Data-driven discovery of spatiotemporal dynamical systems with sparse interpretable neural networks

Data-driven discovery of spatiotemporal dynamical systems with sparse interpretable neural networks | 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 Data-driven discovery of spatiotemporal dynamical systems with sparse interpretable neural networks Siyuan Xing, Qingyu Han, Efstathios Charalampidis, Ying-Cheng Lai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7048656/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 Existing approaches to data-driven model discovery of nonlinear dynamical systems are mainly sparse optimization, symbolic regression, and Kolmogorov-Arnold networks, but they all suffer from the “curse of dimensionality”, i.e., the number of candidate functions grows exponentially with the dimension. Spatiotemporal dynamical systems, when represented by coupled ordinary differential equations, often involve hundreds or even thousands dimensions. Discovering the high-dimensional velocity field using large datasets presents a formidable challenge. We develop a machine-learning framework that integrates an interpretable neural network incorporating the matrix formulation of sparse regression with a specially designed sparsity promoting pruning scheme. Utilizing five paradigmatic spatiotemporal dynamical systems, we demonstrate that our framework is capable of accurately finding the velocity field of more than 100 dimensions and extrapolating to generate the correct coherent structures from untrained data. We further validate the effectiveness of our framework on an empirical dataset from a triple pendulum experiment. Our framework can potentially be scaled up to systems with thousands of dimensions, rendering data-driven model discovery of large complex systems feasible. Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Nonlinear phenomena 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 SREINetSI.pdf Supplementary Info 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. 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-7048656","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":483444991,"identity":"c57dfa8c-4a56-4786-a589-1e232e03cd0d","order_by":0,"name":"Siyuan Xing","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVRIiWNgGAWjYDACZgaGAwwMNgwM7EDOA5DIAeK0pIEZDAlEaYGAwyRokW/nMTxc8Ou8PH8z78EHiW0Mcnw3EvBrMTjMlnB4Zt9twxmH+ZINgFqMJQlqYWY+cJi353YCw2EeMwmglsQNhLTINzM2ALWcS5CHaqknqIXhMNAWnh8HEgygWhIMiPILb0Oy4UaQXxLOSRjOPPOAgMP6zxh/5vljJy93vPfggw9lNvJ8xwk5DAQY20AkD5DBJkGEcjD4A9UCYYyCUTAKRsEoQAUAr/FGZKTQfh4AAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-6916-719X","institution":"California Polytechnic State University","correspondingAuthor":true,"prefix":"","firstName":"Siyuan","middleName":"","lastName":"Xing","suffix":""},{"id":483444992,"identity":"968b378a-4650-424b-a6dd-b0312a65dbac","order_by":1,"name":"Qingyu Han","email":"","orcid":"","institution":"California Polytechnic State University","correspondingAuthor":false,"prefix":"","firstName":"Qingyu","middleName":"","lastName":"Han","suffix":""},{"id":483444993,"identity":"537753c7-4fb3-44d4-98ee-bcdc3b8693bd","order_by":2,"name":"Efstathios Charalampidis","email":"","orcid":"","institution":"San Diego State University","correspondingAuthor":false,"prefix":"","firstName":"Efstathios","middleName":"","lastName":"Charalampidis","suffix":""},{"id":483444994,"identity":"4c89509b-de52-4a6e-847b-4e8e9eccf3a0","order_by":3,"name":"Ying-Cheng Lai","email":"","orcid":"https://orcid.org/0000-0002-0723-733X","institution":"[email protected]","correspondingAuthor":false,"prefix":"","firstName":"Ying-Cheng","middleName":"","lastName":"Lai","suffix":""}],"badges":[],"createdAt":"2025-07-04 16:55:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7048656/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7048656/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104401465,"identity":"83dfba46-5914-4fa8-8bec-008d38e799c4","added_by":"auto","created_at":"2026-03-11 12:12:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":11484867,"visible":true,"origin":"","legend":"Article File","description":"","filename":"SREINetmain.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7048656/v1_covered_381dc674-9764-4b60-b3bd-248979a3842d.pdf"},{"id":86490172,"identity":"00b37108-ff39-4b80-aab4-bcb20ac678c3","added_by":"auto","created_at":"2025-07-11 08:55:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":14999424,"visible":true,"origin":"","legend":"Supplementary Info","description":"","filename":"SREINetSI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7048656/v1/44a9f7afe83d381ff5b98cb1.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Data-driven discovery of spatiotemporal dynamical systems with sparse interpretable neural networks","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":"","lastPublishedDoi":"10.21203/rs.3.rs-7048656/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7048656/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Existing approaches to data-driven model discovery of nonlinear dynamical systems are mainly sparse optimization, symbolic regression, and Kolmogorov-Arnold networks, but they all suffer from the “curse of dimensionality”, i.e., the number of candidate functions grows exponentially with the dimension. 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