An interpretable latent linear model for nonlinear coupled oscillators on graphs

An interpretable latent linear model for nonlinear coupled oscillators on graphs | 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 An interpretable latent linear model for nonlinear coupled oscillators on graphs Agam Goyal, Zhaoxing Wu, Richard P. Yim, Binhao Chen, Zihong Xu, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4210117/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 system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear behavior has been a key challenge in predicting whether all oscillators in such a system will eventually synchronize. In this paper, we demonstrate that, surprisingly, such nonlinear behavior of coupled oscillators can be effectively linearized in certain latent dynamic spaces. The key insight is that there is a small number of ‘latent dynamics filters’, each with a specific association with synchronizing and non-synchronizing dynamics on subgraphs so that any observed dynamics on subgraphs can be approximated by a suitable linear combination of such elementary dynamic patterns. Taking an ensemble of subgraph-level predictions provides an interpretable predictor for whether the system on the whole graph reaches global synchronization. We propose algorithms based on supervised matrix factorization to learn such latent dynamics filters. We demonstrate that our method performs competitively in synchronization prediction tasks against baselines and black-box classification algorithms, despite its simple and interpretable architecture. Physical sciences/Mathematics and computing/Applied mathematics Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Complex networks Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Nonlinear phenomena 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-4210117","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":299998117,"identity":"1c802ab6-563d-447b-a09b-36dbceca50e1","order_by":0,"name":"Agam Goyal","email":"","orcid":"","institution":"University of Wisconsin - Madison","correspondingAuthor":false,"prefix":"","firstName":"Agam","middleName":"","lastName":"Goyal","suffix":""},{"id":299998119,"identity":"32c9f809-a4a5-4814-9668-e859c5dfb3b5","order_by":1,"name":"Zhaoxing Wu","email":"","orcid":"","institution":"University of Washington","correspondingAuthor":false,"prefix":"","firstName":"Zhaoxing","middleName":"","lastName":"Wu","suffix":""},{"id":299998121,"identity":"b6ee5c6c-7033-49a5-91bf-38237a4bbfa1","order_by":2,"name":"Richard P. 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