CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks

TL;DR

CrystalGRW is a novel diffusion-based generative model on Riemannian manifolds that creates stable, symmetry-preserving crystal structures with targeted properties, aiding materials discovery and inverse design.

Contribution

It introduces a Riemannian manifold diffusion model for crystal generation that incorporates symmetry and stability considerations, advancing computational materials science.

Findings

Generates realistic, near ground-state crystal structures

Achieves accuracy comparable to existing models

Enables conditional control of crystal properties

Abstract

Determining whether a candidate crystalline material is thermodynamically stable depends on identifying its true ground-state structure, a central challenge in computational materials science. We introduce CrystalGRW, a diffusion-based generative model on Riemannian manifolds that proposes novel crystal configurations and can predict stable phases validated by density functional theory. The crystal properties, such as fractional coordinates, atomic types, and lattice matrices, are represented on suitable Riemannian manifolds, ensuring that new predictions generated through the diffusion process preserve the periodicity of crystal structures. We incorporate an equivariant graph neural network to also account for rotational and translational symmetries during the generation process. CrystalGRW demonstrates the ability to generate realistic crystal structures that are close to their ground states with accuracy comparable to existing models, while also enabling conditional control, such as specifying a desired crystallographic point group. These features help accelerate materials discovery and inverse design by offering stable, symmetry-consistent crystal candidates for experimental validation.