Port-Hamiltonian Neural Networks: From Theory to Simulation of Interconnected Stochastic Systems

Port-Hamiltonian Neural Networks: From Theory to Simulation of Interconnected Stochastic Systems | 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 Port-Hamiltonian Neural Networks: From Theory to Simulation of Interconnected Stochastic Systems Luca Di Persio, Matthias Ehrhardt, Youness Outaleb, Sofia Rizzotto This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7572939/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 This work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochastic modeling of complex dynamical systems. We introduce new mathematical formulations and computational methods that expand the geometric structure of PHS to account for uncertainty, environmental noise, and random perturbations. Building on these advances, we introduce stochastic port-Hamiltonian neural networks (pHNNs), which facilitate the accurate learning and prediction of non-autonomous and interconnected stochastic systems. \\ Our proposed framework generalizes passivity concepts to the stochastic regime, ensuring stability while maintaining the system's energy-consistent structure. Extensive simulations, including those involving damped mass-spring systems, Duffing oscillators, and robotic control tasks, demonstrate the capability of pHNNs to capture complex dynamics with high fidelity, even under noise and uncertainty. This unified approach establishes a foundation for the robust, data-driven modeling and control of nonlinear stochastic systems. AMS subject classifications: 37N40, 37B52, 60G10, 60H10, 93C55. Stochastic Port-Hamiltonian System Port-Hamiltonian Neural Networks Discrete stochastic Port-Hamiltonian system Passivity Interconnection 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-7572939","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":535808240,"identity":"8f20b805-a604-423b-8d20-eaf61c718f98","order_by":0,"name":"Luca Di Persio","email":"","orcid":"","institution":"University of Verona","correspondingAuthor":false,"prefix":"","firstName":"Luca","middleName":"Di","lastName":"Persio","suffix":""},{"id":535808241,"identity":"dc6c2df0-3fd5-452c-9dd3-3e51dcec6358","order_by":1,"name":"Matthias Ehrhardt","email":"","orcid":"","institution":"University of Wuppertal","correspondingAuthor":false,"prefix":"","firstName":"Matthias","middleName":"","lastName":"Ehrhardt","suffix":""},{"id":535808242,"identity":"6fc981e8-450c-4803-b585-346b2a45eb6f","order_by":2,"name":"Youness Outaleb","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVRIiWNgGAWjYNCDBwwH5BgYGBuATAli1DMzMCQwHDAGamkE6pEgRg9ES2IDIWsMjveYPfjwp46BXyL/4IeEijvpG243tz8uYLCow6nlzBlzw5lthxkkZyQzSySceZa74c7BxuYZeBxmcCPHTJq34QCQkcwgkdh2OHfDjcTGZh5CWv4AHQbUwvwj8d/hdAOitDCwMYO0sEkkNhxOIKhF8syxMsnetsM8kj2PzSwSjj0znAnUMpvHQEKyAYcWvuPN2yR+/KmT42dPfHzjQ80deb4b6Q8+81TU8eOyReEAhOZBdzAuDQwM8risHwWjYBSMglEABwC4slpqN+VE/QAAAABJRU5ErkJggg==","orcid":"","institution":"University of Trento","correspondingAuthor":true,"prefix":"","firstName":"Youness","middleName":"","lastName":"Outaleb","suffix":""},{"id":535808243,"identity":"b8dedb60-1b3b-4c07-9ba7-b468f4b31210","order_by":3,"name":"Sofia Rizzotto","email":"","orcid":"","institution":"University of Verona","correspondingAuthor":false,"prefix":"","firstName":"Sofia","middleName":"","lastName":"Rizzotto","suffix":""}],"badges":[],"createdAt":"2025-09-09 10:53:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7572939/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7572939/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":95178955,"identity":"6ddca465-1447-434c-b2ba-581085a6dda3","added_by":"auto","created_at":"2025-11-05 08:04:31","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5312,"visible":true,"origin":"","legend":"","description":"","filename":"a03ca2cd5dd0443f9d58f34f5b0c01e2.json","url":"https://assets-eu.researchsquare.com/files/rs-7572939/v1/cba2e9ddbfea97b67667e57b.json"},{"id":104402990,"identity":"b597e6fd-a400-45ad-9ca7-5bb31d63a4a8","added_by":"auto","created_at":"2026-03-11 12:17:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1214726,"visible":true,"origin":"","legend":"","description":"","filename":"PortHamiltonianNeuralNetworksFromTheorytoSimulationofInterconnectedStochasticSystems.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7572939/v1_covered_ab95d8bf-a3c5-4a29-a148-c38b047315a8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Port-Hamiltonian Neural Networks: From Theory to Simulation of Interconnected Stochastic Systems","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":"Stochastic Port-Hamiltonian System, Port-Hamiltonian Neural Networks, Discrete stochastic Port-Hamiltonian system, Passivity, Interconnection","lastPublishedDoi":"10.21203/rs.3.rs-7572939/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7572939/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. 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