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Machine Learning Hidden Symmetries

Ziming Liu and Max Tegmark
Phys. Rev. Lett. 128, 180201 – Published 6 May 2022
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Abstract

We present an automated method for finding hidden symmetries, defined as symmetries that become manifest only in a new coordinate system that must be discovered. Its core idea is to quantify asymmetry as violation of certain partial differential equations, and to numerically minimize such violation over the space of all invertible transformations, parametrized as invertible neural networks. For example, our method rediscovers the famous Gullstrand-Painlevé metric that manifests hidden translational symmetry in the Schwarzschild metric of nonrotating black holes, as well as Hamiltonicity, modularity, and other simplifying traits not traditionally viewed as symmetries.

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  • Received 21 September 2021
  • Accepted 29 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.180201

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsGravitation, Cosmology & Astrophysics

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

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Issue

Vol. 128, Iss. 18 — 6 May 2022

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