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