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 <html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>ExpectationProblem · SciMLExpectations.jl</title><meta name="title" content="ExpectationProblem · SciMLExpectations.jl"/><meta property="og:title" content="ExpectationProblem · SciMLExpectations.jl"/><meta property="twitter:title" content="ExpectationProblem · SciMLExpectations.jl"/><meta name="description" content="Documentation for SciMLExpectations.jl."/><meta property="og:description" content="Documentation for SciMLExpectations.jl."/><meta property="twitter:description" content="Documentation for SciMLExpectations.jl."/><meta property="og:url" content="https://docs.sciml.ai/SciMLExpectations/stable/manual/problem/"/><meta property="twitter:url" content="https://docs.sciml.ai/SciMLExpectations/stable/manual/problem/"/><link rel="canonical" href="https://docs.sciml.ai/SciMLExpectations/stable/manual/problem/"/><script data-outdated-warner 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class="tocitem" href="../../">Home</a></li><li><span class="tocitem">Tutorials</span><ul><li><a class="tocitem" href="../../tutorials/introduction/">An Introduction to Expectations via SciMLExpectations.jl</a></li><li><a class="tocitem" href="../../tutorials/optimization_under_uncertainty/">Optimization Under Uncertainty</a></li><li><a class="tocitem" href="../../tutorials/gpu_bayesian/">GPU-Accelerated Data-Driven Bayesian Uncertainty Quantification with Koopman Operators</a></li><li><a class="tocitem" href="../../tutorials/process_noise/">Expectation of Process Noise</a></li></ul></li><li><span class="tocitem">Manual</span><ul><li class="is-active"><a class="tocitem" href>ExpectationProblem</a></li><li><a class="tocitem" href="../solve/">Solving Expectation Problems</a></li><li><a class="tocitem" href="../algorithms/">Expectation Algorithms</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Manual</a></li><li class="is-active"><a href>ExpectationProblem</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>ExpectationProblem</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/SciML/SciMLExpectations.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/SciML/SciMLExpectations.jl/blob/master/docs/src/manual/problem.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="ExpectationProblem"><a class="docs-heading-anchor" href="#ExpectationProblem">ExpectationProblem</a><a id="ExpectationProblem-1"></a><a class="docs-heading-anchor-permalink" href="#ExpectationProblem" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="SciMLExpectations.ExpectationProblem" href="#SciMLExpectations.ExpectationProblem"><code>SciMLExpectations.ExpectationProblem</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">ExpectationProblem(S, g, h, pdist, params, nout)
 ExpectationProblem(g, pdist, params; nout = 1)
-ExpectationProblem(sm::SystemMap, g, h, d; nout = 1)</code></pre><p>Defines ∫ g(S(h(x,u0,p)))*f(x)dx</p><p><strong>Arguments</strong></p><p>Let 𝕏 = uncertainty space, 𝕌 = Initial condition space, ℙ = model parameter space</p><ul><li>S: 𝕌 × ℙ → 𝕌 also known as system map.</li><li>g: 𝕌 × ℙ → ℝⁿᵒᵘᵗ also known as the observables or output function.</li><li>h: 𝕏 × 𝕌 × ℙ → 𝕌 × ℙ also known as covariate function.</li><li>pdf(d,x): 𝕏 → ℝ the uncertainty distribution of the initial states.</li><li>params</li><li>nout</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/SciMLExpectations.jl/blob/575b99e7522e65d144759279f79c4a841a99bbe8/src/problem_types.jl#L3-L22">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="SciMLExpectations.SystemMap" href="#SciMLExpectations.SystemMap"><code>SciMLExpectations.SystemMap</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">SystemMap(prob, args...; kwargs...)</code></pre><p>Representation of a system solution map for a given <code>prob::DEProblem</code>. <code>args</code> and <code>kwargs</code> are forwarded to the equation solver.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/SciMLExpectations.jl/blob/575b99e7522e65d144759279f79c4a841a99bbe8/src/system_utils.jl#L2-L9">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="SciMLExpectations.ProcessNoiseSystemMap" href="#SciMLExpectations.ProcessNoiseSystemMap"><code>SciMLExpectations.ProcessNoiseSystemMap</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">ProcessNoiseSystemMap(prob, n, args...; kwargs...)</code></pre><p>Representation of a system solution map for a given <code>prob::SDEProblem</code>. <code>args</code> and <code>kwargs</code> are forwarded to the equation solver. <code>n</code> is the number of terms in the Kosambi–Karhunen–Loève representation of the process noise.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/SciMLExpectations.jl/blob/575b99e7522e65d144759279f79c4a841a99bbe8/src/system_utils.jl#L36-L44">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="SciMLExpectations.GenericDistribution" href="#SciMLExpectations.GenericDistribution"><code>SciMLExpectations.GenericDistribution</code></a> — <span class="docstring-category">Type</span></header><section><div><p><code>GenericDistribution(d, ds...)</code></p><p>Defines a generic distribution that just wraps functions for pdf function, rand and bounds. User can use this for define any arbitrary joint pdf. Included b/c Distributions.jl Product method of mixed distributions are type instable.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/SciMLExpectations.jl/blob/575b99e7522e65d144759279f79c4a841a99bbe8/src/distribution_utils.jl#L1-L7">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../tutorials/process_noise/">« Expectation of Process Noise</a><a class="docs-footer-nextpage" href="../solve/">Solving Expectation Problems »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.2 on <span class="colophon-date" title="Saturday 28 October 2023 11:15">Saturday 28 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+ExpectationProblem(sm::SystemMap, g, h, d; nout = 1)</code></pre><p>Defines ∫ g(S(h(x,u0,p)))*f(x)dx</p><p><strong>Arguments</strong></p><p>Let 𝕏 = uncertainty space, 𝕌 = Initial condition space, ℙ = model parameter space</p><ul><li>S: 𝕌 × ℙ → 𝕌 also known as system map.</li><li>g: 𝕌 × ℙ → ℝⁿᵒᵘᵗ also known as the observables or output function.</li><li>h: 𝕏 × 𝕌 × ℙ → 𝕌 × ℙ also known as covariate function.</li><li>pdf(d,x): 𝕏 → ℝ the uncertainty distribution of the initial states.</li><li>params</li><li>nout</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/SciMLExpectations.jl/blob/075c05d8709d45a7d71ec8bab3d05e2d72dc387a/src/problem_types.jl#L3-L22">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="SciMLExpectations.SystemMap" href="#SciMLExpectations.SystemMap"><code>SciMLExpectations.SystemMap</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">SystemMap(prob, args...; kwargs...)</code></pre><p>Representation of a system solution map for a given <code>prob::DEProblem</code>. <code>args</code> and <code>kwargs</code> are forwarded to the equation solver.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/SciMLExpectations.jl/blob/075c05d8709d45a7d71ec8bab3d05e2d72dc387a/src/system_utils.jl#L2-L9">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="SciMLExpectations.ProcessNoiseSystemMap" href="#SciMLExpectations.ProcessNoiseSystemMap"><code>SciMLExpectations.ProcessNoiseSystemMap</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">ProcessNoiseSystemMap(prob, n, args...; kwargs...)</code></pre><p>Representation of a system solution map for a given <code>prob::SDEProblem</code>. <code>args</code> and <code>kwargs</code> are forwarded to the equation solver. <code>n</code> is the number of terms in the Kosambi–Karhunen–Loève representation of the process noise.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/SciMLExpectations.jl/blob/075c05d8709d45a7d71ec8bab3d05e2d72dc387a/src/system_utils.jl#L36-L44">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="SciMLExpectations.GenericDistribution" href="#SciMLExpectations.GenericDistribution"><code>SciMLExpectations.GenericDistribution</code></a> — <span class="docstring-category">Type</span></header><section><div><p><code>GenericDistribution(d, ds...)</code></p><p>Defines a generic distribution that just wraps functions for pdf function, rand and bounds. User can use this for define any arbitrary joint pdf. Included b/c Distributions.jl Product method of mixed distributions are type instable.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/SciMLExpectations.jl/blob/075c05d8709d45a7d71ec8bab3d05e2d72dc387a/src/distribution_utils.jl#L1-L7">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../tutorials/process_noise/">« Expectation of Process Noise</a><a class="docs-footer-nextpage" href="../solve/">Solving Expectation Problems »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Saturday 2 December 2023 16:10">Saturday 2 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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