Constrained Neural Networks Approach of the Cahn-hilliard Equation With u-dependent Mobility

Constrained Neural Networks Approach of the Cahn-hilliard Equation With u-dependent Mobility | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Constrained Neural Networks Approach of the Cahn-hilliard Equation With u-dependent Mobility Abdou Wahidi BELLO, Jamal ADETOLA, Said Amana ABDILLAH, Charbel Z. J. MAMLANKOU This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6202289/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper presents a comparative study between the finite element method and neural networks for the numerical resolution of the Cahn-Hilliard equation with concentration-dependent mobility. The neural approach introduced here is based on c-PINNs (constrained Physics-Informed Neural Networks), which incorporate physical constraints directly into their architecture. This integration enables them to effectively capture the complex dynamics of phase separation. Compared to the classical finite element method, c-PINNs adapt flexibly to local variations and resolve phase interfaces with high precision. Their ability to dynamically adjust to spatial gradients reduces the need for fine discretization and extensive mathematical analysis, making them particularly well-suited for complex and high-order problems. Error analysis confirms their robustness and predic-tive strength, highlighting their convergence toward the desired solution. This approach thus paves the way for more accurate and efficient simulations in the field of materials science and engineering. Cahn-Hilliard Phase separation concentration-dependent mobility c-PINNs Finite Element Method Neural networks Physical constraints Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6202289","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":436547283,"identity":"73e9c9cd-2c63-463a-8cda-67b565e5a560","order_by":0,"name":"Abdou Wahidi BELLO","email":"","orcid":"","institution":"Université d'Abomey-Calavi","correspondingAuthor":false,"prefix":"","firstName":"Abdou","middleName":"Wahidi","lastName":"BELLO","suffix":""},{"id":436547285,"identity":"5262599e-6823-47cc-99cb-51339f4a5413","order_by":1,"name":"Jamal ADETOLA","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIiWNgGAWjYFCCBCAuYGAGkowHPoAEmEGIB68WxgYGA7AWhoMzgAQPsVrA4DBIIQ/EItyAvz35+IMPBnbs/NMOPzhs23bH3p6dO4G5QAa3FokzzxIbZxgkM0vcTjM4nNv2LLGHmXcD8wx8DruRY9jMY8DMzHA7AaTlcAIPSAsPHi3yN/I/ArXUM8vfTv9w2LLtsD1BLQY3chiBWg4zG9zOMTjM2HaYsYeQFsMzzwxnzjA4zmx4O6fgYM+5w4k9h3k3HMbnF7njyQ8+fKioTpa7nb7xwY+yw/bs/Wc3Pi7sweN9KEhG4R1gJEKLHRr/B2Eto2AUjIJRMGIAABfvUtPDySaJAAAAAElFTkSuQmCC","orcid":"","institution":"National University of Sciences, Technologies, Engineering and Mathematics","correspondingAuthor":true,"prefix":"","firstName":"Jamal","middleName":"","lastName":"ADETOLA","suffix":""},{"id":436547287,"identity":"c92d748e-43a2-4f1c-a9fc-58e27204d3c3","order_by":2,"name":"Said Amana ABDILLAH","email":"","orcid":"","institution":"Université des comores","correspondingAuthor":false,"prefix":"","firstName":"Said","middleName":"Amana","lastName":"ABDILLAH","suffix":""},{"id":436547288,"identity":"f4db7f39-75b4-4fb9-bebe-ba6b10ba415c","order_by":3,"name":"Charbel Z. 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