Interface Physics-Informed Neural Networks (I-PINNs) to Solve Inverse Problems in Heterogeneous Materials

Interface Physics-Informed Neural Networks (I-PINNs) to Solve Inverse Problems in Heterogeneous Materials | 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 Interface Physics-Informed Neural Networks (I-PINNs) to Solve Inverse Problems in Heterogeneous Materials Dibakar Roy Sarkar, Chandrasekhar Annavarapu, Pratanu Roy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7259124/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 study develops a physics-informed neural networks framework to solve inverse problems, specifically determining discontinuous material properties and the location of interfaces within heterogeneous materials. We propose using distinct neural networks for field variables and material properties in each material that employ identical activation functions but are trained separately for all other parameters. The neural networks used in different materials, on the other hand, have distinct activation functions but are identical in other parameters. Additionally, for a priori unknown interfaces, additional trainable variables that represent the coordinates of points on the interface are provided to the neural networks. The interface topology is obtained from these trained coordinates through a piecewise linear approximation. The proposed framework is tested on several 1-D and 2-D benchmark examples. The results demonstrate that the proposed methodology can determine both the material properties and the interface location with a root-mean-square error of $ \mathcal{O}(10^{-2}) $ to $ \mathcal{O}(10^{-3}) $ , highlighting its potential as an alternative approach for addressing inverse problems for heterogeneous materials. Physics-informed neural networks Data-driven scientific computing Inverse problems Interface determination Heterogeneous materials SciML Discontinuous material properties 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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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-7259124","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":498881922,"identity":"60f99410-72ac-4656-9c06-bf84eeaaa497","order_by":0,"name":"Dibakar Roy Sarkar","email":"","orcid":"","institution":"Johns Hopkins University","correspondingAuthor":false,"prefix":"","firstName":"Dibakar","middleName":"Roy","lastName":"Sarkar","suffix":""},{"id":498881923,"identity":"dedc2aa9-1239-4438-b320-6802b35c4c09","order_by":1,"name":"Chandrasekhar Annavarapu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABC0lEQVRIiWNgGAWjYJADxgcMBgw8fAyMDQegAg2EtDAbgLSwgbQcIFILmwSYBBEH8Cjjn9178DNPzT15c4nkZxU/Cg7LsDEwNx7+mMMgz9/A3PYAixaJO+eSpXmOFRvunJFmdrPH4DDEYQe3MRjOOMDYboDNmhs5BpIz2BIYN9zIYbvNYJAG18K4gYGxTQKLDvkbOcY/Z/xLsAdpKUbWYo9Li8GNHDOJj20JiSAtzAwGNnAtibi0GAK1WHzsS0je2fPMWLIHpIUZqOXsNonkGYexa5EDOuxGwrcE2+3syQ8//PgjYc/P3v74Q+U2G9v+9vZn2LQgXAhnMUOCEsYgRssoGAWjYBSMAjQAABYhYBTfxchaAAAAAElFTkSuQmCC","orcid":"","institution":"Indian Institute of Technology Madras","correspondingAuthor":true,"prefix":"","firstName":"Chandrasekhar","middleName":"","lastName":"Annavarapu","suffix":""},{"id":498881924,"identity":"649d6710-8948-471d-8549-d1f332acdf10","order_by":2,"name":"Pratanu Roy","email":"","orcid":"","institution":"Lawrence Livermore National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Pratanu","middleName":"","lastName":"Roy","suffix":""}],"badges":[],"createdAt":"2025-07-31 07:23:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7259124/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7259124/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90421732,"identity":"cbfa9258-1f9c-475a-94b5-5637ee07e112","added_by":"auto","created_at":"2025-09-02 14:07:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4028962,"visible":true,"origin":"","legend":"","description":"","filename":"RoySarkaretalMLCSE2025.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7259124/v1_covered_524a9a94-f1b5-4b41-ab00-22f5416d956b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Interface Physics-Informed Neural Networks (I-PINNs) to Solve Inverse Problems in Heterogeneous Materials","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Physics-informed neural networks, Data-driven scientific computing, Inverse problems, Interface determination, Heterogeneous materials, SciML, Discontinuous material properties","lastPublishedDoi":"10.21203/rs.3.rs-7259124/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7259124/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study develops a physics-informed neural networks framework to solve inverse problems, specifically determining discontinuous material properties and the location of interfaces within heterogeneous materials. We propose using distinct neural networks for field variables and material properties in each material that employ identical activation functions but are trained separately for all other parameters. The neural networks used in different materials, on the other hand, have distinct activation functions but are identical in other parameters. Additionally, for \u003cem\u003ea priori\u003c/em\u003e unknown interfaces, additional trainable variables that represent the coordinates of points on the interface are provided to the neural networks. The interface topology is obtained from these trained coordinates through a piecewise linear approximation. The proposed framework is tested on several 1-D and 2-D benchmark examples. 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