Manifold-constrained Gaussian process inference for time-varying parameters in dynamic systems

Manifold-constrained Gaussian process inference for time-varying parameters in dynamic systems | 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 Manifold-constrained Gaussian process inference for time-varying parameters in dynamic systems Yan Sun, Shihao Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2102691/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 16 Oct, 2023 Read the published version in Statistics and Computing → Version 1 posted 7 You are reading this latest preprint version Abstract Identification of parameters in ordinary differential equations (ODEs) is an important and challenging task when modeling dynamic systems in biomedical research and other scientific areas, especially with the presence of time-varying parameters. This article proposes a fast and accurate method, TVMAGI (Time-Varying MAnifold-constrained Gaussian process Inference), to estimate both time-constant and time-varying parameters in the ODE using noisy and sparse observation data. TVMAGI imposes a Gaussian process model over the time series of system components as well as time-varying parameters, and restricts the derivative process to satisfy ODE conditions. Consequently, TVMAGI completely bypasses numerical integration and achieves substantial savings in computation time. By incorporating the ODE structures through manifold constraints, TVMAGI enjoys a principled statistical construct under the Bayesian paradigm, which further enables it to handle systems with missing data or unobserved components. The Gaussian process prior also alleviates the identifiability issue often associated with the time-varying parameters in ODE. Unlike existing approaches, TVMAGI can be applied to general nonlinear systems without specific structural assumptions. Three simulation examples, including an infectious disease compartmental model, are provided to illustrate the robustness and efficiency of our method compared with numerical integration and Bayesian filtering methods. ordinary differential equations inverse problem time-varying parameter estimation Gaussian process Bayesian inference Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 16 Oct, 2023 Read the published version in Statistics and Computing → Version 1 posted Editorial decision: Major revision 11 Nov, 2022 Reviews received at journal 21 Oct, 2022 Reviewers agreed at journal 11 Oct, 2022 Reviewers invited by journal 27 Sep, 2022 Editor assigned by journal 27 Sep, 2022 Submission checks completed at journal 26 Sep, 2022 First submitted to journal 25 Sep, 2022 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-2102691","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":139516018,"identity":"2af75102-c4da-4f6f-b7c2-157bc8457084","order_by":0,"name":"Yan Sun","email":"","orcid":"","institution":"Georgia Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Yan","middleName":"","lastName":"Sun","suffix":""},{"id":139516020,"identity":"51879ae1-55ca-4f76-aa44-5e0017692e1e","order_by":1,"name":"Shihao Yang","email":"data:image/png;base64,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","orcid":"","institution":"Georgia Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Shihao","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2022-09-26 02:59:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2102691/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2102691/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11222-023-10319-y","type":"published","date":"2023-10-16T15:00:58+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":27050239,"identity":"1022c474-9a72-4165-94a3-2c90a6b02222","added_by":"auto","created_at":"2022-09-27 20:59:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":13134788,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2102691/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Manifold-constrained Gaussian process inference for time-varying parameters in dynamic systems","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-2102691/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"statistics-and-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"stco","sideBox":"Learn more about [Statistics and Computing](http://link.springer.com/journal/11222)","snPcode":"11222","submissionUrl":"https://submission.nature.com/new-submission/11222/3","title":"Statistics and Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"ordinary differential equations, inverse problem, time-varying parameter estimation, Gaussian process, Bayesian inference","lastPublishedDoi":"10.21203/rs.3.rs-2102691/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2102691/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIdentification of parameters in ordinary differential equations (ODEs) is an important and challenging task when modeling dynamic systems in biomedical research and other scientific areas, especially with the presence of time-varying parameters. 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