{"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-poisson-systems-and-trajectories-of","title":"Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks","arxiv_id":"2012.03133","date":"2020-12-05","proceeding":null,"authors":["Pengzhan Jin","Zhen Zhang","Ioannis G. Kevrekidis","George Em Karniadakis"],"abstract":"We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data. Based on the Darboux-Lie theorem, the phase flow of a Poisson system can be written as the composition of (1) a coordinate transformation, (2) an extended symplectic map and (3) the inverse of the transformation. In this work, we extend this result to the unknotted trajectories of autonomous systems. We employ structured neural networks with physical priors to approximate the three aforementioned maps. We demonstrate through several simulations that PNNs are capable of handling very accurately several challenging tasks, including the motion of a particle in the electromagnetic potential, the nonlinear Schr{\\\"o}dinger equation, and pixel observations of the two-body problem.","url_abs":"https://arxiv.org/abs/2012.03133v1","url_pdf":"https://arxiv.org/pdf/2012.03133v1.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-poisson-systems-and-trajectories-of","repo_url":"https://github.com/jpzxshi/learner","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2012.03133","atlas_url":"https://app.syntology.ai/?focus=2012.03133","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}