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dev/DiffEqUncertainty/01-expectation_introduction/index.html

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[67601950-bd08-11e9-3c89-fd23fb4432d2] Quadrature 1.3.0</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../advanced/02-diffusion_implicit_heat_equation/">« Solving the heat equation with diffusion-implicit time-stepping</a><a class="docs-footer-nextpage" href="../02-AD_and_optimization/">Optimization Under Uncertainty with DiffEqUncertainty.jl »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Sunday 27 November 2022 00:10">Sunday 27 November 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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[67601950-bd08-11e9-3c89-fd23fb4432d2] Quadrature 1.3.0</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../advanced/02-diffusion_implicit_heat_equation/">« Solving the heat equation with diffusion-implicit time-stepping</a><a class="docs-footer-nextpage" href="../02-AD_and_optimization/">Optimization Under Uncertainty with DiffEqUncertainty.jl »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Thursday 1 December 2022 08:52">Thursday 1 December 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/DiffEqUncertainty/02-AD_and_optimization/index.html

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[76087f3c-5699-56af-9a33-bf431cd00edd] NLopt 0.6.0
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[67601950-bd08-11e9-3c89-fd23fb4432d2] Quadrature 1.3.0</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../01-expectation_introduction/">« An Intro to Expectations via DiffEqUncertainty.jl</a><a class="docs-footer-nextpage" href="../../perturbation/01-perturbation_algebraic/">Mixed Symbolic/Numerical Methods for Perturbation Theory - Algebraic Equations »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Sunday 27 November 2022 00:10">Sunday 27 November 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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[67601950-bd08-11e9-3c89-fd23fb4432d2] Quadrature 1.3.0</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../01-expectation_introduction/">« An Intro to Expectations via DiffEqUncertainty.jl</a><a class="docs-footer-nextpage" href="../../perturbation/01-perturbation_algebraic/">Mixed Symbolic/Numerical Methods for Perturbation Theory - Algebraic Equations »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Thursday 1 December 2022 08:52">Thursday 1 December 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/Testing/test/index.html

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[3f19e933] p7zip_jll</code></pre></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Sunday 27 November 2022 00:10">Sunday 27 November 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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[3f19e933] p7zip_jll</code></pre></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Thursday 1 December 2022 08:52">Thursday 1 December 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/advanced/01-beeler_reuter/index.html

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[3f19e933] p7zip_jll</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../jumps/spatial/">« Tutorial on using spatial SSAs in DiffEqJump</a><a class="docs-footer-nextpage" href="../02-diffusion_implicit_heat_equation/">Solving the heat equation with diffusion-implicit time-stepping »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Sunday 27 November 2022 00:10">Sunday 27 November 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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[3f19e933] p7zip_jll</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../jumps/spatial/">« Tutorial on using spatial SSAs in DiffEqJump</a><a class="docs-footer-nextpage" href="../02-diffusion_implicit_heat_equation/">Solving the heat equation with diffusion-implicit time-stepping »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Thursday 1 December 2022 08:52">Thursday 1 December 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/advanced/02-diffusion_implicit_heat_equation/index.html

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p2 = Plots.plot(zf, abs.(T_end .- T_analytic.(zf)), label=&quot;error&quot;, markershape=:circle, markersize=6)
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Plots.plot(p1, p2)</code></pre><p><img src="figures/04-diffusion_implicit_heat_equation_9_1.png" alt/></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../01-beeler_reuter/">« An Implicit/Explicit CUDA-Accelerated Solver for the 2D Beeler-Reuter Model</a><a class="docs-footer-nextpage" href="../../DiffEqUncertainty/01-expectation_introduction/">An Intro to Expectations via DiffEqUncertainty.jl »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Sunday 27 November 2022 00:10">Sunday 27 November 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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Plots.plot(p1, p2)</code></pre><p><img src="figures/04-diffusion_implicit_heat_equation_9_1.png" alt/></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../01-beeler_reuter/">« An Implicit/Explicit CUDA-Accelerated Solver for the 2D Beeler-Reuter Model</a><a class="docs-footer-nextpage" href="../../DiffEqUncertainty/01-expectation_introduction/">An Intro to Expectations via DiffEqUncertainty.jl »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Thursday 1 December 2022 08:52">Thursday 1 December 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/exercises/01-workshop_exercises/index.html

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sol = [Array(solve(prob,SOSRI())(0.0:1.0:10.0)) for i in 1:20] # 20 solution samples</code></pre><p>Train a neural stochastic differential equation <span>$dX = f(X)dt + g(X)dW_t$</span> where both the drift (<span>$f$</span>) and the diffusion (<span>$g$</span>) functions are neural networks. See if constraining <span>$g$</span> can make the problem easier to fit.</p><h2 id="Part-5:-Optimizing-the-training-behavior-with-minibatching-(E)"><a class="docs-heading-anchor" href="#Part-5:-Optimizing-the-training-behavior-with-minibatching-(E)">Part 5: Optimizing the training behavior with minibatching (E)</a><a id="Part-5:-Optimizing-the-training-behavior-with-minibatching-(E)-1"></a><a class="docs-heading-anchor-permalink" href="#Part-5:-Optimizing-the-training-behavior-with-minibatching-(E)" title="Permalink"></a></h2><p>Use minibatching on the data to improve the training procedure. An example <a href="https://github.com/FluxML/model-zoo/pull/88">can be found at this PR</a>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../perturbation/02-perturbation_differential/">« Mixed Symbolic/Numerical Methods for Perturbation Theory - Differential Equations</a><a class="docs-footer-nextpage" href="../02-workshop_solutions/">SciML Workshop Exercise Solutions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Sunday 27 November 2022 00:10">Sunday 27 November 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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sol = [Array(solve(prob,SOSRI())(0.0:1.0:10.0)) for i in 1:20] # 20 solution samples</code></pre><p>Train a neural stochastic differential equation <span>$dX = f(X)dt + g(X)dW_t$</span> where both the drift (<span>$f$</span>) and the diffusion (<span>$g$</span>) functions are neural networks. See if constraining <span>$g$</span> can make the problem easier to fit.</p><h2 id="Part-5:-Optimizing-the-training-behavior-with-minibatching-(E)"><a class="docs-heading-anchor" href="#Part-5:-Optimizing-the-training-behavior-with-minibatching-(E)">Part 5: Optimizing the training behavior with minibatching (E)</a><a id="Part-5:-Optimizing-the-training-behavior-with-minibatching-(E)-1"></a><a class="docs-heading-anchor-permalink" href="#Part-5:-Optimizing-the-training-behavior-with-minibatching-(E)" title="Permalink"></a></h2><p>Use minibatching on the data to improve the training procedure. An example <a href="https://github.com/FluxML/model-zoo/pull/88">can be found at this PR</a>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../perturbation/02-perturbation_differential/">« Mixed Symbolic/Numerical Methods for Perturbation Theory - Differential Equations</a><a class="docs-footer-nextpage" href="../02-workshop_solutions/">SciML Workshop Exercise Solutions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.23 on <span class="colophon-date" title="Thursday 1 December 2022 08:52">Thursday 1 December 2022</span>. Using Julia version 1.8.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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