Generation of Periodic Orbits in the Restricted Three-Body Problem with a Variational Autoencoder

Generation of Periodic Orbits in the Restricted Three-Body Problem with a Variational Autoencoder | 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 Generation of Periodic Orbits in the Restricted Three-Body Problem with a Variational Autoencoder Walther Litteri, Álvaro Francisco Gil, Massimiliano Vasile, Victor Rodriguez-Fernandez, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8651179/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract This work presents the application of Variational Autoencoders (VAEs) to the generation and analysis of periodic orbits in the Circular Restricted Three-Body Problem (CR3BP). A VAE architecture based on Convolutional Neural Networks (CNNs) was trained on a dataset of time series representing periodic trajectories. The encoder provided a compact, low-dimensional representation that captured the underlying geometric and dynamical features of the trajectories. By sampling the latent space, the model was able to generate approximations of new quasi-periodic trajectories with prescribed characteristics. A continuation technique was subsequently implemented both in the physical and latent domains. Continuation in physical space enabled the convergence toward periodic orbits by starting from the approximations produced by the VAE, whereas continuation in latent space facilitated the systematic generation of trajectories belonging to selected orbital families. The results demonstrate the potential use of generative models to design trajectories as well as automatically discover periodic orbits in complex dynamical systems. Three-Body Problem Periodic Orbits Generative AI Variational Autoencoder Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 08 Mar, 2026 Reviews received at journal 07 Mar, 2026 Reviews received at journal 10 Feb, 2026 Reviewers agreed at journal 26 Jan, 2026 Reviewers agreed at journal 23 Jan, 2026 Reviewers invited by journal 23 Jan, 2026 Editor assigned by journal 22 Jan, 2026 Submission checks completed at journal 22 Jan, 2026 First submitted to journal 20 Jan, 2026 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. 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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-8651179","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":580624697,"identity":"6e9cbc9e-2d24-415d-825e-76d6f95b3d1f","order_by":0,"name":"Walther Litteri","email":"","orcid":"","institution":"University of Strathclyde","correspondingAuthor":false,"prefix":"","firstName":"Walther","middleName":"","lastName":"Litteri","suffix":""},{"id":580624698,"identity":"4b7f19a3-dc00-430f-b635-75191541d36f","order_by":1,"name":"Álvaro Francisco Gil","email":"","orcid":"","institution":"Universidad Politécnica de 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