Finding symmetry breaking order parameters with Euclidean neural networks

2020/07/31 by Tess E. Smidt, Mario Geiger, Benjamin Kurt Miller · 2 citations
Computer Science · Materials Science · Physics and Astronomy · #Artificial neural network #Asymmetry #Equivariant map #Euclidean geometry #Machine Learning in Materials Science #Model Reduction and Neural Networks #Neural Networks and Reservoir Computing #Rectangle #Simple (philosophy) #Symmetry (geometry) #Symmetry breaking #cond-mat.dis-nn #cs.LG #physics.comp-ph

paper · pdf · doi:10.1103/physrevresearch.3.l012002

published as Phys. Rev. Research 3, 012002 (2021) · 6 pages, 3 figures

openalex created_date 2020/07/10 · arxiv created 2020/10/26 · openalex publication_date 2021/01/04 · arxiv updated 2021/01/20 · openalex updated_date 2026/08/05

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.

Citations

• Quasi-Particles and Gauge Invariance in the Theory of Superconductivity
• Broken Symmetries and the Masses of Gauge Bosons
• Global Conservation Laws and Massless Particles
• Theory of Superconductivity
• More Is Different
• Broken Symmetry and the Mass of Gauge Vector Mesons
• The idea of the neutrino
• SchNet – A deep learning architecture for molecules and materials
• Machine learning and the physical sciences

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