Crystal structure prediction using graph neural combinatorial optimization

2026-04-26

AI Summary

This work addresses the discrete combinatorial optimization challenge in crystal structure prediction arising from the absence of symmetry constraints by introducing, for the first time, graph neural combinatorial optimization to this domain. The proposed method constructs an extended graph to simultaneously model both short-range and long-range atomic interactions and integrates the Gumbel-Sinkhorn mechanism to efficiently generate crystal structures that satisfy a target stoichiometry within an unsupervised framework. Evaluated across diverse chemical compositions, the approach significantly outperforms classical heuristic algorithms and achieves performance comparable to commercial optimization solvers, thereby establishing a new paradigm for GPU-accelerated, large-scale crystal structure prediction.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Crystalline materials are widely used in technological applications, yet their discovery remains a significant challenge. As their properties are driven by structure, crystal structure prediction (CSP) methods play a central role in computational approaches aiming to accelerate this process. Previously, CSP has been approached from a combinatorial optimization perspective, with the core challenge of allocating atoms on a fine grid of predefined discrete positions within a unit cell while minimizing their interaction energy. Exact mathematical optimization methods provide guaranteed solutions, but they become computationally expensive for large-scale instances, where the atomic configuration space grows rapidly, particularly in the absence of additional symmetry constraints. In this work, we introduce a neural combinatorial optimization approach to the atom allocation challenge and, subsequently, CSP, based on graph neural networks (GNNs), which can effectively sample from the distribution of feasible structures in an unsupervised manner. We leverage expander graphs to construct computational graphs over discrete positions that capture both short- and long-range interactions between atoms, and employ the Gumbel-Sinkhorn approach to enforce the desired stoichiometry of the generated structures. We demonstrate that our method outperforms classical heuristic approaches and is competitive with a commercial optimization solver across a range of chemical compositions. This enables the use of ever-expanding GPU infrastructure to tackle the inherent combinatorial challenges of CSP, paving the way for scaling beyond current capabilities.

Problem

• crystal structure prediction
• combinatorial optimization
• atom allocation
• interaction energy
• discrete positions

Innovation

• graph neural networks
• combinatorial optimization
• crystal structure prediction
• expander graphs
• Gumbel-Sinkhorn