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| <html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>- · Luminescent.jl</title><meta name="title" content="- · Luminescent.jl"/><meta property="og:title" content="- · Luminescent.jl"/><meta property="twitter:title" content="- · Luminescent.jl"/><meta name="description" content="Documentation for Luminescent.jl."/><meta property="og:description" content="Documentation for Luminescent.jl."/><meta property="twitter:description" content="Documentation for Luminescent.jl."/><script data-outdated-warner src="../warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../documenter.js"></script><script src="../../search_index.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../../">Luminescent.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="../../guide/">Guide</a></li><li><span class="tocitem">Tutorials</span><ul><li><a class="tocitem" href="../../periodic_scattering/">Periodic Scattering</a></li><li><a class="tocitem" href="../../quarter_wavelength_antenna/">Quarter Wavelength Antenna</a></li><li><a class="tocitem" href="../../inverse_design_waveguide_bend/">Inverse Design Waveguide Bend</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 class="is-active"><a href>-</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>-</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/paulxshen/fdtd" 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/paulxshen/fdtd/blob/master/makedocs/src/assets/guide copy.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"><h2 id><a class="docs-heading-anchor" href="#"></a><a id="-1"></a><a class="docs-heading-anchor-permalink" href="#" title="Permalink"></a></h2><p>Engineers run simulations to improve designs. Each time the design changes, the simulation is re-run. This can be done systematically in "parameter sweeps" where different combinations of parameter values are simulated to determine the best design. However, this scales exponentially wrt the number of parameters or DOFs. </p><h2 id="General-workflow"><a class="docs-heading-anchor" href="#General-workflow">General workflow</a><a id="General-workflow-1"></a><a class="docs-heading-anchor-permalink" href="#General-workflow" title="Permalink"></a></h2><p>We use gradient descent, the same as in machine learning. In lieu of optimizing neural network parameters, we're optimizing geometry (or source) parameters. In each training iteration, we generate geometry, run the simulation, calculate the objective metric, and do a backward pass to derive the gradient wrt the geometry parameters. We then do a gradient based parameter update in preparation for the next iteration.</p><p>The geometry is thus the first maxwell_update. It typically has a static component which we can't change such as interfacing waveguides. Then there's a design component which we can change or optimize. The user is responsible for generating the design geometry wrt design parameters. If any pattern is allowed in the design region, our sister package <code>Jello.jl</code> can be used as a length scale controlled geometry generator. In any case, the result needs to be a 2d/3d array of each relevant materials property eg permitivity. </p><p>With geometry ready, we can run the simulation. Duration is roughly the time it takes to reach steady state, such as how long it take for the signal to reach output port. The objective is usually a steady state metric which can be computed using values from the final period. We optimize geometry for some objective. </p></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><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="Friday 29 March 2024 00:05">Friday 29 March 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> | ||
| <html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>- · Luminescent.jl</title><meta name="title" content="- · Luminescent.jl"/><meta property="og:title" content="- · Luminescent.jl"/><meta property="twitter:title" content="- · Luminescent.jl"/><meta name="description" content="Documentation for Luminescent.jl."/><meta property="og:description" content="Documentation for Luminescent.jl."/><meta property="twitter:description" content="Documentation for Luminescent.jl."/><script data-outdated-warner src="../warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../documenter.js"></script><script src="../../search_index.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../../">Luminescent.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="../../guide/">Guide</a></li><li><span class="tocitem">Tutorials</span><ul><li><a class="tocitem" href="../../periodic_scattering/">Periodic Scattering</a></li><li><a class="tocitem" href="../../quarter_wavelength_antenna/">Quarter Wavelength Antenna</a></li><li><a class="tocitem" href="../../inverse_design_waveguide_bend/">Inverse Design Waveguide Bend</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 class="is-active"><a href>-</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>-</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/paulxshen/fdtd" 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/paulxshen/fdtd/blob/master/makedocs/src/assets/guide copy.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"><h2 id><a class="docs-heading-anchor" href="#"></a><a id="-1"></a><a class="docs-heading-anchor-permalink" href="#" title="Permalink"></a></h2><p>Engineers run simulations to improve designs. Each time the design changes, the simulation is re-run. This can be done systematically in "parameter sweeps" where different combinations of parameter values are simulated to determine the best design. However, this scales exponentially wrt the number of parameters or DOFs. </p><h2 id="General-workflow"><a class="docs-heading-anchor" href="#General-workflow">General workflow</a><a id="General-workflow-1"></a><a class="docs-heading-anchor-permalink" href="#General-workflow" title="Permalink"></a></h2><p>We use gradient descent, the same as in machine learning. In lieu of optimizing neural network parameters, we're optimizing geometry (or source) parameters. In each training iteration, we generate geometry, run the simulation, calculate the objective metric, and do a backward pass to derive the gradient wrt the geometry parameters. We then do a gradient based parameter update in preparation for the next iteration.</p><p>The geometry is thus the first maxwell_update. It typically has a static component which we can't change such as interfacing waveguides. Then there's a design component which we can change or optimize. The user is responsible for generating the design geometry wrt design parameters. If any pattern is allowed in the design region, our sister package <code>Jello.jl</code> can be used as a length scale controlled geometry generator. In any case, the result needs to be a 2d/3d array of each relevant materials property eg permitivity. </p><p>With geometry ready, we can run the simulation. Duration is roughly the time it takes to reach steady state, such as how long it take for the signal to reach output port. The objective is usually a steady state metric which can be computed using values from the final period. We optimize geometry for some objective. </p></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><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="Friday 29 March 2024 12:08">Friday 29 March 2024</span>. Using Julia version 1.10.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> |
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