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Finding symmetry breaking is essential for understanding the fundamentalchanges in the behaviors and properties of physical systems, from microscopicparticle interactions to macroscopic phenomena like fluid dynamics and cosmicstructures. Relaxed group convolution emerges as a solution for instances whenphysical systems without perfect symmetries and perfectly equivariant modelsare restrictive. In this paper, we provide both theoretical and empiricalevidence that this flexible convolution technique allows the model to maintainthe highest level of equivariance that is consistent with data and discover thesubtle symmetry-breaking factors in various physical systems. We employ variousrelaxed group convolution architectures to uncover various symmetry-breakingfactors in different physical systems, including the phase transition ofcrystal structure, the isotropy and homogeneity breaking in turbulence, and thetime-reversal symmetry breaking in pendulum systems.

Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution