Crystal Generative Modeling with Explicit Autoregressive Conditional Likelihoods and Nontrivial Space Group Stabilizers

Inverse crystalline materials design is a grand challenge in materials science. Most crystals have atoms at high-symmetry subspaces of 3D Euclidean space (i.e., positions with nontrivial stabilizer groups); yet, most existing crystal generative models cannot place atoms in these positions with nonzero probability. In this paper, we propose Wyckoff- and Asymmetric Unit-based Generative model (WyckoffAUGen), which sequentially builds crystals with explicit autoregressive-like conditional likelihoods and hard space group constraints. While prior methods parametrize distributions over unit cells with periodic translation symmetry, our model learns distributions over asymmetric units, which tile $\mathbb{R}^3$ upon applying the space group actions. This choice equips WyckoffAUGen with space group invariant model densities and reduces representations and generation trajectories to that of only symmetrically inequivalent atoms. To model continuous distributions over atom positions on facets of asymmetric units, WyckoffAUGen introduces a differentiable bijection from the simplex to any 2D polygon. Since experimental crystal synthesis can be hindered by unknown competing compounds in the same composition space, we enable masked in-filling from composition spaces.