Data-driven Koopman linearization of nonlinear elastodynamics problems

Data-driven Koopman linearization of nonlinear elastodynamics problems | 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 Data-driven Koopman linearization of nonlinear elastodynamics problems Konstantinos Spiliotis, Constantinos Koutsoumaris, Dimitris Sfyris This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8882605/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 A data-driven Koopman procedure is utilized to linearize the one-dimensional nonlinear constitutive equations of elastodynamics. Initially, we transform the nonlinear elastodynamics problem into a nonlinear system of equations, which is integrated through an established numerical scheme. The integration produces high-dimensional data (displacements), which constitutes the input of our approach. Then, the Koopman theory and the Dynamic Mode Decomposition (DMD) algorithm for system identification are applied, which produces a numerical linearization setup of the initial problem. The results demonstrate that, although the Koopman operator is an infinite-dimensional linear operator, it admits accurate low-dimensional approximations. The significance of this approach lies in its ability to leverage machine learning and system identification techniques to address nonlinear elastodynamics problems. Moreover, the method is well-suited for elastodynamic experimental applications, as it requires only displacement measurements as input and is independent of the underlying numerical scheme. 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. 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-8882605","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":595614231,"identity":"e3985ebe-b028-4170-b1f2-8bc3b8e01c59","order_by":0,"name":"Konstantinos Spiliotis","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVRIie3RvQrCMBDA8QuCU7HrFT+e4aTQqQ+TLk4ijk6iCDqpa32LPoBDJFCXiqubdXHuInRwMLW4iIaOgvlD2kL5wYUDMJl+MFRHpARgA5sAHxZPqwLhBOhMCkKK1CsQ4OpNoviqQpz1YSf40B+7ezlHNWE7Oi8Fu22/kyYOuBqsh14SzFEN5kZxg9da1++kgxYpItE7sRkpEkSxRTUUGmInJXHDqqQJ/ZIQsmn6IizTECcs7+KESVAQdDdxnyRoCB4PMsvuvm0v9ukuH/ntlUy6l1xD4G3Xzz2B1K/m01+Wa4nJZDL9WQ/0e1QH4/EfewAAAABJRU5ErkJggg==","orcid":"","institution":"Democritus University of Thrace","correspondingAuthor":true,"prefix":"","firstName":"Konstantinos","middleName":"","lastName":"Spiliotis","suffix":""},{"id":595614232,"identity":"ac32211b-eb59-4872-b0e2-65145147b09c","order_by":1,"name":"Constantinos Koutsoumaris","email":"","orcid":"","institution":"National Technical University of Athens","correspondingAuthor":false,"prefix":"","firstName":"Constantinos","middleName":"","lastName":"Koutsoumaris","suffix":""},{"id":595614234,"identity":"7ef82dc5-c9f9-40b5-a52c-e805539f6539","order_by":2,"name":"Dimitris Sfyris","email":"","orcid":"","institution":"Foundation for Research and Technology","correspondingAuthor":false,"prefix":"","firstName":"Dimitris","middleName":"","lastName":"Sfyris","suffix":""}],"badges":[],"createdAt":"2026-02-14 21:38:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8882605/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8882605/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105563852,"identity":"60e6ad6f-368c-4332-b762-ef4d7ea06b0e","added_by":"auto","created_at":"2026-03-27 12:47:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2498278,"visible":true,"origin":"","legend":"","description":"","filename":"DatadrivenKoopmanlinearisationofnonlinearelastodynamicsproblems.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8882605/v1_covered_06b8a1dd-9ff4-48df-9b75-d8379121ef9c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Data-driven Koopman linearization of nonlinear elastodynamics problems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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-8882605/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8882605/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"A data-driven Koopman procedure is utilized to linearize the one-dimensional nonlinear constitutive equations of elastodynamics. 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