WyckoffTransformer: Generation of Symmetric Crystals

We propose WyckoffTransformer, a generative model for inorganic materials that takes advantage of the high order symmetry present in most known crystals. Wyckoff positions, a mathematical object from space group theory, is used as the basis for an elegant, compressed, and discrete structure representation. To model the distribution we develop a permutation–invariant autoregressive model based on Transformer. Our experiments demonstrate that Wyckoff Transformer has better performance compared to the baseline in generating novel stable structures conditioned on the space group symmetry, while also having competitive metric values when compared to a model not conditioned on space group symmetry.