Incorporating Crystallographic Symmetries into Probabilistic Learning Approaches for Materials

Crystallographic symmetries, defined by space groups, are essential for constraining material property phase space and are widely used in physical modeling. However, integrating these discrete but infinite symmetries into machine learning models for inorganic crystals remains a challenge. In this presentation, I will discuss our recent efforts to incorporate crystallographic symmetries into machine learning models. Two key examples include: (i) embedding many-body symmetries into neural network ansatzes for variational quantum Monte Carlo, achieving high-accuracy solutions to the many-body Schrödinger equation. We compare symmetry-aware approaches, such as group averaging and invariant neural network layers, against symmetry-agnostic baselines. (ii) Developing generative models for inorganic crystals that learn probability distributions over space groups and Wyckoff sites, enabling the generation of structures spanning various symmetries and site dimensionalities. These methods illustrate pathways for bridging crystallographic symmetries with modern machine learning techniques.