{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-hamiltonians-of-constrained","title":"Learning Hamiltonians of constrained mechanical systems","arxiv_id":"2201.13254","date":"2022-01-31","proceeding":null,"authors":["Elena Celledoni","Andrea Leone","Davide Murari","Brynjulf Owren"],"abstract":"Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined by one scalar function, the Hamiltonian. The solution trajectories are often constrained to evolve on a submanifold of a linear vector space. In this work, we propose new approaches for the accurate approximation of the Hamiltonian function of constrained mechanical systems given sample data information of their solutions. We focus on the importance of the preservation of the constraints in the learning strategy by using both explicit Lie group integrators and other classical schemes.","url_abs":"https://arxiv.org/abs/2201.13254v2","url_pdf":"https://arxiv.org/pdf/2201.13254v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-hamiltonians-of-constrained","repo_url":"https://github.com/davidemurari/learningConstrainedHamiltonians","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2201.13254","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}