Modeling the inverse MEG problem inneuro-imaging using Physics Informed NeuralNetworks

Modeling the inverse MEG problem inneuro-imaging using Physics Informed NeuralNetworks | 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 Modeling the inverse MEG problem inneuro-imaging using Physics Informed NeuralNetworks Ourania Giannopoulou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9072729/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 11 You are reading this latest preprint version Abstract Magnetoencephalography (MEG) forward and inverse modeling is fundamen-tal to neuroscientific discovery, yet the inversion of partial differential equations(PDEs) remains one of the most difficult challenges due to its inherent ill-posedness. While traditional numerical methods often struggle with the computa-tional burden and regularization requirements of these problems, neural networkshave recently emerged as a highly viable alternative, offering the ability to learncomplex, non-linear mappings and provide efficient, real-time inference. Thispaper presents a framework for the MEG forward and inverse problems, integrat-ing finite element modeling with neural network techniques. The forward problemis solved using FEniCS to model the electric potential governed by the Poissonequation on a realistic anatomical brain mesh, with magnetic fields computed viathe Biot-Savart law. For the inverse problem, we introduce a Physics-InformedNeural Network (PINN) approach in order to deal with the ill condition of theproblem. Unlike purely data-driven deep learning approaches that treat this prob-lem as a black box learned from massive datasets, the proposed PINN frameworkdirectly embeds the governing physics—Maxwell’s equations and the Biot-Savartlaw—into the loss function, ensuring that the reconstructed sources satisfy thefundamental electromagnetic laws even in data-scarce regimes. We validate theframework on a high-resolution anatomical mesh and compared against the stan-dard Minimum Norm Estimation (MNE). Results demonstrate that the PINNapproach achieves a 30.2% improvement over the MNE baseline. Magnetoencephalography Inverse Problem Finite Element Method FEniCS Ellipsoidal MEG Geometry Physics Informed Neural Networks Full Text Additional Declarations No competing interests reported. Supplementary Files megpinnssuppl.zip Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 10 May, 2026 Reviews received at journal 29 Apr, 2026 Reviews received at journal 17 Apr, 2026 Reviews received at journal 09 Apr, 2026 Reviewers agreed at journal 01 Apr, 2026 Reviewers agreed at journal 29 Mar, 2026 Reviewers agreed at journal 29 Mar, 2026 Reviewers invited by journal 29 Mar, 2026 Editor assigned by journal 11 Mar, 2026 Submission checks completed at journal 11 Mar, 2026 First submitted to journal 09 Mar, 2026 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-9072729","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":615816723,"identity":"3f4a3380-b755-476d-8776-b04699b84832","order_by":0,"name":"Ourania Giannopoulou","email":"data:image/png;base64,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","orcid":"","institution":"University of Rome Tor Vergata","correspondingAuthor":true,"prefix":"","firstName":"Ourania","middleName":"","lastName":"Giannopoulou","suffix":""}],"badges":[],"createdAt":"2026-03-09 12:11:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9072729/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9072729/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106094129,"identity":"bcc8c19c-b209-4320-9624-59f1ef61e661","added_by":"auto","created_at":"2026-04-03 11:41:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3673788,"visible":true,"origin":"","legend":"","description":"","filename":"jcnsmegarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9072729/v1_covered_ed259198-6c23-4c7a-a0b6-9dd3315ee65e.pdf"},{"id":105991547,"identity":"305c1cde-8f1b-4ec4-920e-d40826beff89","added_by":"auto","created_at":"2026-04-02 08:29:17","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":4389081,"visible":true,"origin":"","legend":"","description":"","filename":"megpinnssuppl.zip","url":"https://assets-eu.researchsquare.com/files/rs-9072729/v1/e89fab5a10b09f7e33a85147.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modeling the inverse MEG problem inneuro-imaging using Physics Informed NeuralNetworks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"neuroinformatics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nein","sideBox":"Learn more about [Neuroinformatics](http://link.springer.com/journal/12021)","snPcode":"12021","submissionUrl":"https://submission.nature.com/new-submission/12021/3","title":"Neuroinformatics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":" Magnetoencephalography, Inverse Problem, Finite Element Method, FEniCS, Ellipsoidal MEG Geometry, Physics Informed Neural Networks","lastPublishedDoi":"10.21203/rs.3.rs-9072729/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9072729/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Magnetoencephalography (MEG) forward and inverse modeling is fundamen-tal to neuroscientific discovery, yet the inversion of partial differential equations(PDEs) remains one of the most difficult challenges due to its inherent ill-posedness. 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