_images/mlgeo_4.7_PINN_10_1.png" src="../_images/mlgeo_4.7_PINN_10_1.png" />
+<img alt="../_images/mlgeo_4.7_PINN_11_1.png" src="../_images/mlgeo_4.7_PINN_11_1.png" />
 </div>
 </div>
 </section>
@@ -1201,28 +1221,28 @@ <h2>PINN<a class="headerlink" href="#pinn" title="Permalink to this headline">#<
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">net</span> <span class="o">=</span> <span class="n">Net</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span> <span class="n">loss2</span><span class="o">=</span><span class="n">physics_loss</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="mi">30000</span><span class="p">,</span> <span class="n">loss2_weight</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-5</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">DEVICE</span><span class="p">)</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">net_PINN</span> <span class="o">=</span> <span class="n">Net</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span> <span class="n">loss2</span><span class="o">=</span><span class="n">physics_loss</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="mi">10000</span><span class="p">,</span> <span class="n">loss2_weight</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">lr</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">DEVICE</span><span class="p">)</span>
 
-<span class="n">losses</span> <span class="o">=</span> <span class="n">net</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">T</span><span class="p">)</span>
+<span class="n">losses</span> <span class="o">=</span> <span class="n">net_PINN</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">T</span><span class="p">)</span>
 <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">losses</span><span class="p">)</span>
 <span class="n">plt</span><span class="o">.</span><span class="n">yscale</span><span class="p">(</span><span class="s1">&#39;log&#39;</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch 0/30000, loss: 4776.84
-Epoch 3000/30000, loss: 2437.13
-Epoch 6000/30000, loss: 556.53
-Epoch 9000/30000, loss: 2.05
-Epoch 12000/30000, loss: 1.41
-Epoch 15000/30000, loss: 1.39
-Epoch 18000/30000, loss: 1.36
-Epoch 21000/30000, loss: 1.36
-Epoch 24000/30000, loss: 1.33
-Epoch 27000/30000, loss: 1.33
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Epoch 0/30000, loss: 4392.25
+Epoch 3000/30000, loss: 1.61
+Epoch 6000/30000, loss: 2.39
+Epoch 9000/30000, loss: 1.37
+Epoch 12000/30000, loss: 4.35
+Epoch 15000/30000, loss: 1.74
+Epoch 18000/30000, loss: 1.40
+Epoch 21000/30000, loss: 2.01
+Epoch 24000/30000, loss: 1.89
+Epoch 27000/30000, loss: 1.84
 </pre></div>
 </div>
-<img alt="../_images/mlgeo_4.7_PINN_13_1.png" src="../_images/mlgeo_4.7_PINN_13_1.png" />
+<img alt="../_images/mlgeo_4.7_PINN_14_1.png" src="../_images/mlgeo_4.7_PINN_14_1.png" />
 </div>
 </div>
 <div class="cell docutils container">
@@ -1242,7 +1262,7 @@ <h2>PINN<a class="headerlink" href="#pinn" title="Permalink to this headline">#<
 <div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Text(0.5, 0, &#39;Time (s)&#39;)
 </pre></div>
 </div>
-<img alt="../_images/mlgeo_4.7_PINN_14_1.png" src="../_images/mlgeo_4.7_PINN_14_1.png" />
+<img alt="../_images/mlgeo_4.7_PINN_15_1.png" src="../_images/mlgeo_4.7_PINN_15_1.png" />
 </div>
 </div>
 <p>Yes, <strong>Darcy flow</strong> is an excellent alternative example for introducing physics-informed neural networks (PINNs) in geosciences. Darcy’s law governs the flow of fluid through porous media, which is fundamental in hydrogeology, groundwater modeling, and petroleum reservoir engineering. Here’s how it can be framed for the class.</p>
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diff --git a/_sources/Chapter4-DeepLearning/mlgeo_4.4_RNN.ipynb b/_sources/Chapter4-DeepLearning/mlgeo_4.4_RNN.ipynb
index 0bca5f6..8a53dad 100644
--- a/_sources/Chapter4-DeepLearning/mlgeo_4.4_RNN.ipynb
+++ b/_sources/Chapter4-DeepLearning/mlgeo_4.4_RNN.ipynb
@@ -6,7 +6,8 @@
    "source": [
     "# 4.4  Recurrent Neural Networks: Processing sequences\n",
     "\n",
-    "They are used for time series predictions. Regular dense networks can also do it, and CNNs can also work for very long time series.\n",
+    "They are used for time series ***forecast***. Regular dense networks can also do it, and CNNs can also work for very long time series.\n",
+    "\n",
     "A recurrent neuron  receives an input *and* the output from the neuron at the previous time step. Because each neuron learns from the previous time step, it has *memory*; but these simple cells have relatively short memory (10 cells about).\n",
     "RNNs take in a sequence and output a sequence.\n",
     "\n",
@@ -15,34 +16,40 @@
     "\n",
     "From D2DL: example of an RNN with a hidden state. \n",
     "The RNN takes the multiplication of the weights and the data plus other weights with the hidden states to the next layer.\n",
+    "\n",
+    "\n",
     "\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
     "import pandas as pd\n",
-    "import tensorflow as tf\n",
-    "from tensorflow import keras"
+    "import torch"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "In time series forecasting, the goal is to predict future values based on historical data. Two important concepts in this process are context data and prediction length.\n",
+    "\n",
+    "1. **Context Data** refers to the historical data used by the forecasting model to make predictions. This data provides the context or background information needed to understand the patterns, trends, and seasonality in the time series. The length of the context data is often referred to as the look-back window or input window.\n",
+    "2. **Prediction length** refers to the number of future time steps the model aims to predict. This is also known as the ***forecast horizon***. The number of future time steps the model predicts. For example, if the forecast horizon is 5, the model predicts the next 5 time steps.\n",
+    "\n",
     "**Synthetic data**\n",
     "\n",
-    "Let's create a synthetic time series"
+    "Let's create a synthetic time series. We will overlap 2 frequencies with noise."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -52,12 +59,19 @@
     "    y = 0.5*np.sin( (t-off1)*(f1*10+10) ) # first wave\n",
     "    y += 0.5*np.sin( (t-off2)*(f2*20+20) ) # second wave\n",
     "    y += 0.3* (np.random.rand(batch_size,n_steps)-0.5) # noise\n",
-    "    return y[...,np.newaxis].astype(np.float32) \n",
-    "# here we added a dimension to the output time series because most ML algorithms can be multidimensional, but here we are just doing a single time series.\n",
-    "\n",
-    "# we generate 10k time series of 51 points.\n",
-    "n_steps=50\n",
-    "y = generate_time_series(10000,n_steps+1)"
+    "    return y.astype(np.float32)  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# we generate 10k time series of context+prediction_horizon points.\n",
+    "context=50\n",
+    "prediction_horizon=10\n",
+    "data = generate_time_series(10000,context+prediction_horizon)"
    ]
   },
   {
@@ -66,29 +80,57 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "plt.plot(y[5000,:]);plt.grid(True)"
+    "# plot some of the time series in a 2x3 grid\n",
+    "plt.figure(figsize=(6,4))\n",
+    "for i in range(6):\n",
+    "    plt.subplot(2,3,i+1)\n",
+    "    # plot context data\n",
+    "    plt.plot(range(context),data[i,:context],'b-',label='context')\n",
+    "    # plot prediction horizon\n",
+    "    plt.plot(range(context,context+prediction_horizon),data[i,context:],'r-',label='prediction')\n",
+    "    plt.grid(True)\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "**train-validation-test split**\n",
-    "\n",
-    "In forecasting problem, we do not want to shuffle the training and test set since we want to make sure test is a prediction from the past (training).\n",
+    "## Design a vanilla RNN\n",
     "\n",
-    "The training data are time series of 50 points, the \"label\" or \"model output\" is the **last value** of the time series."
+    "The RNN will take context"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
-    "x_train,y_train = y[:7000,:n_steps],y[:7000,-1] \n",
-    "x_val,y_val = y[7000:9000,:n_steps],y[7000:9000,-1] \n",
-    "x_test,y_test = y[9000:,:n_steps],y[9000:,-1] "
+    "class VanillaRNN(torch.nn.Module):\n",
+    "    def __init__(self, input_size, hidden_size, output_size):\n",
+    "        super(VanillaRNN, self).__init__()\n",
+    "        self.rnn = torch.nn.RNN(input_size, hidden_size, batch_first=True) # RNN layer, batch_size is the first dimension\n",
+    "        self.fc = torch.nn.Linear(hidden_size, output_size) # Fully connected layer\n",
+    "    \n",
+    "    def forward(self, x):\n",
+    "        out, _ = self.rnn(x) # out: tensor of shape (batch_size, seq_length, hidden_size)\n",
+    "        out = self.fc(out[:, -1, :]) # out: tensor of shape (batch_size, output_size)\n",
+    "        return out\n",
+    "\n",
+    "def create_rnn_and_data(time_series, context, prediction_horizon):\n",
+    "    input_size = time_series.shape[-1]\n",
+    "    hidden_size = 20  # You can adjust this value\n",
+    "    output_size = prediction_horizon\n",
+    "    \n",
+    "    model = VanillaRNN(input_size, hidden_size, output_size)\n",
+    "    \n",
+    "    # Prepare the input and target data\n",
+    "    x = time_series[:, :context,np.newaxis ] # Add a dummy dimension for the input size\n",
+    "    y = time_series[:, context:context + prediction_horizon]\n",
+    "    \n",
+    "    return model, x, y"
    ]
   },
   {
@@ -97,29 +139,91 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "plt.plot(np.arange(n_steps),x_train[5000,:],'b')\n",
-    "plt.plot(51,y_train[5000],'r+')\n",
-    "plt.grid(True)"
+    "model, x, y = create_rnn_and_data(data, context, prediction_horizon)\n",
+    "\n",
+    "# Print model summary\n",
+    "print(model)"
    ]
   },
   {
-   "attachments": {},
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "Now prepare the training function "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def train(model, x_train, y_train, x_val, y_val, n_epochs=100, lr=0.001):\n",
+    "\n",
+    "    '''\n",
+    "    Function to train the model.\n",
     "\n",
-    "We can use the past values to predict the state, called *naive forecasting*:\n",
-    "```python\n",
-    "y_pred=x_val[:,-1]\n",
-    "```\n",
+    "    Parameters:\n",
+    "    model: torch.nn.Module\n",
+    "        The model to train\n",
+    "    x_train: np.ndarray\n",
+    "        The input data for training (context)\n",
+    "    y_train: np.ndarray\n",
+    "        The target data for training (prediction horizon)\n",
+    "    x_val: np.ndarray\n",
+    "        The input data for validation (context)\n",
+    "    y_val: np.ndarray\n",
+    "        The target data for validation (prediction horizon)\n",
+    "    n_epochs: int\n",
+    "        The number of epochs\n",
+    "    lr: float\n",
+    "        The learning rate\n",
     "\n",
-    "Or we can use a fully connected network and predict the value as a MLP regression:\n",
+    "    Returns:\n",
+    "    train_losses: list\n",
+    "        The training losses for each epoch\n",
+    "    val_losses: list\n",
+    "        The validation losses for each epoch    \n",
+    "    \n",
+    "    \n",
+    "    '''\n",
     "\n",
-    "```python\n",
-    "model.keras.models.Sequential([keras.layers.Flatten(input_shape=[50,1]),\n",
-    "                              keras.layers.Dense(1)])\n",
-    "```\n",
-    "They don't do too bad in this problem. The simple block is a ``simpleRNN``. The simplest recurrent neuron is a ``SimpleRNN(1,input_shape=[None,1])`` that takes any input scalar since it can process any number of time steps. The default activation function is ``tanh``. To return a time series, and not its final output, you need to set ``return_sequences=True``. It turns out that the simplest and single recurrent neuron won't work. So we stack several simpleRNNs."
+    "    optimizer = torch.optim.Adam(model.parameters(), lr=lr)\n",
+    "    loss_fn = torch.nn.MSELoss()\n",
+    "    train_losses = []\n",
+    "    val_losses = []\n",
+    "    \n",
+    "    for epoch in range(n_epochs):\n",
+    "        model.train()\n",
+    "        optimizer.zero_grad()\n",
+    "        y_pred = model(torch.from_numpy(x_train).float())\n",
+    "        print(f\"Shape of outputs: {y_pred.shape}\")\n",
+    "        print(f\"Shape of y_train: {y_train.shape}\")\n",
+    "\n",
+    "        loss = loss_fn(y_pred, torch.from_numpy(y_train).float())\n",
+    "        train_losses.append(loss.item())\n",
+    "        loss.backward()\n",
+    "        optimizer.step()\n",
+    "        \n",
+    "        if epoch % 10 == 0:\n",
+    "            model.eval()\n",
+    "            with torch.no_grad():\n",
+    "                y_val_pred = model(torch.from_numpy(x_val).float())\n",
+    "                print(f\"Shape of val_outputs: {y_val_pred.shape}\")\n",
+    "                print(f\"Shape of y_val: {y_val.shape}\")\n",
+    "  \n",
+    "                val_loss = loss_fn(y_val_pred, torch.from_numpy(y_val).float())\n",
+    "                val_losses.append(val_loss.item())\n",
+    "            print(f'Epoch {epoch}, Loss {loss.item():.6f}, Val loss {val_loss.item():.6f}')\n",
+    "    \n",
+    "    return train_losses, val_losses\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Train the VanillaRNN by first splitting the data between training and validation data"
    ]
   },
   {
@@ -128,12 +232,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "model=keras.models.Sequential([\n",
-    "    keras.layers.SimpleRNN(20,input_shape=[None,1],return_sequences=True),\n",
-    "    keras.layers.SimpleRNN(20,return_sequences=True),\n",
-    "    keras.layers.SimpleRNN(1)\n",
-    "    ])\n",
-    "model.summary()"
+    "y.shape"
    ]
   },
   {
@@ -142,8 +241,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "model.compile(optimizer='adam',loss='mse',metrics=['mse'])\n",
-    "history=model.fit(x_train,y_train,validation_data=(x_val,y_val), epochs=20, batch_size=128) "
+    "prediction_horizon, context"
    ]
   },
   {
@@ -152,9 +250,19 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "pd.DataFrame(history.history).plot(figsize=(8,5))\n",
-    "plt.grid(True)\n",
-    "plt.xlabel('epochs')"
+    "data.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# split y into training and validation sets\n",
+    "n_train = 7000\n",
+    "x_train, y_train = data[:n_train, :context], data[:n_train, context:context + prediction_horizon]\n",
+    "x_val, y_val = data[n_train:, :context], data[n_train:, context:context + prediction_horizon]"
    ]
   },
   {
@@ -163,12 +271,18 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "model=keras.models.Sequential([\n",
-    "    keras.layers.SimpleRNN(20,input_shape=[None,1],return_sequences=True),\n",
-    "    keras.layers.SimpleRNN(20),\n",
-    "    keras.layers.Dense(1)\n",
-    "    ])\n",
-    "model.summary()"
+    "x_train.shape, y_train.shape, x_val.shape, y_val.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# remove the last dimnsion of y_train and y_val\n",
+    "y_train = y_train.squeeze()\n",
+    "y_val = y_val.squeeze()"
    ]
   },
   {
@@ -177,8 +291,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "model.compile(optimizer='adam',loss='mse',metrics=['mse'])\n",
-    "history=model.fit(x_train,y_train,validation_data=(x_val,y_val), epochs=20, batch_size=128) "
+    "train_losses, val_losses = train(model, x_train, y_train, x_val, y_val, n_epochs=100, lr=0.001)"
    ]
   },
   {
@@ -187,11 +300,56 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "pd.DataFrame(history.history).plot(figsize=(8,5))\n",
+    "# plot the loss curves\n",
+    "plt.plot(train_losses, label='train')\n",
+    "plt.plot(val_losses, label='val')\n",
+    "plt.legend()\n",
     "plt.grid(True)\n",
-    "plt.xlabel('epochs')"
+    "plt.yscale('log')\n",
+    "\n"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "y_val.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# now show examples on the validation set with the ground truth and the prediction\n",
+    "# add a dimension to x_val\n",
+    "# x_val = x_val[...,np.newaxis]\n",
+    "model.eval()\n",
+    "with torch.no_grad():\n",
+    "    y_val_pred = model(torch.from_numpy(x_val).float()).numpy()\n",
+    "\n",
+    "# plot some of the time series in a 2x3 grid\n",
+    "plt.figure(figsize=(6,4))\n",
+    "for i in range(6):\n",
+    "    plt.subplot(2,3,i+1)\n",
+    "    plt.plot(np.concatenate([x_val[i],y_val[i]]), label='GT')\n",
+    "    plt.plot(np.concatenate([x_val[i],y_val_pred[i,np.newaxis].T]), label='Prediction')\n",
+    "    plt.legend()\n",
+    "    plt.grid(True)\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -341,7 +499,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3.8.5",
+   "display_name": "mlgeo",
    "language": "python",
    "name": "python3"
   },
@@ -355,12 +513,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.5"
-  },
-  "vscode": {
-   "interpreter": {
-    "hash": "bf1c1ab31e530e60b58e3d6ad0457a0c579c03efa8f6c28b6cdd125835b5a825"
-   }
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/_sources/Chapter4-DeepLearning/mlgeo_4.6_AutoEncoder.ipynb b/_sources/Chapter4-DeepLearning/mlgeo_4.6_AutoEncoder.ipynb
index 66bfa02..c647c11 100644
--- a/_sources/Chapter4-DeepLearning/mlgeo_4.6_AutoEncoder.ipynb
+++ b/_sources/Chapter4-DeepLearning/mlgeo_4.6_AutoEncoder.ipynb
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 185,
+   "execution_count": 1,
    "id": "fd035ac6-55ed-4cb2-aa54-4c42ded3b602",
    "metadata": {},
    "outputs": [],
@@ -59,10 +59,92 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 186,
+   "execution_count": 2,
    "id": "bb21fc37-6e62-41bb-820a-4ff575e8e1c5",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz\n",
+      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-images-idx3-ubyte.gz to ./FashionMNIST/raw/train-images-idx3-ubyte.gz\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 26421880/26421880 [00:02<00:00, 10417165.17it/s]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Extracting ./FashionMNIST/raw/train-images-idx3-ubyte.gz to ./FashionMNIST/raw\n",
+      "\n",
+      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz\n",
+      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/train-labels-idx1-ubyte.gz to ./FashionMNIST/raw/train-labels-idx1-ubyte.gz\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 29515/29515 [00:00<00:00, 175578.14it/s]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Extracting ./FashionMNIST/raw/train-labels-idx1-ubyte.gz to ./FashionMNIST/raw\n",
+      "\n",
+      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz\n",
+      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-images-idx3-ubyte.gz to ./FashionMNIST/raw/t10k-images-idx3-ubyte.gz\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 4422102/4422102 [00:01<00:00, 3538808.13it/s]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Extracting ./FashionMNIST/raw/t10k-images-idx3-ubyte.gz to ./FashionMNIST/raw\n",
+      "\n",
+      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz\n",
+      "Downloading http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/t10k-labels-idx1-ubyte.gz to ./FashionMNIST/raw/t10k-labels-idx1-ubyte.gz\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 5148/5148 [00:00<00:00, 8317518.10it/s]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Extracting ./FashionMNIST/raw/t10k-labels-idx1-ubyte.gz to ./FashionMNIST/raw\n",
+      "\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
    "source": [
     "dataset = datasets.FashionMNIST(root=\"./\",download=True,\n",
     "transform=Compose([ToTensor(),Normalize([0.5],[0.5])]))\n",
@@ -75,7 +157,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 187,
+   "execution_count": 3,
    "id": "6dc978de",
    "metadata": {},
    "outputs": [
@@ -83,7 +165,6 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "<torch.utils.data.dataset.Subset object at 0x2af90f8b0>\n",
       "torch.Size([50, 1, 28, 28])\n"
      ]
     }
@@ -105,7 +186,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 188,
+   "execution_count": 4,
    "id": "26d4fa44-54b2-4e74-973a-65631213306d",
    "metadata": {},
    "outputs": [
@@ -140,7 +221,7 @@
        "=========================================================================================="
       ]
      },
-     "execution_count": 188,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -203,7 +284,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 189,
+   "execution_count": 5,
    "id": "869b2658",
    "metadata": {},
    "outputs": [],
@@ -303,7 +384,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 191,
+   "execution_count": 6,
    "id": "e6277b83",
    "metadata": {},
    "outputs": [
@@ -311,11 +392,11 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[Epoch 1] train loss: 0.596 - val loss: 0.594\n",
-      "[Epoch 2] train loss: 0.596 - val loss: 0.593\n",
-      "[Epoch 3] train loss: 0.595 - val loss: 0.593\n",
-      "[Epoch 4] train loss: 0.595 - val loss: 0.593\n",
-      "[Epoch 5] train loss: 0.595 - val loss: 0.593\n"
+      "[Epoch 1] train loss: 0.617 - val loss: 0.603\n",
+      "[Epoch 2] train loss: 0.599 - val loss: 0.599\n",
+      "[Epoch 3] train loss: 0.596 - val loss: 0.597\n",
+      "[Epoch 4] train loss: 0.595 - val loss: 0.597\n",
+      "[Epoch 5] train loss: 0.595 - val loss: 0.596\n"
      ]
     }
    ],
@@ -333,23 +414,23 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 192,
+   "execution_count": 7,
    "id": "adced269",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x2d0523130>]"
+       "[<matplotlib.lines.Line2D at 0x3154edbb0>]"
       ]
      },
-     "execution_count": 192,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -373,7 +454,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 193,
+   "execution_count": 8,
    "id": "19e8d636-2c7f-445d-9f49-b23ffe4f0edb",
    "metadata": {},
    "outputs": [],
@@ -395,13 +476,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 194,
+   "execution_count": 9,
    "id": "39cb28fe-5a60-490b-9af8-20f08a0af970",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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jM1selWUCxkwtZynIrPTAz8/KByxndPQddVGdSIXHi2ktxuzJmk2sQuecc07E3/rWtyLm+WDauY7HnOlPHuNsrY3qMeB9wnuAr/Oe4+gPpiqJk7qMHz8+Yl4TrfRq72jiMe4rJ3ipq/PPPz/iSy65JGKeZz4PFy1a1PRz2JOe6lKC4e/gHP9c7pyv8xpjL36mzjmyrZTGNDxT+jvttFPEvFYPO+ywiPm8Y2mG5U+m6jkigmUF/k6O6uHIher+8T5hGZ7rH7C0vXDhwtJZ7XvlSJKk1cYGgSRJ6pqSAdM6TLlUUzlZb2qmF9n7nb2WGTNFyteZkuM+ZZMdZUvLdgdHHXVUw39ffvnlEWcjOriWQSuYissmO+J10NklZNsBJ0lhyYCyyYeqsmuUx+3b3/72Cvfpsssui/iQQw5Z4XdlSy1X559nmpT3NEc41FW1PLpctqZDZ9O9HZWV2gnLUuzRz78bTL2zfMCS5fXXXx8xlwGu4jXJ0Qd//etfI2aZ7cgjj4z4rrvuipjLFDO1z/OYTRbGe6H6N5HHgO9haYClEo4+WJk1Qtr3ypEkSauNDQJJktQ1JQOmF9nrspoC5vzdnJiD75k1a1bE7OXJXqgcrcCUHJc/JqYss1IFyxCl1L+EMGLEiIb/bqXX+8svv9x0+2wSG65ZkKXF2ds3S7u2sy233DJiXsM8ZvzdHZVNmKLPJqphj+TM1ltvHTEng2LPd5YGqku2ZrJrqC7rUnQkW5uAJVCmeMeNGxcxU9bsdU48nkyjtxumvPncZ+qckxfxGc0JeliKq5YM5syZEzHvOV733/jGNyLmGgJ8L2OOzBk1alTELIFwIiOWFVgOqZZdFyxYEDHLGywtMD744IMj5jFrlRkCSZJkg0CSJHVRySDrSc0USCmN6ZVly5ZFzElWOKkEX2fKjJ/LlDPTdtyGqcxWlxFleqmOqr1dd91114iZ4uI543n+5S9/GXErPdtZJmCKnGlDxnXBiYmya7K6TDjxusxGZLAkxjJNK7IRPvzeVkY3lNJYBmEJrp1T3CuDKWWuLcGSz7Rp05q+tzphWDPtfDz53Bk0aFDEfNZTVlZg7/7qiCmWZliC4XezjMWSA0sMBx54YMR8JnJfs9dZMuA9xs8vpZQDDjggYv5Wfi7fz3NffYa3wgyBJEmyQSBJkrqoZMBUYzYnfimNqRy+hz0vmXZk2pKjEvhepjNZhmAaNZsUh3G1x2Z3mH+dzj777IjHjh0bMUduMB3961//OuKsZJCNGuB1wDR6HXujc/50XtvZZFnVSWeyUhlfz9KtreAyrZyjfWUm7eJ7+vXrFzHLgN3BmDFjIp44cWLEfKZUl+xdLitV8nwz1d7O+PeBJQBe5zxmHE3DuPrs5v3Qp0+fiJl6z3r3M+bnZvuUTUDE38btq/dqtqwyvy97Xlb/vrbCDIEkSbJBIEmSbBBIkqTSRX0IOLSK9fpqPZS1ENamuR3fn60pzToMt2edjfVMxpyNLVvEp7p/3cFZZ50V8bXXXhsxF9lgn4AZM2ZEnPXdyM4Ba208Z5w1ry523HHHiLNhh9miXKXkw2S5XSs1/qwOyVp/1r8mG45YXawpO/fZLH51NXz48IizZxtr2NS3b9+m7+V9Mnjw4NWxm2tENpyOcbYIFF9fmT5e2eJbndXZ4dHZb6v+W3WYfmc+t1VmCCRJkg0CSZLURSUDpteZyqmmQLLZ2Zj6YFqN6aVsaEiW9meakqk3zu7E91ZnkOoOa7gTjxeHPs2bNy9inltuc9ttt0V8xhlnRJytD87zwXPWyixt7YbHlUOleG13lP7Pjltn04vZ8EWW+/jdWcxSQDVtm5UuulvJgDPcsRzUSmmH22cLgnEoa7sZOHDgmt6Fbs0MgSRJskEgSZK6qGSQ9fisLrTC0QFMgbHX5tKlSyPmWvJM73ObLA3HMkRW0uA+VEcVdDYl226YQi6lsff4BRdcEPF5550XcXXUyHL33XdfxCwZcHummrNFerh4Uh3xmmJpjGUBvl5KnrrPFv5q5buJpTJeA9yPVs5ddTvGLEt0B7yOOftmK+vXc0QHz+uGG24YMUeGSJ1hhkCSJNkgkCRJXVQyYHowW+yhlLx3eTb5CksJWbo1W/AlS21yG6ZIO9rXOuro951yyikR//znP4+YExAxhTl+/Pimn8O0NmNeLzx/LBHVESedmTx5csTshV+9Dnnt8npl2YxrpGeye+zYY4+N+OKLL46Yo4CYxibuT/U9LBO080Q6q4q//eGHH46Y1wJlExmx/MpJ2qTOqPdfNUmS1BIbBJIkqWtKBsSJNZhWrv4bSwZMh3Ht9GzO6FYmaGFpgHE233rVqqwx3w5aLYkMHTo04rvuuitiTrKTre1OL7zwQsTsJc10NHtk1xHLL6NGjYq4lVECpeRrchxzzDFNt+exza5nTtTFVPTEiRMj5rnO1kSo7tNBBx3U9PvqKpu8ic88rv0wf/78pp/DtUOysg3PmdQZZggkSZINAkmS1EUlA6bL2PO4mqbMJhHKRiZky39yHvhsLQOWBpi2y0oM1X2t+yiDKh5H/vaf/vSnEY8bNy5ippEnTJiwws8fOXJkxDwHTK8OGjSo9R1uQ+xxftxxxzXdpjrSgvcGU85vv/12xF/5yleaflY2MVQ20uayyy6LmCNHmKLO7vVSGte9OPLII5vuU11l5ccf/vCHEfN8nHDCCU23P/TQQyM+6aSTIuY6HyyrSp3Rvf6qSZKkpmwQSJKkss4nray5KUmSas0MgSRJskEgSZJsEEiSpGKDQJIkFRsEkiSp2CCQJEnFBoEkSSo2CCRJUrFBIEmSig0CSZJUbBBIkqRig0CSJBUbBJIkqdggkCRJxQaBJEkqNggkSVKxQSBJkooNAkmSVGwQSJKkYoNAkiQVGwSSJKnYIJAkScUGgSRJKjYIJElSsUEgSZKKDQJJklRsEEiSpGKDQJIkFRsEkiSp2CCQJEnFBoEkSSo2CCRJUrFBIEmSig0CSZJUbBBIkqRig0CSJBUbBJIkqdggkCRJxQaBJEkqNggkSVKxQSBJkooNAkmSVGwQSJKkYoNAkiQVGwSSJKnYIJAkScUGgSRJKjYIJElSsUEgSZKKDQJJklRsEEiSpGKDQJIkFRsEkiSp2CCQJEnFBoEkSSo2CCRJUrFBIEmSig0CSZJUbBBIkqRig0CSJBUbBJIkqdggkCRJxQaBJEkqNggkSVKxQSBJkooNAkmSVGwQSJKkYoNAkiQVGwSSJKnYIJAkScUGgSRJKjYIJElSsUEgSZKKDQJJklRsEEiSpGKDQJIkFRsEkiSp2CCQJEnFBoEkSSo2CCRJUrFBIEmSig0CSZJUbBBIkqRig0CSJBUbBJIkqdggkCRJxQaBJEkqNggkSVKxQSBJkooNAkmSVGwQSJKkYoNAkiQVGwSSJKnYIJAkScUGgSRJKjYIJElSsUEgSZKKDQJJklRsEEiSpGKDQJIkFRsEkiSp2CCQJEnFBoEkSSo2CCRJUrFBIEmSig0CSZJUbBBIkqRig0CSJBUbBJIkqdggkCRJxQaBJEkqNggkSVKxQSBJkooNAkmSVGwQSJKkYoNAkiQVGwSSJKnYIJAkSaWU9db0DnTWBx98EPFrr70W8euvvx5xz549I95yyy0jXmeddSJeb731mr6uFXvsscci3n///SP+6KOPIt50000j/vjjjyNef/31I+Z5+vDDD5tuc/LJJ0d8xRVXrMpu10Kr1yqPbY8ePSJeunRp08/i9m+++WbT15ctWxbxu+++GzHvSdpqq60a/vvVV19tad/rbubMmREPGzYs4m233TbiBQsWRLzJJptEvMEGG0T81ltvRczzsdFGG0XM56K0ImYIJEmSDQJJklTKOp988skna3onVlYru245YPXr1atXxEuWLIl46623jphlAp4Dvs6yzfvvvx/xuuuuGzFLPvfcc0/Effv2XZldbxuHHnpoxA888EDEG264YcN2O+ywQ8RM9X//+9+PeNq0aREz7T969OiIWRqYMmVKxE899VTEX/7ylyOeM2dOxLfeemvEvDYeffTRhn0dMmRI08/tbj7/+c9HPGnSpIhZNiPeDyzL8V7q06dPxM8++2zE77zzzqrtrLoVMwSSJMkGgSRJasNRBmQ5oOswPcme6uz1zLQzU8fsAc0SA9Pfb7zxRsQsE8yePTvim266KeILL7ywM7vfdubOnRsxjxNLCaWU8vTTT0fM4/yvf/0rYo74YLx48eKIWbLhufjMZ/77/ww8dywHcP/22muvpu8tpZSpU6dGzHJfd7uP77vvvog5gqB3794Rs5zG+41lBca8PxlLnWGGQJIk2SCQJEltXjJQ13n77bebvt6vX7+ImXaeN29exOxdzl7S7PHOtDE/h6nlyZMnd3a328r06dMj5u/eb7/9IuZkXKWU8vLLL0e8+eabRzxgwICIee7YY5090HleOFqEWMZYtGhRxDx3d999d8QDBw5seH///v0jvuWWWyL+4he/2PT76oTnk6l+ltzee++9iDmZFGPeG3yd91JWSqiWcKQqrxBJkmSDQJIkWTJQi9gjnanKHXfcMeJXXnklYvaSZiqUKUxOqsNUNlPW/K66z8vONRyYYmZZoDrRzMYbbxwx58Jn73WWDDbbbLOImern9nx9m222iZhrE7AMxFEG48aNi/ill15q2FfOvc/yQ3fAND7LMywBZOeG9w+PNc8Ht+FaBpysiiUlqRkzBJIkyQaBJEmyZKAW3XHHHREznbnPPvtEzDnU2Qt9/vz5ETPlyRQyU9+cjCibJKeOnnnmmYi5pDB7ojPdXErjMeH6DpzcKSu18Dv4OUxj8zwy5cxJqF544YWIhw4dGjF7vlf3vbomQ92x1MMy2CGHHBIx7wdO/MRyA0txPH8sufF1ngNLBlqRej9hJUlSS2wQSJIkSwZqzfPPPx8x58xn+pOTFDHVz57qu+++e8QsQ3C0wh577BExU6EsPdTR5ZdfHjFHYyxcuDDiasmAKWSWBrjuAEeIcBueO47sYOknG+3AssJnP/vZiBcsWBBxtWTA0seECRMiPvfcc5v+njphyYDnlseUIz04OoBLG3PkBu8Njjhg+YejD9Q1eM/QyqzZwc/idZOVFFd1XRAzBJIkyQaBJEmyQSBJkspa1oeglXoJZ3PL6iWss7LORnwv4+68TntHbr/99oh5jLjYDtdtZx168ODBEY8ePTriP//5zxGzTs6hWE8++WTErIXX8Tzxut10000jZl2dx7j6Hm7HGj9rypy1cMSIERE/99xzEbOfAYeDchven9wn9hepzqrI88Shitwn9keoE/bp4HFhvxgeU9b+zzrrrIgvuuiiiFk7Zh8Czhha96G67WRlnll8D/tu8dyvzmehV4skSbJBIEmS1nDJoDo8g2myOXPmNH190KBBETM9wrRltv47F/3ge7moCN/Lmb3qkpZeWUxXEYcjcuggU9kHH3xwxAcccEDTbThLG4dicaY8lovqgr+bwy3//e9/R8z0IGetq/4b0+0c8sfXeQ+wLMGhbTNmzIi4OsxxuQEDBkTMsgJLQhMnTmx4D4fM8d5n2ny33XZr+n3t7qGHHmr6OssEPNZ83lx44YUR/+QnP2n6OSy58V7ls02fHpa1ee6yRa14z3T0t4UlH5YEsyHAAwcO7Mxu/+/3rdK7JUlSLdggkCRJa7ZkwNnsSmlMnzIFM23atIhZAmBalOuwc5GY888/P2KWA9g7nilVLipy3HHHRcwZ9krpfiUEnhvKek8zjcXe7Ntuu23EnJmNqVMuzMPzxDRz1ru+3WSL1TDmseQxK6VxkaA999wzYqYUed3znuEx57lj+YAjC1hu4PYclcDv5bVRSmNam+/niJS6lgyy+6dXr14Rs/zG5xzjLNXM+2ru3LkRu6DR6sVnEK/vbKQa72/OPpmNlstGxVW322677SL+zW9+E/F5553X8Q9YATMEkiTJBoEkSVoDJQOmQv/zn/80/BtTh0wb33nnnRE/9dRTETPtwlQlPf300xEzdcr0zc477xzx3//+94hZqvjVr37V8LlM3XWU5qmLrAc0J6LhZDNMc7PnOVPeQ4cOjZjnialspqmZds0WEGk3TDuydzhT6uzRz+NaSuPx4SgFjszhvcFeyxyx07Nnz4h57/E+4eQ3THXz2uDiRtV7kv/G3u+PPfZYxMcff3zEdbqveNx5/7AkxudT1lucJQCOwKkuJLVcnY7h2oDPJpbrqvdlMyyRc3QQS278zFIaFx3jtcLSAO8fSwaSJGmV2SCQJEldUzLI1v/+7W9/27Ddww8/HPERRxwR8RNPPBEx05mMOcnKrFmzImZajekzTobCMgTTLywZfP3rX2/YV37fPvvsE3GWGmw3PGelNKag+bv4e5n2Z091pqP5XpZ8mHZmupy9aWfPnh0x06v8/HbD0tPhhx8e8aRJkyLO5qkvpbHkwF7qLM0NGzYsYvZ6ZomB9wnvDZbxmObnvccJh5gKrfZw577z/uG553VXp3Q3J+3idc/zxzLYySef3PRzeL/xWGUTh2n14vHPRoLwHiA+p/h3cOzYsRFXJ5LiOhZXXXVVxGeffXbEv/jFLyLmNbEy61iYIZAkSTYIJEnSGigZMCXPSU9KaUwxMkU9fPjwiLmULpfDve222yJmz2t+91577RUx0ylM0zCVyd6f9957b8O+Hn300RFnSym3s2rJgJM3MT3JiWSYXh45cmTE2THJ5vlmWpslA6bl2nkyImJq/5FHHomY6WP2YGZP41IajxvT+Ly+WXJg2pIjBThahOuCsLc7yzRMe/fu3TtintMePXo07Cv3id/NSXXqcv9U7bvvvhHz2GXXcZZ2ZomJ1wjPWV3ujbVFtiw17z3+LePoKV7PvPf4t+UHP/hBxNVRBjvssEPEV199dcR8HmfLo69MKdUMgSRJskEgSZI+xZJBlvKcMmVKxAcddFDDew455JCI2dN53rx5ETMtyl7nnFyIKe2+fftGzElxmJphuufYY4+NmOsaHHbYYQ37yvn5V6Y359quOvEPSyksvTD1y/M8ZsyYiLM08AknnBDx1KlTI2Y6jGk5ngOmr6vz+7cTltC4RC7LYZzwice7lMYUJktu2bogTEWzVMbzzclQOFokG7HDc8E1Pzj6ppTGURD8Dv7WuuI1zes1W6q9ep6X22WXXSLmmi0s1dS17LKm8BnEMhifd7xPeC9lo6r4N2PXXXeNuHovsPydjWDjdcPtV0b9/pJJkqROs0EgSZK6ZpQBe0Ey7VudhIE9nXfaaaeImdJnOobLEzNVwhTr6aef3nSfpk+fHvGoUaMi3n///SO+7rrrImZvz1L+tzdo3bEnOUcWcH569sZtZRlb9rxmKpspbqbDuLxvXdKiTPnzWPKe6devX8RbbLFFw/u5pDB7FXMNAqalWXLjd/C+2n777SNm6YH7ym3Gjx8fMdPYp512WsO+suzE8gZHQdSx/FZKY7qYx4Hz2/PcZvcP08u33357xLxntHrxWcPyAUvT2b3Ee+bFF1+MmGUjjjioru/D0hrLQtkzkq9XR/m0op53nyRJ6hQbBJIk6dMrGWS9K9nrn6mzUhrTiCwBMJXGee5ZcmBKm3Omc4lXplaYpmR6lXOOf/Ob32y636WsXDqmnfA4l9KYiuIaD5w4KJtnPcMSEdNsHN3BdBq3qe5fu2LZhMscZ0sWVyed4X1WLcEtx3uJ9wnvB6YjOfkNS2M85jwv3J7bMB1eSmOvbJYxWHI455xzIq5T+YDniWlgrgNBWW9xrj9BPLZ1fzatTnymZDHLBCwB8Prm6yx/8r7iPcO/ddyeo3Sq3819ytZRaOW525H63HGSJGml2SCQJEldM8qA6TKm/6s9prkdU6NMu7AnNVOKnJiIqddskptszQKm29iTuiqbfKIuqpP9sIc/l6Pm3NlMLzON3Mp3ZPP1v/rqqxGzbMEyD3vhtwNeh0wN85piSpFzo/M4VT+LMdOZHFmQpZP53dyGowyyVOjee+8dMZcwr5YwssnKmAavU5kgw/Qyn3NM97LUSbwWMq5l0KiaRs+e13y+cBuWwXiPcXveJxz5w/ubzzWOWuP1UF1/gKU1jmrg/cOYI/I4Yq5V9b/7JEnSCtkgkCRJXVMyYKqQqfqO0oNM2WTzdGfLPjJFxJQNUzzVufqbvZelBKaESmnsXc8Ua5aOarcSQ3UfDzjggIjvv//+iFkmqPYqXxG+t5XzzePMElG7Ya9gllaGDRsWMScpGj16dMQzZsxo+CymM3nt9u/fv+k2LKFxP4ifw7IezwuXLGZ6m5OvDBkypOFzOZHYwQcf3DTO9qlO+BziMV22bFnEXPeBx5rPIT5T+DndoeyyHH83j0erx4BpeK6Nw5Fxd955Z8QcIcK/PyyPsRzAsihLY3yu/exnP4uYJYlSSrnhhhsi5gR6HKF10kknRXzggQeWVdF9rhxJkpSyQSBJkrp+lAHTkdW0Pf+b2zGNmKXJ2NMyK0sw5czPz1L+/ByWJKr71Ip2KBNQ9dyceOKJEV988cVN35Ol/TPZ+gU8H0xxH3XUUU23aWc8zlwOmtft4MGDI672Qh45cmTEnDyLKUWmmVmi4Hcw5j5xhAKX3uW5y8pGPHelNC5vzpJPdYKyumNpaNasWRHznqmmjpfj+eBx5zGsTqJWZ9mIiuzvRCmNz24eQ95nfP8XvvCFiLksdTZRULZkMV/ns/Kaa65p+jmllPJ///d/EWeTGa3OUSVmCCRJkg0CSZLURSWDTEdpdKZOssk7+H6mSInvZRqOqZysJMF536sT9fA97VYOaEX1N/FYcP59pqNZtslGcRDPAdN6nMCDPeTruOQ0j9OcOXMizo4rJzEppbHXM5f95vli7/VWzguxVMZJTxYvXhzxwIEDI547d27EXI+hlMYJW3g/cWIppkLrikuy/+Mf/4iY1zrPJbFkwJ7wPJ4cYdJdZaPRqv9G2bWXHc/VNXIsW4OklHxNi0/rb44ZAkmSZINAkiSt4ZJBVdazNlsCkuUDzvmcLb2cTd6Rzcff0bKz7TbRUGdVfxN/L48XU5tMuTHt30oKMxtVkpWL6oLHmSMGOGEKJ6a59957G97P48PJjDhqgz3QO3utMp3JEQqcOGfy5MkRM+1dLeNxoqJsqfPugJOaZes78DyfcsopEXNpdx5r3m91fB6tik/reHTFce7qc2mGQJIk2SCQJEk2CCRJUlkDfQhYZ67WR1ZlKF82JC0bfsLXt99++6bbEPsirMz+tZvq72N/Cta058+fHzHPwYMPPhjxiBEjVvh9nNWOn8OaaR3Xeec1z5o7+2YsWbIk4nnz5jW8f6uttoqYCwvxPuOwvmzRl1b6xHBfZ86cGTEXc9l1110jZr+eUhr7MnDGxc4OhWx3nEmQx+HNN9+MmPcVcXueS/Y/6E4zFWbq3sfr02KGQJIk2SCQJElroGTQUdp3VdbxXpW0UCup6GrJoLvh8WV6n4vZbLHFFhG3MkSQaT0Ob2OqOVtApC54XDlUkDPScZ32qVOnNryfiwRxKB/vJV672X2SpVhZeuDns8yWDe3lzISlNA63y8p33QFLJ5xpkkM5OSskcQZL4jE8/PDDV3UX2153u6ZWFzMEkiTJBoEkSVoDJYOu6P35aXxHtSd0d05JccY5ziK5aNGiiCdNmrTCz2Fam2nUbNa1Oi5uREzDs8c50/YcSVBKKRMnToyYKfkePXpEzDQ+SzmtlOi4DXu4cyZFevTRRyOuprevuuqqiHmOmTbvDlhi2XPPPSPmseOskJQ923iehg4dulr2U92PGQJJkmSDQJIkrYGSQbsuCNGdSwRVZ5xxRsQ33nhjxEwDc/KiVko47FXPSXlWZWGedsPfOmXKlIi51v17773X8B6WGY444oiIFy9eHDFHcGRlglbWiGcZgpPf8PyylMBRE6U0lhx4vus44VRHOFqGkzq1Mhpk2bJlEbOExveydCR1hhkCSZJkg0CSJHVRycB5peuFqeAxY8ZE/Lvf/S7ip59+OuJWzvmAAQOavpfqfh0xnT937tyIBw4cGDHXLiillDlz5kT8z3/+M+Jddtkl4tdffz3i3r17R8zjydEiTGlzspy//OUvEY8fPz5iTqLDa6M6QQ4nseLIh0GDBpXuisfosssuizgr7fD8Ecs5jKXOMEMgSZJsEEiSpFLW+aS7rT0q6X/UvRwjacXMEEiSJBsEkiRpDUxMJGntY5lAkhkCSZJkg0CSJNkgkCRJxQaBJEkqNggkSVKxQSBJkooNAkmSVGwQSJKkYoNAkiSVUv4f4WRqA9SiRe4AAAAASUVORK5CYII=",
       "text/plain": [
        "<Figure size 640x480 with 10 Axes>"
       ]
@@ -434,7 +515,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 195,
+   "execution_count": 10,
    "id": "128be833",
    "metadata": {},
    "outputs": [],
@@ -469,7 +550,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 196,
+   "execution_count": 11,
    "id": "98c8ffa5",
    "metadata": {},
    "outputs": [
@@ -503,7 +584,7 @@
        "=========================================================================================="
       ]
      },
-     "execution_count": 196,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -517,7 +598,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 197,
+   "execution_count": 12,
    "id": "aa84d294",
    "metadata": {},
    "outputs": [
@@ -525,11 +606,11 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[Epoch 1] train loss: 0.609 - val loss: 0.574\n",
-      "[Epoch 2] train loss: 0.574 - val loss: 0.571\n",
-      "[Epoch 3] train loss: 0.572 - val loss: 0.570\n",
-      "[Epoch 4] train loss: 0.571 - val loss: 0.569\n",
-      "[Epoch 5] train loss: 0.571 - val loss: 0.569\n"
+      "[Epoch 1] train loss: 0.611 - val loss: 0.578\n",
+      "[Epoch 2] train loss: 0.574 - val loss: 0.574\n",
+      "[Epoch 3] train loss: 0.572 - val loss: 0.573\n",
+      "[Epoch 4] train loss: 0.571 - val loss: 0.573\n",
+      "[Epoch 5] train loss: 0.571 - val loss: 0.572\n"
      ]
     }
    ],
@@ -539,13 +620,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 199,
+   "execution_count": 13,
    "id": "7bc48a2c-cecf-437b-964c-41143fddbc6a",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 10 Axes>"
       ]
@@ -576,29 +657,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 17,
    "id": "2e412be4-9164-47ac-8e10-df57f9073391",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Model: \"sequential_15\"\n",
-      "_________________________________________________________________\n",
-      "Layer (type)                 Output Shape              Param #   \n",
-      "=================================================================\n",
-      "encoder_cnn (Sequential)     (None, 3, 3, 64)          23296     \n",
-      "_________________________________________________________________\n",
-      "decoder_cnn (Sequential)     (None, 28, 28)            23233     \n",
-      "=================================================================\n",
-      "Total params: 46,529\n",
-      "Trainable params: 46,529\n",
-      "Non-trainable params: 0\n",
-      "_________________________________________________________________\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "\n",
     "# Define the CNN autoencoder model in PyTorch\n",
@@ -608,7 +670,7 @@
     "\n",
     "        # Encoder\n",
     "        self.encoder = nn.Sequential(\n",
-    "            nn.DropOut(0.2), #  Dropout layer to mimic noisy data\n",
+    "            nn.Dropout(0.2), #  Dropout layer to mimic noisy data\n",
     "            nn.Conv2d(1, 16, kernel_size=3, stride=2, padding=1),\n",
     "            nn.ReLU(),\n",
     "            nn.Conv2d(16, 32, kernel_size=3, stride=2, padding=1),\n",
@@ -629,6 +691,17 @@
     "        return x"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "1a2f6474",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Instantiate the model\n",
+    "model_denoised_CNNAE = DenoiseCNNAE()"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -639,51 +712,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Epoch 1/20\n",
-      "1719/1719 [==============================] - 25s 14ms/step - loss: 0.2551 - val_loss: 0.2533\n",
-      "Epoch 2/20\n",
-      "1719/1719 [==============================] - 26s 15ms/step - loss: 0.2565 - val_loss: 0.2543\n",
-      "Epoch 3/20\n",
-      "1719/1719 [==============================] - 26s 15ms/step - loss: 0.2554 - val_loss: 0.2525\n",
-      "Epoch 4/20\n",
-      "1719/1719 [==============================] - 25s 14ms/step - loss: 0.2551 - val_loss: 0.2531\n",
-      "Epoch 5/20\n",
-      "1719/1719 [==============================] - 26s 15ms/step - loss: 0.2557 - val_loss: 0.2524\n",
-      "Epoch 6/20\n",
-      "1719/1719 [==============================] - 27s 16ms/step - loss: 0.2550 - val_loss: 0.2526\n",
-      "Epoch 7/20\n",
-      "1719/1719 [==============================] - 26s 15ms/step - loss: 0.2552 - val_loss: 0.2539\n",
-      "Epoch 8/20\n",
-      "1719/1719 [==============================] - 26s 15ms/step - loss: 0.2549 - val_loss: 0.2521\n",
-      "Epoch 9/20\n",
-      "1719/1719 [==============================] - 26s 15ms/step - loss: 0.2558 - val_loss: 0.2527\n",
-      "Epoch 10/20\n",
-      "1719/1719 [==============================] - 25s 15ms/step - loss: 0.2552 - val_loss: 0.2524\n",
-      "Epoch 11/20\n",
-      "1719/1719 [==============================] - 25s 15ms/step - loss: 0.2548 - val_loss: 0.2525\n",
-      "Epoch 12/20\n",
-      "1719/1719 [==============================] - 25s 15ms/step - loss: 0.2564 - val_loss: 0.2523\n",
-      "Epoch 13/20\n",
-      "1719/1719 [==============================] - 23s 13ms/step - loss: 0.2556 - val_loss: 0.2522\n",
-      "Epoch 14/20\n",
-      "1719/1719 [==============================] - 23s 13ms/step - loss: 0.2550 - val_loss: 0.2520\n",
-      "Epoch 15/20\n",
-      "1719/1719 [==============================] - 23s 13ms/step - loss: 0.2550 - val_loss: 0.2524\n",
-      "Epoch 16/20\n",
-      "1719/1719 [==============================] - 23s 13ms/step - loss: 0.2553 - val_loss: 0.2526\n",
-      "Epoch 17/20\n",
-      "1719/1719 [==============================] - 23s 13ms/step - loss: 0.2541 - val_loss: 0.2533\n",
-      "Epoch 18/20\n",
-      "1719/1719 [==============================] - 23s 14ms/step - loss: 0.2550 - val_loss: 0.2520\n",
-      "Epoch 19/20\n",
-      "1719/1719 [==============================] - 22s 13ms/step - loss: 0.2555 - val_loss: 0.2519\n",
-      "Epoch 20/20\n",
-      "1719/1719 [==============================] - 23s 13ms/step - loss: 0.2550 - val_loss: 0.2540\n"
+      "[Epoch 1] train loss: 0.612 - val loss: 0.585\n"
      ]
     }
    ],
    "source": [
-    "(loss, loss_val) = train(DenoiseCNNAE, 30,loaded_train, loaded_test)"
+    "(loss, loss_val) = train(model_denoised_CNNAE, 30,loaded_train, loaded_test)"
    ]
   },
   {
diff --git a/_sources/Chapter4-DeepLearning/mlgeo_4.7_PINN.ipynb b/_sources/Chapter4-DeepLearning/mlgeo_4.7_PINN.ipynb
index 3b39e77..5b0d107 100644
--- a/_sources/Chapter4-DeepLearning/mlgeo_4.7_PINN.ipynb
+++ b/_sources/Chapter4-DeepLearning/mlgeo_4.7_PINN.ipynb
@@ -58,7 +58,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -93,7 +93,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -104,7 +104,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -113,7 +113,7 @@
        "Text(0.5, 0, 'Time (s)')"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     },
@@ -149,7 +149,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -264,28 +264,38 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Epoch 0/20000, loss: 4713.87\n",
-      "Epoch 2000/20000, loss: 2509.96\n",
-      "Epoch 4000/20000, loss: 2140.79\n",
-      "Epoch 6000/20000, loss: 724.98\n",
-      "Epoch 8000/20000, loss: 87.96\n",
-      "Epoch 10000/20000, loss: 1.94\n",
-      "Epoch 12000/20000, loss: 0.40\n",
-      "Epoch 14000/20000, loss: 0.35\n",
-      "Epoch 16000/20000, loss: 0.34\n",
-      "Epoch 18000/20000, loss: 0.33\n"
+      "Epoch 0/2000, loss: 4816.01\n",
+      "Epoch 200/2000, loss: 2511.37\n",
+      "Epoch 400/2000, loss: 2074.74\n",
+      "Epoch 600/2000, loss: 613.42\n",
+      "Epoch 800/2000, loss: 95.27\n",
+      "Epoch 1000/2000, loss: 25.84\n",
+      "Epoch 1200/2000, loss: 8.47\n",
+      "Epoch 1400/2000, loss: 3.51\n",
+      "Epoch 1600/2000, loss: 2.66\n",
+      "Epoch 1800/2000, loss: 2.31\n"
      ]
     },
     {
      "data": {
-      "image/png": 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",
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x16a576310>]"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -295,17 +305,51 @@
     }
    ],
    "source": [
-    "net = Net(1,1, loss2=None, epochs=20000, lr=1e-5).to(DEVICE)\n",
+    "net = Net(1,1, loss2=None, epochs=2000, lr=1e-4).to(DEVICE)\n",
     "\n",
     "losses = net.fit(t, T)\n",
     "\n",
     "plt.plot(losses)\n",
-    "plt.yscale('log')"
+    "# plt.yscale('log')"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x16a5cf580>"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "prediction_temp_baseline = net.predict(times)\n",
+    "\n",
+    "plt.plot(times, prediction_temp_baseline, alpha=0.8)\n",
+    "plt.plot(t, T, 'o')\n",
+    "plt.legend(['Prediction', 'Training data'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -316,28 +360,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Epoch 0/20000, loss: 11220.99\n",
-      "Epoch 2000/20000, loss: 3922.64\n",
-      "Epoch 4000/20000, loss: 2426.29\n",
-      "Epoch 6000/20000, loss: 1615.85\n",
-      "Epoch 8000/20000, loss: 1198.53\n",
-      "Epoch 10000/20000, loss: 1020.56\n",
-      "Epoch 12000/20000, loss: 923.80\n",
-      "Epoch 14000/20000, loss: 848.24\n",
-      "Epoch 16000/20000, loss: 783.72\n",
-      "Epoch 18000/20000, loss: 719.29\n"
+      "Epoch 0/20000, loss: 11694.52\n",
+      "Epoch 2000/20000, loss: 4116.99\n",
+      "Epoch 4000/20000, loss: 2410.78\n",
+      "Epoch 6000/20000, loss: 1415.76\n",
+      "Epoch 8000/20000, loss: 904.16\n",
+      "Epoch 10000/20000, loss: 697.12\n",
+      "Epoch 12000/20000, loss: 616.28\n",
+      "Epoch 14000/20000, loss: 566.81\n",
+      "Epoch 16000/20000, loss: 523.32\n",
+      "Epoch 18000/20000, loss: 484.77\n"
      ]
     },
     {
      "data": {
-      "image/png": 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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -357,7 +401,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
@@ -366,13 +410,13 @@
        "Text(0.5, 0, 'Time (s)')"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -384,13 +428,13 @@
    "source": [
     "predsreg = netreg.predict(times)\n",
     "\n",
-    "preds = net.predict(times)\n",
+    "prediction_temp_regularized = netreg.predict(times)\n",
     "plt.plot(times, temps, alpha=0.8)\n",
     "plt.plot(t, T, 'o')\n",
-    "plt.plot(times, preds, alpha=0.8)\n",
-    "plt.plot(times, predsreg, alpha=0.8)\n",
+    "plt.plot(times, prediction_temp_regularized, alpha=0.8)\n",
+    "plt.plot(times, prediction_temp_baseline, alpha=0.8)\n",
     "\n",
-    "plt.legend(labels=['Equation','Training data', 'Network', 'L2 Network'])\n",
+    "plt.legend(labels=['Equation','Training data', 'Regularized', 'Baseline'])\n",
     "plt.ylabel('Temperature (C)')\n",
     "plt.xlabel('Time (s)')"
    ]
@@ -404,7 +448,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -418,28 +462,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Epoch 0/30000, loss: 4776.84\n",
-      "Epoch 3000/30000, loss: 2437.13\n",
-      "Epoch 6000/30000, loss: 556.53\n",
-      "Epoch 9000/30000, loss: 2.05\n",
-      "Epoch 12000/30000, loss: 1.41\n",
-      "Epoch 15000/30000, loss: 1.39\n",
-      "Epoch 18000/30000, loss: 1.36\n",
-      "Epoch 21000/30000, loss: 1.36\n",
-      "Epoch 24000/30000, loss: 1.33\n",
-      "Epoch 27000/30000, loss: 1.33\n"
+      "Epoch 0/30000, loss: 4392.25\n",
+      "Epoch 3000/30000, loss: 1.61\n",
+      "Epoch 6000/30000, loss: 2.39\n",
+      "Epoch 9000/30000, loss: 1.37\n",
+      "Epoch 12000/30000, loss: 4.35\n",
+      "Epoch 15000/30000, loss: 1.74\n",
+      "Epoch 18000/30000, loss: 1.40\n",
+      "Epoch 21000/30000, loss: 2.01\n",
+      "Epoch 24000/30000, loss: 1.89\n",
+      "Epoch 27000/30000, loss: 1.84\n"
      ]
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ]
@@ -449,9 +493,9 @@
     }
    ],
    "source": [
-    "net = Net(1,1, loss2=physics_loss, epochs=30000, loss2_weight=1, lr=1e-5).to(DEVICE)\n",
+    "net_PINN = Net(1,1, loss2=physics_loss, epochs=10000, loss2_weight=1, lr=1e-4).to(DEVICE)\n",
     "\n",
-    "losses = net.fit(t, T)\n",
+    "losses = net_PINN.fit(t, T)\n",
     "plt.plot(losses)\n",
     "plt.yscale('log')\n"
    ]
diff --git a/reports/mlgeo_4.4_RNN.log b/reports/mlgeo_4.4_RNN.log
index b576dfc..a0729ea 100644
--- a/reports/mlgeo_4.4_RNN.log
+++ b/reports/mlgeo_4.4_RNN.log
@@ -20,8 +20,7 @@ nbclient.exceptions.CellExecutionError: An error occurred while executing the fo
 import numpy as np
 import matplotlib.pyplot as plt
 import pandas as pd
-import tensorflow as tf
-from tensorflow import keras
+import torch
 ------------------
 
 ---------------------------------------------------------------------------
diff --git a/searchindex.js b/searchindex.js
index a6e6f9b..c4b4869 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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Open Reproducible Science","1.3 Jupyter Environment","1.3 Python Ecosystem","1.4 Computing Environments","1.5 Version Control &amp; GitHub","1.6 Data Gallery","Getting Started","2.10 Synthetic noise","2.11 Feature Engineering","2.12 Dimensionality Reduction","2.13 ML-ready data","2.1 Data Definitions","Assignment: <strong>Preparing AI-Ready Data for The Final Project</strong>","2.2 Data Formats","2.3 Pandas","2.4 DataFrame Exploration","2.5 Data Arrays","2.6 Resampling Methods","2.7 Statistical Considerations for geoscientific Data and Noise","2.8 Spectral Transforms","2.9 Filtering Data","3.10 AutoML","3.1 Concepts in training supervision","3.20 Final Project - Classic Machine Learning","3.2 Classification and Regression","3.3 Clustering: Unsupervied Classification","3.4 Binary classification","3.5 Multiclass Classification","3.6 Logistic regression","3.7 Random Forests","3.8 Robust Training","3.9 Ensemble learning","Homework Classic Machine Learning (50 points)","4.0 The Perceptron","4.1 Neural Networks","4.2 Multi Layer Perceptrons","4.3 Convolutional Neural Networks","4.4  Recurrent Neural Networks: Processing sequences","4.5 Model Training","4.6 Auto-encoders","4.7 Physics-Informed Neural Networks","4.8 NAS: Network Architecture Search","This chapter focuces on model workflow and ML reproducibility","The MLGeo Project","Machine Learning in the Geosciences","Acknowledgements from 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Open Reproducible Science","1.3 Jupyter Environment","1.3 Python Ecosystem","1.4 Computing Environments","1.5 Version Control &amp; GitHub","1.6 Data Gallery","Getting Started","2.10 Synthetic noise","2.11 Feature Engineering","2.12 Dimensionality Reduction","2.13 ML-ready data","2.1 Data Definitions","Assignment: <strong>Preparing AI-Ready Data for The Final Project</strong>","2.2 Data Formats","2.3 Pandas","2.4 DataFrame Exploration","2.5 Data Arrays","2.6 Resampling Methods","2.7 Statistical Considerations for geoscientific Data and Noise","2.8 Spectral Transforms","2.9 Filtering Data","3.10 AutoML","3.1 Concepts in training supervision","3.20 Final Project - Classic Machine Learning","3.2 Classification and Regression","3.3 Clustering: Unsupervied Classification","3.4 Binary classification","3.5 Multiclass Classification","3.6 Logistic regression","3.7 Random Forests","3.8 Robust Training","3.9 Ensemble learning","Homework Classic Machine Learning (50 points)","4.0 The Perceptron","4.1 Neural Networks","4.2 Multi Layer Perceptrons","4.3 Convolutional Neural Networks","4.4  Recurrent Neural Networks: Processing sequences","4.5 Model Training","4.6 Auto-encoders","4.7 Physics-Informed Neural Networks","4.8 NAS: Network Architecture Search","This chapter focuces on model workflow and ML reproducibility","The MLGeo Project","Machine Learning in the Geosciences","Acknowledgements from Contributors","Bibliography","Glossaries"],titleterms:{"0":[33,36],"1":[0,1,2,3,4,5,7,8,9,11,13,14,16,17,18,19,22,24,25,26,27,29,30,31,32,34,35,36,38,40,43],"10":[7,21,32],"11":8,"12":9,"13":10,"1d":[7,16,40],"2":[7,8,9,10,11,13,14,15,16,17,18,19,20,22,24,25,26,27,29,30,31,32,34,35,36,37,38,40,43],"20":[23,32],"2d":[7,16,19],"3":[1,2,9,13,14,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,34,35,36,38,40,43],"30":32,"4":[3,7,9,14,15,16,19,22,25,26,29,31,32,33,34,35,36,37,38,39,40,41,43],"5":[4,9,14,16,27,29,30,32,34,35,36,38,43],"50":32,"6":[5,9,14,16,17,22,28,29,30,32,38,39,43],"7":[18,22,29,40,43],"8":[19,30,41],"9":[20,31],"case":[19,20],"class":34,"do":2,"final":[12,15,23],"function":[14,34,35,38],"import":[19,20,29,32],"new":[4,8],"transient":7,A:36,And:32,But:13,One:[29,30],The:[12,18,25,33,36,43],To:36,about:33,account:4,acknowledg:45,activ:[22,35,36],adaboost:31,addit:4,advanc:14,advantag:[9,19,20,22],aggreg:14,ahead:37,ai:12,algorithm:[22,24],among:8,an:[2,4,36],analysi:[9,15],app:4,appendix:28,applic:[7,20],approach:22,ar:[2,19],architectur:41,arrai:[11,13,16,34],ascens:32,asid:36,aslgorithm:24,assembl:36,assess:29,assign:[12,23],authent:4,auto:39,autoencod:39,automat:28,automl:21,aw:3,azur:3,b:32,bag:31,baselin:29,basic:[1,2,14,16],batch:38,bay:32,befor:25,best:21,between:9,bibliographi:46,binari:26,bonu:16,boost:31,bootstrap:17,build:44,c:32,can:37,canon:18,carlo:17,challeng:[9,22],chapt:43,chapter:[42,43],check:[15,21,29],checklist:38,choic:[25,36],choos:16,classic:[14,23,32],classif:[8,24,25,26,27,38],classifi:[26,31,32],clean:[8,32],clever:38,climat:[9,20],cloud:3,cluster:[25,32],cnn:36,code:[2,40],colab:3,column:[14,21],comma:13,command:[1,2],common:24,compar:[21,22],comparison:[16,32],compon:[9,22],comput:[3,16,29],concept:[22,29],conclus:[19,20],conda:2,condit:14,confus:32,connect:36,consider:18,continu:19,contribut:4,contributor:45,control:4,convers:16,convex:38,convolut:[36,39],correl:[7,8,9,15,32],cours:44,covari:9,creat:[4,14,33,34,40],criteria:[12,23],cross:[30,32],csv:[13,14],custom:[34,38],cwt:19,d:32,darci:40,data:[5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,25,26,27,29,32,33,35,36,39,40,43],datafram:[8,14,15],dataload:34,dataset:[5,33,34],deal:2,dec:32,decis:29,declin:32,decod:39,deep:38,defin:36,definit:[11,36,47],deliver:[12,23],denois:39,descent:[28,38],descript:5,design:[34,35,37,43],desktop:4,determin:9,differ:9,differenti:28,dimension:[9,32,39,43],directori:4,discuss:[32,40],displai:21,distanc:[16,25],distribut:[15,18,32],domin:9,download:[5,29,43],e:32,earli:38,earthquak:14,ecosystem:2,elast:38,elbow:25,encod:[29,39],engin:8,enhanc:4,ensembl:31,environ:[1,2,3],equat:40,evalu:[12,21],event:7,exampl:[2,4,7,8,14,17,19,20,36,39,40],exercis:[7,8,14,15,16,24,38],exist:4,explan:[4,7],explor:[8,9,15,26,29,32],extens:40,extract:[9,16],far:37,featur:[8,9,15,18,29,32],file:[2,4,5,14],filter:[20,32],find:32,fine:35,first:[21,29],fit:[33,38],flow:40,focuc:42,fold:[30,32],forecast:37,forest:[29,32],format:[11,13],forward:35,fourier:19,fractal:8,frame:[11,43],framework:40,freez:2,from:[5,6,14,45],fulli:36,fundament:14,futur:37,g:32,galleri:5,gener:[7,14,47],geodet:17,geojson:13,geolog:18,geopanda:13,geoscienc:[7,9,11,19,20,40,44],geoscientif:[16,18],geospati:[7,9,13],geotiff:13,get:[6,21],git:4,github:[4,44],global:9,glossari:47,googl:3,grade:[12,23],gradient:[28,31,38],grid:30,handl:[13,15],hassl:21,hdf5:13,heat:40,hierarch:[13,25],high:16,homework:[32,44],hot:29,how:[2,5,36,37],hpc:3,hub:1,hyper:30,hyperparamet:35,i:[13,32],ica:9,imag:36,implement:[28,36,40],independ:9,infer:17,inform:[7,40],initi:29,intermedi:14,interpret:[21,32],introduct:[7,8,19,20,28,40],iri:33,javascript:13,json:13,jupyt:1,k:[25,30,32],kei:[4,9,22,40],kmean:32,kurtosi:18,lab:1,label:29,lambda:14,larg:13,lasso:38,latent:39,layer:[32,35,36],learn:[6,22,23,25,31,32,35,38,44],leav:30,lectur:11,lenet:36,let:[33,36],level:[7,16,17,18,19],librari:32,line:33,linear:[17,24],littl:33,load:34,local:3,logic:14,logist:28,loss:[34,38],low:39,lstm:37,machin:[23,32,44],magnitud:14,main:4,manipul:[14,16],map:14,markdown:1,mathemat:40,matplotlib:16,matrix:[9,32],mean:[9,18,25],measur:16,metadata:8,method:[17,25],metric:[21,26],mini:38,miss:15,mix:9,ml:[10,36,42],mlgeo:[5,43],mlp:35,modal:11,model:[17,21,26,29,32,34,35,36,38,39,42,43],mont:17,more:21,motion:17,multi:[32,35,39],multiclass:27,multipl:14,na:41,naiv:32,nan:15,nearest:32,need:2,neighbor:32,net:[38,39],netcdf4:13,netcdf:13,network:[34,35,36,37,40,41],neural:[34,35,36,37,40],nois:[7,18],non:9,norm:16,notat:13,note:[4,36],notebook:1,number:[25,32],numpi:16,nyquist:19,o:13,object:[6,12,13,23,44],open:0,optim:[32,34,35,38],organ:43,other:[9,24],our:[33,36],out:[30,33],outcom:9,overfit:38,overview:[22,44],panda:14,paramet:[30,36],parquet:[13,14],past:31,pca:[9,25],perceptron:[32,33,35],perform:[26,29,32],physic:[7,40],pink:7,pinn:40,plate:17,plot:16,plotli:14,point:[32,40],pool:36,practic:[25,29,36],predict:37,preliminari:32,prep:36,prepar:[12,27,29,32,35,43],preprocess:9,prereq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