Flow-consistent identification of governing equations from sparsely sampled measurements

Flow-consistent identification of governing equations from sparsely sampled measurements | 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 Article Flow-consistent identification of governing equations from sparsely sampled measurements Ye Yuan, Zhexuan Zeng, Dongming Xie, Kaiqi Fang, Jiahao Shi, Ruoying Yan, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8856625/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 Extracting continuous-time governing equations from sparsely sampled measurements remains a fundamental challenge across science and engineering. Under severe temporal sparsity, conventional data-driven approaches often lose physical consistency, leading to distorted dynamics and unreliable qualitative behavior. Here we propose Hybrid Analytic Neural Dynamics Identification (HANDI), a flow-consistent framework that enables accurate identification of governing equations from sparsely sampled time series. Rather than relying on noisy numerical differentiation or integration, HANDI operates directly on the flow map, bridging discrete measurements and continuous-time dynamics through a Koopman-based formulation. By constructing a hybrid observable space that integrates interpretable analytic structures with neural representations, HANDI enables a sampling-robust linearization of the underlying dynamics. Across canonical nonlinear systems (e.g., limit cycles and bistability) and real-world datasets (e.g., inverted-flag flapping and wheel shimmy dynamics), HANDI consistently attains high mechanistic fidelity under extreme temporal sparsity, reliably uncovering the underlying physics and dynamical geometry from limited measurements. Physical sciences/Mathematics and computing/Computational science Physical sciences/Engineering/Electrical and electronic engineering Continuous-time dynamical system System identification Sparse sampling Koopman operator Full Text Additional Declarations There is NO Competing Interest. Supplementary Files Supplementary.pdf Supplementary Information sparsemeasurements.mp4 The challenge of sparse sampling and the intuition of continuous-time system identification from sparse data 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-8856625","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":590518757,"identity":"3c5412d7-af62-4eba-ae08-4907160eab37","order_by":0,"name":"Ye 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