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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Parameter estimation · Fronts.jl</title><meta name="title" content="Parameter estimation · Fronts.jl"/><meta property="og:title" content="Parameter estimation · Fronts.jl"/><meta property="twitter:title" content="Parameter estimation · Fronts.jl"/><meta name="description" content="Documentation for Fronts.jl."/><meta property="og:description" content="Documentation for Fronts.jl."/><meta property="twitter:description" content="Documentation for Fronts.jl."/><meta property="og:url" content="https://gerlero.github.io/Fronts.jl/ParamEstim/"/><meta property="twitter:url" content="https://gerlero.github.io/Fronts.jl/ParamEstim/"/><link rel="canonical" href="https://gerlero.github.io/Fronts.jl/ParamEstim/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" 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class="docs-light-only" src="../assets/logo.png" alt="Fronts.jl logo"/><img class="docs-dark-only" src="../assets/logo-dark.png" alt="Fronts.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">Fronts.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../equations/">Equations</a></li><li><a class="tocitem" href="../problems/">Problems</a></li><li><a class="tocitem" href="../solvers/">Solving</a></li><li><a class="tocitem" href="../solution/">Solutions</a></li><li><a class="tocitem" href="../boltzmann/">Boltzmann transformation</a></li><li><a class="tocitem" href="../inverse/">Inverse problems</a></li><li class="is-active"><a class="tocitem" href>Parameter estimation</a></li><li><a class="tocitem" href="../PorousModels/">Unsaturated flow models</a></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 class="is-active"><a href>Parameter estimation</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Parameter estimation</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/gerlero/Fronts.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/gerlero/Fronts.jl/blob/main/docs/src/ParamEstim.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="Fronts.ParamEstim-module:-parameter-estimation-support"><a class="docs-heading-anchor" href="#Fronts.ParamEstim-module:-parameter-estimation-support"><code>Fronts.ParamEstim</code> module: parameter estimation support</a><a id="Fronts.ParamEstim-module:-parameter-estimation-support-1"></a><a class="docs-heading-anchor-permalink" href="#Fronts.ParamEstim-module:-parameter-estimation-support" title="Permalink"></a></h1><p>The <code>ParamEstim</code> submodule provides support for optimization-based parameter estimation runs using <code>Fronts</code>.</p><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="Fronts.ParamEstim.ScaledSolution" href="#Fronts.ParamEstim.ScaledSolution"><code>Fronts.ParamEstim.ScaledSolution</code></a><span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ScaledSolution</code></pre><p>Wrapper for a solution scaled in <code>o</code> as if affecting the diffusivity by a constant factor <code>D0</code>.</p><p><strong>Extra fields</strong></p><ul><li><code>original</code>: original unscaled solution.</li><li><code>D0</code>: scaling factor.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/gerlero/Fronts.jl/blob/4f4a8f864f811bbd6f9f71721b432df59184a113/src/ParamEstim.jl#L10-L18">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="Fronts.ParamEstim.AbstractCostFunction" href="#Fronts.ParamEstim.AbstractCostFunction"><code>Fronts.ParamEstim.AbstractCostFunction</code></a><span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">abstract type AbstractCostFunction{fit_D0} end</code></pre><p>Abstract cost function for parameter estimation.</p><p><strong>Type parameters</strong></p><ul><li><code>fit_D0::Bool</code>: whether to fit an additional constant factor <code>D0</code> that affects the diffusivity. Values </li></ul><p>of <code>D0</code> can be found with relative efficiency without additional solver calls; so if any such constant factors affecting the diffusivity are unknown, it is recommended not to fit those factors directly but set <code>fit_D0</code> to <code>true</code> instead. Values of <code>D0</code> are found internally by local optimization. If <code>true</code>, the <code>candidate</code> function will return a <code>ScaledSolution</code> that includes the found value of <code>D0</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/gerlero/Fronts.jl/blob/4f4a8f864f811bbd6f9f71721b432df59184a113/src/ParamEstim.jl#L58-L69">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="Fronts.ParamEstim.RSSCostFunction" href="#Fronts.ParamEstim.RSSCostFunction"><code>Fronts.ParamEstim.RSSCostFunction</code></a><span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RSSCostFunction{fit_D0}(func, prob::InverseProblem[; D0tol, oi_hint]) &lt;: AbstractCostFunction</code></pre><p>Residual sum of squares cost function for parameter estimation.</p><p><strong>Type parameters</strong></p><ul><li><code>fit_D0::Bool</code>: whether to fit an additional constant factor <code>D0</code> that affects the diffusivity. Values </li></ul><p>of <code>D0</code> can be found with relative efficiency without additional solver calls; so if any such constant factors affecting the diffusivity are unknown, it is recommended not to fit those factors directly but set <code>fit_D0</code> to <code>true</code> instead. Values of <code>D0</code> are found internally by local optimization. If <code>true</code>, the <code>candidate</code> function will return a <code>ScaledSolution</code> that includes the found value of <code>D0</code>.</p><p><strong>Arguments</strong></p><ul><li><code>func</code>: function that takes a vector of parameter values and returns either a <code>Fronts.Solution</code> or a</li></ul><p><code>Fronts.AbstractSemiinfiniteProblem</code>. If func returns an <code>AbstractSemiinfiniteProblem</code>, it is solved with <code>solve</code>. <code>Solution</code>s with successful <code>ReturnCode</code> are passed to the cost function; otherwise, the cost is set to <code>Inf</code>.</p><ul><li><code>prob</code>: inverse problem. See <a href="../inverse/#Fronts.InverseProblem"><code>InverseProblem</code></a>.</li></ul><p><strong>Keyword arguments</strong></p><ul><li><code>D0tol=1e-3</code>: if <code>fit_D0</code> is <code>true</code>, a tolerance for <code>D0</code>.</li><li><code>oi_hint=nothing</code>: if <code>fit_D0</code> is <code>true</code>, an optional hint as to the point in <code>o</code> where the initial</li></ul><p>condition begins. The hint will be used as an aid in finding the optimal value for <code>D0</code>. Otherwise, the fitting process will start by attempting to match sorptivities.</p><p><strong>References</strong></p><p>GERLERO, G. S.; BERLI, C. L. A.; KLER, P. A. Open-source high-performance software packages for direct and inverse solving of horizontal capillary flow. Capillarity, 2023, vol. 6, no. 2, p. 31-40.</p><p>See also: <a href="#Fronts.ParamEstim.candidate"><code>candidate</code></a>, <a href="#Fronts.ParamEstim.ScaledSolution"><code>ScaledSolution</code></a>, <a href="../solution/#Fronts.Solution"><code>Fronts.Solution</code></a>, <a href="../problems/#Fronts.AbstractSemiinfiniteProblem"><code>Fronts.AbstractSemiinfiniteProblem</code></a></p><hr/><pre><code class="nohighlight hljs">(::RSSCostFunction)(p::AbstractVector)</code></pre><p>Return the cost of the solution obtained with parameter values <code>p</code>.</p><p>The <code>RSSCostFunction</code> object is meant to be passed to your optimizer of choice for minimization as the objective function.</p><p>If you need to know more than just the cost, call the <code>candidate</code> function instead.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/gerlero/Fronts.jl/blob/4f4a8f864f811bbd6f9f71721b432df59184a113/src/ParamEstim.jl#L97-L139">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="Fronts.ParamEstim.candidate" href="#Fronts.ParamEstim.candidate"><code>Fronts.ParamEstim.candidate</code></a><span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">candidate(cf::AbstractCostFunction, ::AbstractVector)
candidate(cf::AbstractCostFunction, ::Fronts.AbstractSemiinfiniteProblem)
candidate(cf::AbstractCostFunction, ::Fronts.Solution)</code></pre><p>Return the candidate solution for a given cost function and parameter values, problem, or solution.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/gerlero/Fronts.jl/blob/4f4a8f864f811bbd6f9f71721b432df59184a113/src/ParamEstim.jl#L83-L89">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../inverse/">« Inverse problems</a><a class="docs-footer-nextpage" href="../PorousModels/">Unsaturated flow models »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Tuesday 15 October 2024 15:09">Tuesday 15 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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