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Machine Learning Conservation Laws from Trajectories.

Ziming Liu1, Max Tegmark1

  • 1Department of Physics, Institute for AI and Fundamental Interactions, and Center for Brains, Minds and Machines, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

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|May 21, 2021
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Summary
This summary is machine-generated.

AI Poincaré is a new machine learning algorithm that automatically finds conserved quantities in unknown dynamical systems. It successfully identified exact conservation laws, periodic orbits, and phase transitions in complex systems like the three-body problem.

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Area of Science:

  • Physics
  • Computer Science
  • Applied Mathematics

Background:

  • Dynamical systems are fundamental to understanding physical phenomena.
  • Identifying conserved quantities is crucial for analyzing system behavior.
  • Discovering these quantities in unknown systems is challenging.

Purpose of the Study:

  • To introduce AI Poincaré, a novel machine learning algorithm.
  • To demonstrate its capability in autodiscovering conserved quantities from trajectory data.
  • To validate its performance on diverse Hamiltonian systems.

Main Methods:

  • Developed a machine learning algorithm named AI Poincaré.
  • Utilized trajectory data from unknown dynamical systems as input.
  • Tested the algorithm on five Hamiltonian systems, including the three-body problem.

Main Results:

  • AI Poincaré successfully discovered all exactly conserved quantities.
  • The algorithm identified periodic orbits and phase transitions.
  • It also determined breakdown timescales for approximate conservation laws.

Conclusions:

  • AI Poincaré offers a powerful new method for analyzing unknown dynamical systems.
  • The algorithm's ability to find conserved quantities and other properties enhances our understanding of complex physics.
  • This approach has broad implications for theoretical and computational science.