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Liu, Ziming and Tegmark, Max. 2021. "Machine Learning Conservation Laws from Trajectories." Physical Review Letters, 126 (18).
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Final published version
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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