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  • Letter
  • Open Access

Finding symmetry breaking order parameters with Euclidean neural networks

Tess E. Smidt1,2,*, Mario Geiger1,3, and Benjamin Kurt Miller1,2,4

  • 1Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 2Center for Advanced Mathematics for Energy Research Applications (CAMERA), Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
  • 3Department of Physics, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
  • 4Department of Mathematics, Freie Universität Berlin, Berlin 14195, Germany

  • *tsmidt@lbl.gov
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Phys. Rev. Research 3, L012002 – Published 4 January, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L012002

Abstract

Curie's principle states that “when effects show certain asymmetry, this asymmetry must be found in the causes that gave rise to them.” We demonstrate that symmetry equivariant neural networks uphold Curie's principle and can be used to articulate many symmetry-relevant scientific questions as simple optimization problems. We prove these properties mathematically and demonstrate them numerically by training a Euclidean symmetry equivariant neural network to learn symmetry breaking input to deform a square into a rectangle and to generate octahedra tilting patterns in perovskites.

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Phys. Rev. Research 3, L012002– Published 4 January, 2021
  • Received 1 July 2020
  • Revised 23 October 2020
  • Accepted 8 December 2020
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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