Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution

TL;DR

This paper introduces relaxed group convolutions as a flexible method to identify and interpret symmetry-breaking phenomena in diverse physical systems, providing both theoretical insights and empirical validation.

Contribution

It presents a novel approach using relaxed group convolutions to learn and interpret symmetry-breaking factors in physical data, bridging theory and practical applications.

Findings

Successfully identified symmetry-breaking factors in crystal phase transitions.

Uncovered symmetry-breaking in turbulent flow and pendulum systems.

Demonstrated the method's ability to maintain equivariance while detecting subtle asymmetries.

Abstract

Modeling symmetry breaking is essential for understanding the fundamental changes in the behaviors and properties of physical systems, from microscopic particle interactions to macroscopic phenomena like fluid dynamics and cosmic structures. Thus, identifying sources of asymmetry is an important tool for understanding physical systems. In this paper, we focus on learning asymmetries of data using relaxed group convolutions. We provide both theoretical and empirical evidence that this flexible convolution technique allows the model to maintain the highest level of equivariance that is consistent with data and discover the subtle symmetry-breaking factors in various physical systems. We employ various relaxed group convolution architectures to uncover various symmetry-breaking factors that are interpretable and physically meaningful in different physical systems, including the phase transition of crystal structure, the isotropy and homogeneity breaking in turbulent flow, and the time-reversal symmetry breaking in pendulum systems.