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<!--
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HTML file automatically generated from DocOnce source
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(https://github.com/doconce/doconce/)
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doconce format html back.do.txt --pygments_html_style=perldoc --html_style=solarized3 --html_links_in_new_window --html_output=back-solarized --no_mako
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-->
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<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
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<meta name="description" content="Advanced machine learning and data analysis for the physical sciences">
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<title>Advanced machine learning and data analysis for the physical sciences</title>
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h1 {color: #b58900;} /* yellow */
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<!-- tocinfo
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{'highest level': 2,
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'sections': [('Imports and Utilities', 2, None, 'imports-and-utilities')]}
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end of tocinfo -->
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<body>
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<!-- ------------------- main content ---------------------- -->
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<center>
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<h1>Advanced machine learning and data analysis for the physical sciences</h1>
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</center> <!-- document title -->
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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b>
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</center>
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<!-- institution -->
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<center>
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<b>Department of Physics and Center for Computing in Science Education, University of Oslo, Norway</b>
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</center>
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<br>
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<center>
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<h4>May 8, 2025</h4>
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</center> <!-- date -->
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<br>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="imports-and-utilities">Imports and Utilities </h2>
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<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
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<div class="cell border-box-sizing code_cell rendered">
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<pre style="line-height: 125%;"><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">torch</span>
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<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">torch.nn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">nn</span>
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<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">torch.nn.functional</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">F</span>
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">torchvision</span> <span style="color: #8B008B; font-weight: bold">import</span> datasets, transforms
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">torch.utils.data</span> <span style="color: #8B008B; font-weight: bold">import</span> DataLoader
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<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
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<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">math</span>
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device = <span style="color: #CD5555">&#39;cuda&#39;</span> <span style="color: #8B008B; font-weight: bold">if</span> torch.cuda.is_available() <span style="color: #8B008B; font-weight: bold">else</span> <span style="color: #CD5555">&#39;cpu&#39;</span>
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<span style="color: #228B22"># Training settings</span>
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batch_size = <span style="color: #B452CD">128</span>
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epochs = <span style="color: #B452CD">5</span>
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lr = <span style="color: #B452CD">2e-4</span>
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img_size = <span style="color: #B452CD">28</span>
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channels = <span style="color: #B452CD">1</span>
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<span style="color: #228B22"># Diffusion hyperparameters</span>
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T = <span style="color: #B452CD">300</span> <span style="color: #228B22"># number of diffusion steps [oai_citation:5‡Medium](https://papers-100-lines.medium.com/diffusion-models-from-scratch-mnist-data-tutorial-in-100-lines-of-pytorch-code-a609e1558cee?utm_source=chatgpt.com)</span>
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beta_start, beta_end = <span style="color: #B452CD">1e-4</span>, <span style="color: #B452CD">0.02</span>
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betas = torch.linspace(beta_start, beta_end, T, device=device) <span style="color: #228B22"># linear schedule [oai_citation:6‡Medium](https://medium.com/data-science/diffusion-model-from-scratch-in-pytorch-ddpm-9d9760528946?utm_source=chatgpt.com)</span>
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alphas = <span style="color: #B452CD">1.</span> - betas
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alphas_cumprod = torch.cumprod(alphas, dim=<span style="color: #B452CD">0</span>)
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transform = transforms.Compose([
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transforms.ToTensor(),
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transforms.Normalize((<span style="color: #B452CD">0.5</span>,), (<span style="color: #B452CD">0.5</span>,)),
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])
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train_ds = datasets.MNIST(<span style="color: #CD5555">&#39;.&#39;</span>, train=<span style="color: #8B008B; font-weight: bold">True</span>, download=<span style="color: #8B008B; font-weight: bold">True</span>, transform=transform)
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train_loader = DataLoader(train_ds, batch_size=batch_size, shuffle=<span style="color: #8B008B; font-weight: bold">True</span>)
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<span style="color: #8B008B; font-weight: bold">class</span> <span style="color: #008b45; font-weight: bold">SimpleUNet</span>(nn.Module):
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">__init__</span>(<span style="color: #658b00">self</span>, c):
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<span style="color: #658b00">super</span>().<span style="color: #008b45">__init__</span>()
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<span style="color: #658b00">self</span>.enc1 = nn.Conv2d(c, <span style="color: #B452CD">64</span>, <span style="color: #B452CD">3</span>, padding=<span style="color: #B452CD">1</span>)
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<span style="color: #658b00">self</span>.enc2 = nn.Conv2d(<span style="color: #B452CD">64</span>, <span style="color: #B452CD">128</span>, <span style="color: #B452CD">3</span>, padding=<span style="color: #B452CD">1</span>)
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<span style="color: #658b00">self</span>.dec1 = nn.ConvTranspose2d(<span style="color: #B452CD">128</span>, <span style="color: #B452CD">64</span>, <span style="color: #B452CD">3</span>, padding=<span style="color: #B452CD">1</span>)
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<span style="color: #658b00">self</span>.dec2 = nn.ConvTranspose2d(<span style="color: #B452CD">64</span>, c, <span style="color: #B452CD">3</span>, padding=<span style="color: #B452CD">1</span>)
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<span style="color: #658b00">self</span>.act = nn.ReLU()
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<span style="color: #228B22"># timestep embedding to condition on t</span>
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<span style="color: #658b00">self</span>.time_mlp = nn.Sequential(
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nn.Linear(<span style="color: #B452CD">1</span>, <span style="color: #B452CD">128</span>), <span style="color: #228B22"># Changed from 64 to 128</span>
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nn.ReLU(),
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nn.Linear(<span style="color: #B452CD">128</span>, <span style="color: #B452CD">128</span>), <span style="color: #228B22"># Changed from 64 to 128</span>
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)
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">forward</span>(<span style="color: #658b00">self</span>, x, t):
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<span style="color: #228B22"># x: [B, C, H, W], t: [B]</span>
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h = <span style="color: #658b00">self</span>.act(<span style="color: #658b00">self</span>.enc1(x))
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h = <span style="color: #658b00">self</span>.act(<span style="color: #658b00">self</span>.enc2(h))
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<span style="color: #228B22"># add time embedding</span>
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t = t.unsqueeze(-<span style="color: #B452CD">1</span>)
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temb = <span style="color: #658b00">self</span>.time_mlp(t)
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temb = temb.view(-<span style="color: #B452CD">1</span>, <span style="color: #B452CD">128</span>, <span style="color: #B452CD">1</span>, <span style="color: #B452CD">1</span>) <span style="color: #228B22"># Changed from 64 to 128</span>
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h = h + temb
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h = <span style="color: #658b00">self</span>.act(<span style="color: #658b00">self</span>.dec1(h))
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<span style="color: #8B008B; font-weight: bold">return</span> <span style="color: #658b00">self</span>.dec2(h)
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">q_sample</span>(x0, t, noise=<span style="color: #8B008B; font-weight: bold">None</span>):
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<span style="color: #CD5555">&quot;&quot;&quot;Add noise to x0 at timestep t.&quot;&quot;&quot;</span>
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<span style="color: #8B008B; font-weight: bold">if</span> noise <span style="color: #8B008B">is</span> <span style="color: #8B008B; font-weight: bold">None</span>:
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noise = torch.randn_like(x0)
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sqrt_acp = alphas_cumprod[t]**<span style="color: #B452CD">0.5</span>
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sqrt_1macp = (<span style="color: #B452CD">1</span> - alphas_cumprod[t])**<span style="color: #B452CD">0.5</span>
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<span style="color: #8B008B; font-weight: bold">return</span> sqrt_acp.view(-<span style="color: #B452CD">1</span>,<span style="color: #B452CD">1</span>,<span style="color: #B452CD">1</span>,<span style="color: #B452CD">1</span>)*x0 + sqrt_1macp.view(-<span style="color: #B452CD">1</span>,<span style="color: #B452CD">1</span>,<span style="color: #B452CD">1</span>,<span style="color: #B452CD">1</span>)*noise
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">diffusion_loss</span>(model, x0):
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<span style="color: #CD5555">&quot;&quot;&quot;Compute MSE between predicted noise and true noise.&quot;&quot;&quot;</span>
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B = x0.size(<span style="color: #B452CD">0</span>)
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t = torch.randint(<span style="color: #B452CD">0</span>, T, (B,), device=device).long()
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noise = torch.randn_like(x0)
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x_noisy = q_sample(x0, t, noise)
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pred_noise = model(x_noisy, t.float()/T)
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<span style="color: #8B008B; font-weight: bold">return</span> F.mse_loss(pred_noise, noise)
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model = SimpleUNet(channels).to(device)
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opt = torch.optim.Adam(model.parameters(), lr=lr)
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<span style="color: #8B008B; font-weight: bold">for</span> epoch <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(epochs):
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total_loss = <span style="color: #B452CD">0</span>
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<span style="color: #8B008B; font-weight: bold">for</span> x, _ <span style="color: #8B008B">in</span> train_loader:
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x = x.to(device)
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loss = diffusion_loss(model, x)
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opt.zero_grad()
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loss.backward()
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opt.step()
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total_loss += loss.item()
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<span style="color: #658b00">print</span>(<span style="color: #CD5555">f&quot;Epoch {</span>epoch+<span style="color: #B452CD">1</span><span style="color: #CD5555">}/{</span>epochs<span style="color: #CD5555">}, Loss: {</span>total_loss/<span style="color: #658b00">len</span>(train_loader)<span style="color: #CD5555">:.4f}&quot;</span>)
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<span style="color: #707a7c">@torch</span>.no_grad()
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">p_sample_loop</span>(model, shape):
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x = torch.randn(shape, device=device)
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<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">reversed</span>(<span style="color: #658b00">range</span>(T)):
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t = torch.full((shape[<span style="color: #B452CD">0</span>],), i, device=device).float()/T
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eps_pred = model(x, t)
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beta_t = betas[i]
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alpha_t = alphas[i]
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acp_t = alphas_cumprod[i]
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coef1 = <span style="color: #B452CD">1</span> / alpha_t.sqrt()
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coef2 = beta_t / ( (<span style="color: #B452CD">1</span> - acp_t).sqrt() )
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x = coef1*(x - coef2*eps_pred)
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<span style="color: #8B008B; font-weight: bold">if</span> i &gt; <span style="color: #B452CD">0</span>:
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z = torch.randn_like(x)
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sigma = beta_t.sqrt()
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x = x + sigma*z
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<span style="color: #8B008B; font-weight: bold">return</span> x
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<span style="color: #228B22"># Generate samples</span>
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samples = p_sample_loop(model, (<span style="color: #B452CD">16</span>, channels, img_size, img_size))
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samples = samples.clamp(-<span style="color: #B452CD">1</span>,<span style="color: #B452CD">1</span>).cpu()
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grid = torchvision.utils.make_grid(samples, nrow=<span style="color: #B452CD">4</span>, normalize=<span style="color: #8B008B; font-weight: bold">True</span>)
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plt.figure(figsize=(<span style="color: #B452CD">5</span>,<span style="color: #B452CD">5</span>))
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plt.imshow(grid.permute(<span style="color: #B452CD">1</span>,<span style="color: #B452CD">2</span>,<span style="color: #B452CD">0</span>))
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plt.axis(<span style="color: #CD5555">&#39;off&#39;</span>)
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</pre>
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<!-- ------------------- end of main content --------------- -->
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<center style="font-size:80%">
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<!-- copyright --> &copy; 1999-2025, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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