Bridging Known and Unknown Dynamics: Machine Learning Inference From Sparse Observations

Bridging Known and Unknown Dynamics: Machine Learning Inference From Sparse Observations | 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 Article Bridging Known and Unknown Dynamics: Machine Learning Inference From Sparse Observations Ying-Cheng Lai, Zheng-Meng Zhai, Jun-Yin Huang, Benjamin Stern This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5920918/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 28 Aug, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract In applications, an anticipated issue is where the system of interest has never been encountered before and sparse observations can be made only once. Can the dynamics be faithfully reconstructed? We address this challenge by developing a hybrid transformer and reservoir-computing scheme. The transformer is trained without using data from the target system, but with essentially unlimited synthetic data from known chaotic systems. The trained transformer is then tested with the sparse data from the target system, and its output is further fed into a reservoir computer for predicting its long-term dynamics or the attractor. The power of the proposed hybrid machine-learning framework is demonstrated using various prototypical nonlinear systems, where the dynamics can be faithfully reconstructed even with 80% sparsity. The framework provides a paradigm of reconstructing complex and nonlinear dynamics in the extreme situation where training data do not exist and the observations are random and sparse. Physical sciences/Mathematics and computing/Computational science Physical sciences/Mathematics and computing/Applied mathematics Full Text Additional Declarations There is NO Competing Interest. Supplementary Files SI.pdf Cite Share Download PDF Status: Published Journal Publication published 28 Aug, 2025 Read the published version in Nature Communications → 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-5920918","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":409628806,"identity":"a5281092-55bd-4463-aad5-8f3d05f3cae4","order_by":0,"name":"Ying-Cheng Lai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIiWNgGAWjYBACg8MgsuYAiGQDcm0gwjwEtRyDa0kjrEWyAUgwNsG0MBwmrIWfnffwC8aGO3Lm/AvYGH4UnJeXn5HA+OBtG24tbMx8aRaMDc+MLWc8YGPsMbhtuOFGArPhXLxaeMyM/zYcTtxw4wAbA4/BbcYNEgls0rwEtBgwNhyuB2lh/GNwzn7+jAT23wS0GD9gbDqcYHC+Acg2OJDYcCOBjZmQLcBAPgz0AmMbs4xBcvKGMw+bJeecw6OF/4zxB4aaw/IG5w8f//jmj53t/Pbkgx/elOHWAtIlAaYkEhugAowNuJTCAPMHMMV/gJDCUTAKRsEoGKkAAGcgUJ/WH9DpAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-0723-733X","institution":"[email protected]","correspondingAuthor":true,"prefix":"","firstName":"Ying-Cheng","middleName":"","lastName":"Lai","suffix":""},{"id":409628807,"identity":"9f2742ce-5ca0-47ec-bdce-6d6dca9f95f2","order_by":1,"name":"Zheng-Meng Zhai","email":"","orcid":"https://orcid.org/0000-0003-3702-0454","institution":"Arizona State University","correspondingAuthor":false,"prefix":"","firstName":"Zheng-Meng","middleName":"","lastName":"Zhai","suffix":""},{"id":409628808,"identity":"5253a50f-1645-4d5d-957c-12b9d0e6b0d2","order_by":2,"name":"Jun-Yin Huang","email":"","orcid":"","institution":"Arizona State University - Tempe Campus","correspondingAuthor":false,"prefix":"","firstName":"Jun-Yin","middleName":"","lastName":"Huang","suffix":""},{"id":409628809,"identity":"222b30ed-cd8f-413e-9333-4336230e7426","order_by":3,"name":"Benjamin Stern","email":"","orcid":"https://orcid.org/0000-0003-3866-6505","institution":"Tufts University School of Medicine","correspondingAuthor":false,"prefix":"","firstName":"Benjamin","middleName":"","lastName":"Stern","suffix":""}],"badges":[],"createdAt":"2025-01-28 21:15:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5920918/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5920918/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-63019-8","type":"published","date":"2025-08-28T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":75283322,"identity":"bc360709-d735-457b-aee8-8475e5227f94","added_by":"auto","created_at":"2025-02-03 03:44:26","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":17391501,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"SI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5920918/v1/3ea1e49cd433edc1f4c0d120.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"\u003cp\u003eBridging Known and Unknown Dynamics: Machine Learning Inference From Sparse Observations\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5920918/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5920918/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In applications, an anticipated issue is where the system of interest has never been encountered before and sparse observations can be made only once. 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