Equivariant Hypergraph Diffusion for Crystal Structure Prediction

2025-01-31

AI Summary

To address the challenges of modeling high-order atomic interactions and strictly preserving spatial symmetries in crystal structure prediction (CSP), this work introduces the first hypergraph-based SE(3)-equivariant diffusion generative model. The method employs hypergraphs to represent crystal structures, enabling explicit encoding of many-body atomic relationships via SE(3)-equivariant message passing and score-based noise diffusion—thereby theoretically guaranteeing translation invariance and permutation equivariance, and overcoming the pairwise interaction limitation of conventional graph models. Periodic boundary constraints are incorporated to enhance physical plausibility. Evaluated on four standard benchmarks, the model achieves state-of-the-art performance with single-sample generation, significantly improving structural stability, symmetry fidelity, and physical feasibility.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Crystal Structure Prediction (CSP) remains a fundamental challenge with significant implications for the development of new materials and the advancement of various scientific disciplines. Recent developments have shown that generative models, particularly diffusion models, hold great promise for CSP. However, traditional graph-based representations, where atomic bonds are modeled as pairwise graph edges, fail to fully capture the intricate high-order interactions essential for accurately representing crystal structures. In this work, we propose a novel approach that utilizes hypergraphs to represent crystal structures, providing a more expressive abstraction for modeling multi-way atomic interactions. By adopting hypergraphs, we can effectively capture complex high-order relationships and symmetries, such as permutation and periodic translation invariance, which are crucial for characterizing crystal structures. In this work, we propose the extbf{E}quivariant extbf{H}ypergraph extbf{Diff}usion Model ( extbf{EH-Diff}), a generative model designed to take advantage of the symmetry-preserving properties of hypergraphs. EH-Diff exploits these features to offer an efficient and accurate method for predicting crystal structures with a strong theoretical justification to preserve invariance properties. Empirically, we conduct extensive experiments on four benchmark datasets, and the results demonstrate that EH-Diff outperforms state-of-the-art CSP methods with only one sample.

Problem

• Crystal Structure Prediction
• Atomic Relationships
• Symmetry Understanding

Innovation

• Hypergraph Representation
• EH-Diff Model
• Crystal Structure Prediction