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

2025-01-15

AI Summary

Addressing the challenge of simultaneously satisfying thermodynamic stability and symmetry constraints in crystal ground-state structure prediction, this work introduces the first diffusion generative model formulated on Riemannian manifolds. Methodologically, lattice matrices and fractional coordinates are modeled as geometrically constrained manifolds, where geodesic stochastic processes ensure physically consistent diffusion; equivariant graph neural networks enforce point-group symmetry conditioning, and density functional theory (DFT) validation is integrated into a closed-loop optimization. Compared to state-of-the-art approaches, our model generates structures that better approximate true ground states—achieving energy errors ≤50 meV/atom—while strictly preserving periodicity and space-group compliance. It successfully discovers multiple thermodynamically stable, experimentally synthesizable novel materials, thereby significantly accelerating symmetry-driven inverse materials design.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

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.

Problem

• Materials Science
• Crystal Structure Prediction
• Thermodynamic Stability

Innovation

• CrystalGRW
• Customizable Crystal Symmetry
• Accelerated Material Discovery