🤖 AI Summary
This study addresses the automatic identification and interpretable modeling of symmetry breaking in physical systems. We propose the Relaxed Group Convolution framework, which—while preserving maximal equivariance—enables, for the first time, end-to-end interpretable learning of multiscale and heterogeneous symmetry breaking phenomena, including phase transitions, turbulence anisotropy, and time-reversal violation. Our method integrates equivariant neural networks, physics-constrained representation learning, and interpretable feature disentanglement, substantially enhancing model capability in localizing and quantifying symmetry-breaking sources. Evaluated on three canonical physical scenarios—crystalline phase transitions, turbulent velocity fields, and nonlinear pendulum dynamics—the framework accurately identifies physically meaningful breaking mechanisms. It consistently outperforms standard group convolution baselines in both predictive accuracy and interpretability, offering principled insights into underlying symmetry-breaking origins.
📝 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.
