Product-based topological Lagrangian neural network for learning articulated 2D multi-rigid-body system

Product-based topological Lagrangian neural network for learning articulated 2D multi-rigid-body system | 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 Product-based topological Lagrangian neural network for learning articulated 2D multi-rigid-body system Xiao-Feng Liu, Zhi-Hao Ai, Kang-Hao Wang, Hui-Bo Zhang, Guo-Ping Cai This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4504050/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 Lagrangian neural networks (LNN) is a physical-informed data-driven framework for learning the dynamics of physical systems. The incorporation of strong inductive biases enables LNN to outperform purely data-driven methods. However, its application has predominantly been confined to simple systems like pendulums, springs, or single rigid bodies such as gyroscopes or rigid rotors. In this paper, we present a so-called product-based topological Lagrangian neural network (PTLNN) that can learn the dynamics of articulated multi-rigid-body system by exploiting the coupling nonlinearity and the topological relation of system. Compared to other improved Lagrangian neural networks, such as Lagrangian graph neural network and Constraint Lagrangian neural network, the additional prior-knowledges in PTLNN do not need to be measured, which make PTLNNs easier to use. We demonstrate the performance of PTLNN by learning the dynamics of articulated systems with different degrees of freedom. The testing results illustrates that PTLNN outperforms other physical-informed neural networks such as LNN, HNN and NODE, which only encode prior knowledge without measurement. Dynamics modeling Machine learning Physical-informed data-driven method Product-based topological Lagrangian neural networks Coupling nonlinearity 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. 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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-4504050","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":312174655,"identity":"e8f41fd5-8971-4ce7-868b-b5b5236b55b5","order_by":0,"name":"Xiao-Feng Liu","email":"data:image/png;base64,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","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":true,"prefix":"","firstName":"Xiao-Feng","middleName":"","lastName":"Liu","suffix":""},{"id":312174656,"identity":"332d006a-9c53-4fd6-a885-6798f209f1ae","order_by":1,"name":"Zhi-Hao Ai","email":"","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Zhi-Hao","middleName":"","lastName":"Ai","suffix":""},{"id":312174657,"identity":"cb8c8b41-2255-44e3-bc16-673478e91898","order_by":2,"name":"Kang-Hao Wang","email":"","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Kang-Hao","middleName":"","lastName":"Wang","suffix":""},{"id":312174658,"identity":"bc9bf9d2-ba1c-495c-9391-de0367039776","order_by":3,"name":"Hui-Bo Zhang","email":"","orcid":"","institution":"Harbin Engineering University","correspondingAuthor":false,"prefix":"","firstName":"Hui-Bo","middleName":"","lastName":"Zhang","suffix":""},{"id":312174659,"identity":"91c55d60-744d-4fa8-b1c7-2ac53dc1e5fc","order_by":4,"name":"Guo-Ping Cai","email":"","orcid":"","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Guo-Ping","middleName":"","lastName":"Cai","suffix":""}],"badges":[],"createdAt":"2024-05-30 15:31:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4504050/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4504050/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":68768217,"identity":"be6f303a-ccf0-49ac-849d-c4129d5e3535","added_by":"auto","created_at":"2024-11-11 21:31:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":532834,"visible":true,"origin":"","legend":"","description":"","filename":"manuscirptPTLNN.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4504050/v1_covered_a66292fd-199b-461c-bd35-538b5bdd56a8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Product-based topological Lagrangian neural network for learning articulated 2D multi-rigid-body system","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":"Dynamics modeling, Machine learning, Physical-informed data-driven method, Product-based topological Lagrangian neural networks, Coupling nonlinearity","lastPublishedDoi":"10.21203/rs.3.rs-4504050/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4504050/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLagrangian neural networks (LNN) is a physical-informed data-driven framework for learning the dynamics of physical systems. 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