Space Group Equivariant Crystal Diffusion

TL;DR

SGEquiDiff is a novel generative model for crystalline materials that incorporates space group symmetries, leading to improved inverse design capabilities and state-of-the-art performance in crystal generation tasks.

Contribution

We introduce SGEquiDiff, a space group equivariant diffusion model that naturally enforces symmetry constraints in crystal generation, advancing the field of inverse materials design.

Findings

Achieves state-of-the-art performance on benchmark datasets.

Effectively incorporates space group symmetries into generative modeling.

Demonstrates improved accuracy with quantum mechanical validation.

Abstract

Accelerating inverse design of crystalline materials with generative models has significant implications for a range of technologies. Unlike other atomic systems, 3D crystals are invariant to discrete groups of isometries called the space groups. Crucially, these space group symmetries are known to heavily influence materials properties. We propose SGEquiDiff, a crystal generative model which naturally handles space group constraints with space group invariant likelihoods. SGEquiD-iff consists of an SE(3)-invariant, telescoping discrete sampler of crystal lattices; permutation-invariant, transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space group equivariant diffusion of atomic coordinates. We show that space group equivariant vector fields automatically live in the tangent spaces of the Wyckoff positions. SGEquiDiff achieves state-of-the-art performance on standard benchmark datasets as assessed by quantitative proxy metrics and quantum mechanical calculations. Our code is available at https://github.com/rees-c/sgequidiff.