English

AI Poincar\'e: Machine Learning Conservation Laws from Trajectories

Machine Learning 2021-05-10 v2 Earth and Planetary Astrophysics Exactly Solvable and Integrable Systems Classical Physics

Abstract

We present AI Poincar\'e, a machine learning algorithm for auto-discovering conserved quantities using trajectory data from unknown dynamical systems. We test it on five Hamiltonian systems, including the gravitational 3-body problem, and find that it discovers not only all exactly conserved quantities, but also periodic orbits, phase transitions and breakdown timescales for approximate conservation laws.

Cite

@article{arxiv.2011.04698,
  title  = {AI Poincar\'e: Machine Learning Conservation Laws from Trajectories},
  author = {Ziming Liu and Max Tegmark},
  journal= {arXiv preprint arXiv:2011.04698},
  year   = {2021}
}

Comments

Replaced by accepted PRL version; expanded validation, improved presentation, more legible figs

R2 v1 2026-06-23T20:01:40.285Z