Observation Point Sampling-Based Adaptive Sampling for Region Decomposition Methods

Observation Point Sampling-Based Adaptive Sampling for Region Decomposition Methods | 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 Observation Point Sampling-Based Adaptive Sampling for Region Decomposition Methods Kenan Chen, Beibei Wang, Tingni He, Xinxiang Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8217742/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 Traditional adaptive sampling for Physics-Informed Neural Networks (PINNs) selects collocation points based on partial differential equation (PDE) residuals. However, this approach often fail to significantly reduce the real loss, as high residual areas continue to exhibit substantial loss even after refinement. To address this limitation in interface problems, we propose an Observation Point Sampling-Based Adaptive Sampling strategy to enhance the predictive accuracy of PINNs. Observation Point Sampling-Based Adaptive Sampling is a strategy designed to pinpoint the distribution of real loss using fewer observation points. This strategy selects collocation points strategically to train the networks more efficiently and avoid wasteful sampling. Then we propose two algorithms: the Observation-Based Region Decomposition Method (ORDM) and the Observation-Based Hard-Constrained Region Decomposition Method (OHCRDM), for cases with sufficient and insufficient collocation points, respectively. We also compare our methods to traditional residual-base sampling methods such as residual-based adaptive refinement (RAR) and residual-based Adaptive Distribution (RAD) \cite{WU2023}, for both simple and complex interface problems. As is shown in our experiments, our algorithms achieve state-of-the-art performance. Adaptive sampling Physics-informed neural networks Region decomposition method Hard constrained Interface problems 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. We do this by developing innovative software and high quality services for the global research community. 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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-8217742","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":553428583,"identity":"c910945c-d22f-4cb3-a540-31eb0999bf2f","order_by":0,"name":"Kenan Chen","email":"","orcid":"","institution":"Shanghai University","correspondingAuthor":false,"prefix":"","firstName":"Kenan","middleName":"","lastName":"Chen","suffix":""},{"id":553428584,"identity":"36bf5188-e67f-43b0-bdcf-594d46922271","order_by":1,"name":"Beibei Wang","email":"","orcid":"","institution":"Shanghai University","correspondingAuthor":false,"prefix":"","firstName":"Beibei","middleName":"","lastName":"Wang","suffix":""},{"id":553428587,"identity":"e3bb7758-54ca-40d9-aeb3-9450adce8140","order_by":2,"name":"Tingni He","email":"","orcid":"","institution":"Shanghai University","correspondingAuthor":false,"prefix":"","firstName":"Tingni","middleName":"","lastName":"He","suffix":""},{"id":553428588,"identity":"acd2fd02-a28b-4fff-bc1c-4ecd530a83ae","order_by":3,"name":"Xinxiang Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABC0lEQVRIiWNgGAWjYDACZiBOADHYgfgDEBuAODxEaQEyGGckEKMFWS8zDzFaDI7zHpN4UHPHroGZ+eBj2x8M9uYSCYwP3rYxyJvj0CLZzJdskHDsWXIDM1uycU4CQ+LOGQnMhnPbGAx3NmDXws/MY/ggge1wMtBVZtJALQkGNxLYpHnbgIwD2LWwMfMYHEj4B9LC//23RQKDPVAL+298WsC2JLYdtgPawsYMDDvGDUBbmPFpkWzmMTZI7DsMVMZmLNmTJpG44czDZsk55yQMN+DQYnD+jJnkj2+H7fnZmx9++GFjY29wPPnghzdlNvK4bIGBxDYILQHEjA1QBn5gT1DFKBgFo2AUjFwAAKGkTxJ4VAx3AAAAAElFTkSuQmCC","orcid":"","institution":"Shanghai University","correspondingAuthor":true,"prefix":"","firstName":"Xinxiang","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2025-11-27 04:23:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8217742/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8217742/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":97251366,"identity":"50351c95-79e5-4362-8f49-ec3ff2822678","added_by":"auto","created_at":"2025-12-02 13:16:58","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2187367,"visible":true,"origin":"","legend":"","description":"","filename":"latex.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8217742/v1_covered_207d6880-7bb1-4ad7-8464-51d1a5d10313.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Observation Point Sampling-Based Adaptive Sampling for Region Decomposition Methods","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Adaptive sampling, Physics-informed neural networks, Region decomposition method, Hard constrained, Interface problems","lastPublishedDoi":"10.21203/rs.3.rs-8217742/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8217742/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Traditional adaptive sampling for Physics-Informed Neural Networks (PINNs) selects collocation points based on partial differential equation (PDE) residuals. However, this approach often fail to significantly reduce the real loss, as high residual areas continue to exhibit substantial loss even after refinement. To address this limitation in interface problems, we propose an Observation Point Sampling-Based Adaptive Sampling strategy to enhance the predictive accuracy of PINNs. Observation Point Sampling-Based Adaptive Sampling is a\nstrategy designed to pinpoint the distribution of real loss using fewer observation points.\nThis strategy selects collocation points strategically to train the networks more efficiently and avoid wasteful sampling. Then we propose two algorithms: the Observation-Based Region Decomposition Method (ORDM) and the Observation-Based Hard-Constrained Region Decomposition Method (OHCRDM), for cases with sufficient and insufficient collocation points, respectively. We also compare our methods to traditional residual-base sampling methods such as residual-based adaptive refinement (RAR) and residual-based Adaptive Distribution (RAD) \\cite{WU2023}, for both simple and complex interface problems. 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