AI Poincaré: Machine Learning Conservation Laws from Trajectories

Abstract

We present AI Poincaré, 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.

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