Predicting Future State of Nonlinear Dynamical Systems with Multi-View Embedding

Predicting Future State of Nonlinear Dynamical Systems with Multi-View Embedding | 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 Predicting Future State of Nonlinear Dynamical Systems with Multi-View Embedding Wei Chen, Jürgen Kurths, Yifang MA, Zheng Jiang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6797901/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 Future state prediction of nonlinear dynamical systems has significant applications in diverse fields, ranging from Earth science to social science and neuroscience. Yet, we still lack systematic methods to achieve accurate and synchronous prediction of nonlinear dynamical systems without knowing the underlying dynamical systems. Here we overcome this challenge by developing a data-driven framework based on multi-view embedding with a spatiotemporal information transformation (MVIT). Our approach efficiently converts spatial information of the system into temporal information by reconstructing multiple delayed attractors matched with optimal non-delayed attractor manifolds. By integrating with parallel reservoir computing, MVIT clearly outperforms other existing predictive methods in synchronous dynamic predictions for various paradigmatic models as well as real-world systems from medicine and infrastructure. Notably, our approach also demonstrates robustness against noise and exhibits scalable long-term prediction capabilities. Our approach offers an avenue to discover hidden mechanisms of complex systems and has potential to be applied to more real-world systems from diverse fields. Physical sciences/Mathematics and computing/Applied mathematics Earth and environmental sciences/Natural hazards Full Text Additional Declarations There is NO Competing Interest. Supplementary Files predictionSI.pdf Predicting Future State of Nonlinear Dynamical Systems with Multi-View Embedding 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-6797901","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":470506496,"identity":"c3dcd140-538b-4b80-8bb0-55a5fa24dbf9","order_by":0,"name":"Wei Chen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAv0lEQVRIiWNgGAWjYDACCSBOqDgA4fAQr+UMyVoY20jRwj+7x/DBw3l3EvvbDzA+eNvGIG9O0JI7Z4wNErc9S5xxJoHZcG4bg+HOBgJaDCRyt0kkbjuc2HAggU2at40hweAAYS3bfyTOOZw4//wD9t/EatnGkNhwOHHDjQQ2ZqK0SNzI/yyRcOyZ8cYbD5sl55yTMNxASAv/jLTEjz9q7sjOO5988MObMht5grYgAcYGBkg0jYJRMApGwSigGAAAyjFGhBCLV5QAAAAASUVORK5CYII=","orcid":"","institution":"Beihang University","correspondingAuthor":true,"prefix":"","firstName":"Wei","middleName":"","lastName":"Chen","suffix":""},{"id":470506497,"identity":"b130cd82-fc6e-4f20-a0eb-b90054a50401","order_by":1,"name":"Jürgen Kurths","email":"","orcid":"https://orcid.org/0000-0002-5926-4276","institution":"Potsdam Institute for Climate Impact Research","correspondingAuthor":false,"prefix":"","firstName":"Jürgen","middleName":"","lastName":"Kurths","suffix":""},{"id":470506498,"identity":"cd08ff60-f042-493c-844f-08854e39ce5a","order_by":2,"name":"Yifang MA","email":"","orcid":"https://orcid.org/0000-0003-0326-7993","institution":"Southern University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Yifang","middleName":"","lastName":"MA","suffix":""},{"id":470506499,"identity":"d1bfb538-1451-4de8-8f23-bbac8afc6bcd","order_by":3,"name":"Zheng Jiang","email":"","orcid":"","institution":"Beihang University","correspondingAuthor":false,"prefix":"","firstName":"Zheng","middleName":"","lastName":"Jiang","suffix":""}],"badges":[],"createdAt":"2025-06-01 23:35:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6797901/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6797901/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86940679,"identity":"e091862d-62b9-491e-a306-2b9847d74a4c","added_by":"auto","created_at":"2025-07-17 11:48:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2227161,"visible":true,"origin":"","legend":"Article File","description":"","filename":"predictionMS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6797901/v1_covered_e9fdf1ce-4ede-484e-963c-1f10363a1948.pdf"},{"id":84518251,"identity":"b947c57a-4792-49fa-b0e7-bc4f94aeee80","added_by":"auto","created_at":"2025-06-13 02:30:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2106117,"visible":true,"origin":"","legend":"Predicting Future State of Nonlinear Dynamical Systems with Multi-View Embedding","description":"","filename":"predictionSI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6797901/v1/a5c5ffaf4268cc1a72b0cd99.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Predicting Future State of Nonlinear Dynamical Systems with Multi-View Embedding","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-6797901/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6797901/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Future state prediction of nonlinear dynamical systems has significant applications in diverse fields, ranging from Earth science to social science and neuroscience. 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