Accelerating Quantum Chemistry Calculations: Machine Learning for Efficient Evaluation of Electron-Repulsion Integrals

<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-P63WKM1TM1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-P63WKM1TM1'); </script>  <script type="text/javascript" > (function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)}; m[i].l=1*new Date(); for (var j = 0; j < document.scripts.length; j++) {if (document.scripts[j].src === r) { return; }} k=e.createElement(t),a=e.getElementsByTagName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)}) (window, document, "script", "https://mc.yandex.ru/metrika/tag.js", "ym"); ym(55165297, "init", { clickmap:false, trackLinks:true, accurateTrackBounce:true, webvisor:false }); </script> <noscript><div><img src="https://mc.yandex.ru/watch/55165297" style="position:absolute; left:-9999px;" alt="" /></div></noscript>    <title>Accelerating Quantum Chemistry Calculations: Machine Learning for Efficient Evaluation of Electron-Repulsion Integrals</title> <meta name="description" content="Accelerating Quantum Chemistry Calculations: Machine Learning for Efficient Evaluation of Electron-Repulsion Integrals"> <meta name="keywords" content="Quantum energy calculations, atomic orbitals, electron-repulsion integrals, ensemble machine learning, random forests, neural networks, feature extraction."> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <meta name="citation_title" content="Accelerating Quantum Chemistry Calculations: Machine Learning for Efficient Evaluation of Electron-Repulsion Integrals"> <meta name="citation_author" content="Nishant Rodrigues"> <meta name="citation_author" content="Nicole Spanedda"> <meta name="citation_author" content="Chilukuri K. Mohan"> <meta name="citation_author" content="Arindam Chakraborty"> <meta name="citation_publication_date" content="2024/03/12"> <meta name="citation_journal_title" content="International Journal of Nuclear and Quantum Engineering"> <meta name="citation_volume" content="18"> <meta name="citation_issue" content="3"> <meta name="citation_firstpage" content="48"> <meta name="citation_lastpage" content="53"> <meta name="citation_pdf_url" content="https://publications.waset.org/10013557/pdf"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="" name="q" aria-label="Search"> <button class="btn btn-light my-2 my-sm-0" type="submit"><i class="fas fa-search"></i></button> </form> </div> <div class="collapse navbar-collapse mt-1" id="navbarMenu"> <ul class="navbar-nav ml-auto align-items-center" id="mainNavMenu"> <li class="nav-item"> <a class="nav-link" href="https://waset.org/conferences" title="Conferences in 2024/2025/2026">Conferences</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/disciplines" title="Disciplines">Disciplines</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/committees" rel="nofollow">Committees</a> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownPublications" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Publications </a> <div class="dropdown-menu" aria-labelledby="navbarDropdownPublications"> <a class="dropdown-item" href="https://publications.waset.org/abstracts">Abstracts</a> <a class="dropdown-item" href="https://publications.waset.org">Periodicals</a> <a class="dropdown-item" href="https://publications.waset.org/archive">Archive</a> </div> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/page/support" title="Support">Support</a> </li> </ul> </div> </div> </nav> </div> </header> <main> <div class="container mt-4"> <div class="row"> <div class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value=""> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 33093</div> </div> </div> </div> <div class="card publication-listing mt-3 mb-3"> <h5 class="card-header" style="font-size:.9rem">Accelerating Quantum Chemistry Calculations: Machine Learning for Efficient Evaluation of Electron-Repulsion Integrals</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=Nishant%20Rodrigues">Nishant Rodrigues</a>, <a href="https://publications.waset.org/search?q=Nicole%20Spanedda"> Nicole Spanedda</a>, <a href="https://publications.waset.org/search?q=Chilukuri%20K.%20Mohan"> Chilukuri K. Mohan</a>, <a href="https://publications.waset.org/search?q=Arindam%20Chakraborty"> Arindam Chakraborty</a> </p> <p class="card-text"><strong>Abstract:</strong></p> <p>A crucial objective in quantum chemistry is the computation of the energy levels of chemical systems. This task requires electron-repulsion integrals as inputs and the steep computational cost of evaluating these integrals poses a major numerical challenge in efficient implementation of quantum chemical software. This work presents a moment-based machine learning approach for the efficient evaluation of electron-repulsion integrals. These integrals were approximated using linear combinations of a small number of moments. Machine learning algorithms were applied to estimate the coefficients in the linear combination. A random forest approach was used to identify promising features using a recursive feature elimination approach, which performed best for learning the sign of each coefficient, but not the magnitude. A neural network with two hidden layers was then used to learn the coefficient magnitudes, along with an iterative feature masking approach to perform input vector compression, identifying a small subset of orbitals whose coefficients are sufficient for the quantum state energy computation. Finally, a small ensemble of neural networks (with a median rule for decision fusion) was shown to improve results when compared to a single network.</p> <iframe src="https://publications.waset.org/10013557.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Quantum%20energy%20calculations" title="Quantum energy calculations">Quantum energy calculations</a>, <a href="https://publications.waset.org/search?q=atomic%20orbitals" title=" atomic orbitals"> atomic orbitals</a>, <a href="https://publications.waset.org/search?q=electron-repulsion%20integrals" title=" electron-repulsion integrals"> electron-repulsion integrals</a>, <a href="https://publications.waset.org/search?q=ensemble%20machine%20learning" title=" ensemble machine learning"> ensemble machine learning</a>, <a href="https://publications.waset.org/search?q=random%0D%0Aforests" title=" random forests"> random forests</a>, <a href="https://publications.waset.org/search?q=neural%20networks" title=" neural networks"> neural networks</a>, <a href="https://publications.waset.org/search?q=feature%20extraction." title=" feature extraction."> feature extraction.</a> </p> <a href="https://publications.waset.org/10013557/accelerating-quantum-chemistry-calculations-machine-learning-for-efficient-evaluation-of-electron-repulsion-integrals" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/10013557/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/10013557/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/10013557/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/10013557/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/10013557/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/10013557/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/10013557/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/10013557/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/10013557/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/10013557/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/10013557.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">188</span> </span> <p class="card-text"><strong>References:</strong></p> <br>[1] B. Peng and K. Kowalski, “Highly efficient and scalable compound decomposition of two-electron integral tensor and its application in coupled cluster calculations,” Journal of chemical theory and computation, vol. 13, no. 9, pp. 4179–4192, 2017. <br>[2] F. Weigend, “A fully direct ri-hf algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency,” Physical Chemistry Chemical Physics, vol. 4, no. 18, pp. 4285–4291, 2002. <br>[3] H. Koch, A. S´anchez de Mer´as, and T. B. Pedersen, “Reduced scaling in electronic structure calculations using cholesky decompositions,” The Journal of chemical physics, vol. 118, no. 21, pp. 9481–9484, 2003. <br>[4] J. Jackson, Classical Electrodynamics. Wiley, 2021. <br>[Online]. Available: https://books.google.com/books?id=6VV-EAAAQBAJ <br>[5] B. Nagy and F. Jensen, “Basis sets in quantum chemistry,” Reviews in Computational Chemistry, vol. 30, pp. 93–149, 2017. <br>[6] A. Szabo and N. S. 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Georgiopoulos, “Feed-forward neural networks,” IEEE Potentials, vol. 13, no. 4, pp. 27–31, 1994. </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); });*/ jQuery.get({ url: "https://publications.waset.org/xhr/user-menu", cache: false }).then(function(response){ jQuery('#mainNavMenu').append(response); }); }); </script> </body> </html>

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Accelerating Quantum Chemistry Calculations: Machine Learning for Efficient Evaluation of Electron-Repulsion Integrals