AI Poincar\'e: Machine Learning Conservation Laws from Trajectories
Ziming Liu (MIT), Max Tegmark (MIT)
TL;DR
AI Poincaré is a machine learning method that automatically identifies conserved quantities and dynamical features from trajectory data in complex systems, including discovering exact and approximate invariants.
Contribution
It introduces a novel algorithm capable of uncovering conserved quantities and dynamical behaviors directly from trajectory data of unknown systems.
Findings
Successfully identified all exact conserved quantities in tested systems
Discovered periodic orbits and phase transitions
Estimated breakdown timescales for approximate conservation laws
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.
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