{"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/neural-symplectic-integrator-with-hamiltonian","title":"Neural Symplectic Integrator with Hamiltonian Inductive Bias for the Gravitational $N$-body Problem","arxiv_id":"2111.15631","date":"2021-11-28","proceeding":null,"authors":["Maxwell X. Cai","Simon Portegies Zwart","Damian Podareanu"],"abstract":"The gravitational $N$-body problem, which is fundamentally important in astrophysics to predict the motion of $N$ celestial bodies under the mutual gravity of each other, is usually solved numerically because there is no known general analytical solution for $N>2$. Can an $N$-body problem be solved accurately by a neural network (NN)? Can a NN observe long-term conservation of energy and orbital angular momentum? Inspired by Wistom & Holman (1991)'s symplectic map, we present a neural $N$-body integrator for splitting the Hamiltonian into a two-body part, solvable analytically, and an interaction part that we approximate with a NN. Our neural symplectic $N$-body code integrates a general three-body system for $10^{5}$ steps without diverting from the ground truth dynamics obtained from a traditional $N$-body integrator. Moreover, it exhibits good inductive bias by successfully predicting the evolution of $N$-body systems that are no part of the training set.","url_abs":"https://arxiv.org/abs/2111.15631v1","url_pdf":"https://arxiv.org/pdf/2111.15631v1.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":"neural-symplectic-integrator-with-hamiltonian","repo_url":"https://github.com/maxwelltsai/neural-symplectic-integrator","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"inductive-bias","task_name":"Inductive Bias"}],"methods":[{"method_slug":"gravity","method_name":"Gravity"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2111.15631","atlas_url":"https://app.syntology.ai/?focus=2111.15631","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}