Simulating Vibrations of 1D-Continua with Oscillatory Physics-Informed Neural Networks (oPINN)

Simulating Vibrations of 1D-Continua with Oscillatory Physics-Informed Neural Networks (oPINN) | 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 Simulating Vibrations of 1D-Continua with Oscillatory Physics-Informed Neural Networks (oPINN) Stefan Hildebrand, Julia Ilvi Sachsendahl, Sandra Klinge This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7611510/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 The oscillatory Physics-Informed Neural Network (oPINN) Machine Learning architecture is suggested and analyzed for simulating the oscillatory behavior of continua and to estimate eigenfrequencies and eigenmodes. The analysis suggests that oPINN gives stable and accurate results for both free and excited oscillations, also for cases in which the initial condition is non-harmonic and introduces discontinuous first derivatives. Compared to conventional PINN, oPINN leads to significant reduction in computational effort and great increase in both accuracy and stability. Moreover, the oPINN based solution better fulfills the energy conservation requirement compared to conventional predictor-corrector time integration schemes. This advantage is achieved by the application of second-order central differences both in the spatial and temporal domain. Oscillations Eigenfrequencies PINN Physics-Informed Neural Networks Machine Learning 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-7611510","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":518452614,"identity":"408749a8-940e-4518-aec4-f739d625574c","order_by":0,"name":"Stefan Hildebrand","email":"data:image/png;base64,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","orcid":"","institution":"Technische Universität Berlin","correspondingAuthor":true,"prefix":"","firstName":"Stefan","middleName":"","lastName":"Hildebrand","suffix":""},{"id":518452615,"identity":"9948662b-a9c7-4ade-9eb5-a7e4eae3e828","order_by":1,"name":"Julia Ilvi Sachsendahl","email":"","orcid":"","institution":"Technische Universität Berlin","correspondingAuthor":false,"prefix":"","firstName":"Julia","middleName":"Ilvi","lastName":"Sachsendahl","suffix":""},{"id":518452616,"identity":"353ae6e3-a093-4c4f-ab86-3793b4904fad","order_by":2,"name":"Sandra Klinge","email":"","orcid":"","institution":"Technische Universität Berlin","correspondingAuthor":false,"prefix":"","firstName":"Sandra","middleName":"","lastName":"Klinge","suffix":""}],"badges":[],"createdAt":"2025-09-14 08:53:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7611510/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7611510/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":92277921,"identity":"324c90f3-32ea-4f67-9513-bb49aade0826","added_by":"auto","created_at":"2025-09-26 15:43:22","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4661,"visible":true,"origin":"","legend":"","description":"","filename":"c18051a3793741578b4d4a9aa31cec4a.json","url":"https://assets-eu.researchsquare.com/files/rs-7611510/v1/8eae486d448b15a14e964f4d.json"},{"id":96871377,"identity":"6b1ca28a-dddd-45cd-8f95-2a797980aa89","added_by":"auto","created_at":"2025-11-27 03:38:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":771789,"visible":true,"origin":"","legend":"","description":"","filename":"PaperOscillations20250914II.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7611510/v1_covered_baeb7099-fcb2-44d9-866f-f57178e296d9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Simulating Vibrations of 1D-Continua with Oscillatory Physics-Informed Neural Networks (oPINN)","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":"Oscillations, Eigenfrequencies, PINN, Physics-Informed Neural Networks, Machine Learning","lastPublishedDoi":"10.21203/rs.3.rs-7611510/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7611510/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The oscillatory Physics-Informed Neural Network (oPINN) Machine Learning architecture is suggested and analyzed for simulating the oscillatory behavior of continua and to estimate eigenfrequencies and eigenmodes. 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