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Machine Learning Conservation Laws from Trajectories

Ziming Liu and Max Tegmark
Phys. Rev. Lett. 126, 180604 – Published 6 May 2021
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Abstract

We present AI Poincaré, a machine learning algorithm for autodiscovering conserved quantities using trajectory data from unknown dynamical systems. We test it on five Hamiltonian systems, including the gravitational three-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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  • Received 9 November 2020
  • Revised 20 January 2021
  • Accepted 15 April 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.180604

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsGeneral Physics

Authors & Affiliations

Ziming Liu* and Max Tegmark

  • Department of Physics, Institute for AI and Fundamental Interactions, and Center for Brains, Minds and Machines, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *zmliu@mit.edu

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Issue

Vol. 126, Iss. 18 — 7 May 2021

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