  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.
