Crystal structure prediction using graph neural combinatorial optimization

TL;DR

This paper introduces a graph neural network-based method for crystal structure prediction that efficiently samples feasible atomic arrangements, outperforming classical heuristics and enabling scalable exploration of material configurations.

Contribution

The authors develop a neural combinatorial optimization approach using GNNs and Gumbel-Sinkhorn to improve atomic placement in CSP, addressing scalability issues of traditional methods.

Findings

Outperforms classical heuristic approaches in structure prediction accuracy.

Is competitive with commercial optimization solvers across various chemical compositions.

Enables scalable CSP using GPU infrastructure for larger atomic configuration spaces.

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.