Physics-augmented learning in latent space via Operator Autoencoder for dynamic system response prediction

Physics-augmented learning in latent space via Operator Autoencoder for dynamic system response prediction | 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 Physics-augmented learning in latent space via Operator Autoencoder for dynamic system response prediction Xuandong Lu, Yongming Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8704305/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 novel Fourier-enhanced Operator Autoencoder (F-OAE) is proposed for high-fidelity dynamic system response prediction. High dimensionality poses significant challenges and computational burden for machine-learning-based dynamic system modeling. A classical approach is to use a dimension reduction technique, such as an autoencoder, to map the high-dimensional response to discrete latent vector space. Then, vector-to-vector approximation (e.g., neural network) or vector-to-function approximation (e.g., operator network) is used to model the latent dynamics. Following this, the latent prediction is decoded back to the high-dimensional space. This approach has difficulties in enforcing physics constraints in latent space modeling and additional computational requirements for both the encoding and decoding processes. Thus, we propose a reduced-order modeling approach based on the operator autoencoder (OAE) driven by Deep Operator Network (DeepONet), which maps system response to a latent functional space rather than a discrete vector space for downstream learning. In the proposed formulation, solution snapshots are processed by an operator network in the self-supervised autoencoder setting to find latent coefficients and truncated basis functions. A Fourier-enhanced network is used to generate the basis functions to increase diversity. The latent coefficients and basis functions are analytically combined to reconstruct the full solution field with guaranteed smoothness and differentiability, which enables the easy transformation of physics constraints to the latent space modeling. The proposed framework is demonstrated and validated across four representative dynamic system simulation data. Comparisons with classical autoencoder-based dimension reduction methods demonstrate the feasibility and efficiency of OAE for reduced-order modeling of dynamic systems. dynamic systems reduced-order models DeepONet physics-augmented learning operator autoencoder 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-8704305","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":582437798,"identity":"ed79ae10-ece0-43ee-983e-13d2bfe5fa8c","order_by":0,"name":"Xuandong Lu","email":"","orcid":"","institution":"Arizona State University","correspondingAuthor":false,"prefix":"","firstName":"Xuandong","middleName":"","lastName":"Lu","suffix":""},{"id":582437799,"identity":"84941043-8818-4081-acdd-811bcba9abd4","order_by":1,"name":"Yongming Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYBACgwNgEoglGBsYPkAFidfCOIMYLZINMJYEAwMzDzFa+Nl7D7+6UXDHrkGCuU3apqYusYG9eZsEPi1sPOfSrHMMniU3SDC2SeccO5zYwHOsDL8WiRwz4xyDw8kMYC1sBxIbgCIkaLH4B3SY/BuCWowfA7XYgbUwtjEDbeEhoIXnjBkzUEsCmwRjs2Vv32HjNp60Ygu8Wth7jD/n/Dlszy9//OGNH9/qZPvZD2+8gU8L2G1AIrENziWgHASYQcnEngiFo2AUjIJRMFIBAFoCQeg1b/y1AAAAAElFTkSuQmCC","orcid":"","institution":"Arizona State University","correspondingAuthor":true,"prefix":"","firstName":"Yongming","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2026-01-26 23:53:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8704305/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8704305/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104400761,"identity":"da02762b-b07b-4dbe-83c0-14da3ba89b0b","added_by":"auto","created_at":"2026-03-11 12:10:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1219313,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript0126.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8704305/v1_covered_022ea60e-d64b-4a2c-96c1-eee918366414.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Physics-augmented learning in latent space via Operator Autoencoder for dynamic system response prediction","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":"dynamic systems, reduced-order models, DeepONet, physics-augmented learning, operator autoencoder","lastPublishedDoi":"10.21203/rs.3.rs-8704305/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8704305/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA novel Fourier-enhanced Operator Autoencoder (F-OAE) is proposed for high-fidelity dynamic system response prediction. 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