Space group informed transformer for crystalline materials generation.

We introduce CrystalFormer, a transformer-based autoregressive model specifically designed for space group-controlled generation of crystalline materials. By explicitly incorporating space group symmetry, CrystalFormer greatly reduces the effective complexity of crystal space, which is essential for data-and compute-efficient generative modeling of crystalline materials. Leveraging the prominent discrete and sequential nature of the Wyckoff positions, CrystalFormer learns to generate crystals by directly predicting the species and coordinates of symmetry-inequivalent atoms in the unit cell. We demonstrate the advantages of CrystalFormer in standard tasks such as symmetric structure initialization and element substitution over widely used conventional approaches. Furthermore, we showcase its plug-and-play application to property-guided materials design, highlighting its flexibility. Our analysis reveals that CrystalFormer ingests sensible solid-state chemistry knowledge and heuristics by compressing the material dataset, thus enabling systematic exploration of crystalline materials space. The simplicity, generality, and adaptability of CrystalFormer position it as a promising architecture to be the foundational model of the entire crystalline materials space, heralding a new era in materials discovery and design.