Finding discrete symmetry groups via Machine Learning

TL;DR

This paper presents a machine learning method called Symmetry Seeker Neural Network that automatically discovers discrete symmetry groups in various physical systems without prior knowledge, demonstrating broad applicability.

Contribution

The paper introduces a novel neural network approach for identifying symmetry groups in physical systems, advancing the automation of symmetry detection across disciplines.

Findings

Successfully identifies symmetry groups in diverse systems

Operates without prior symmetry or mathematical knowledge

Applicable to mathematics, nanophotonics, and quantum chemistry

Abstract

We introduce a machine-learning approach (denoted Symmetry Seeker Neural Network) capable of automatically discovering discrete symmetry groups in physical systems. This method identifies the finite set of parameter transformations that preserve the system's physical properties. Remarkably, the method accomplishes this without prior knowledge of the system's symmetry or the mathematical relationships between parameters and properties. Demonstrating its versatility, we showcase examples from mathematics, nanophotonics, and quantum chemistry.