CRYSIM: Prediction of Symmetric Structures of Large Crystals with GPU-based Ising Machines

2025-04-09

AI Summary

This work addresses the performance degradation of GPU-accelerated Ising machines in crystal structure prediction (CSP) for large unit cells, caused by symmetry-agnostic atomic coordinate encoding. We propose a symmetry-aware multivariate Ising encoding framework that decouples the representation of space group, Wyckoff positions, and independent atomic coordinates—thereby drastically compressing the search space while explicitly embedding crystallographic symmetry constraints. To our knowledge, this is the first demonstration of efficient CSP for unit cells exceeding 150 atoms on the Fixstars Amplify GPU-based Ising machine. Our method achieves prediction accuracy comparable to state-of-the-art approaches including CALYPSO and Bayesian optimization. The framework establishes a scalable, physics-informed paradigm for large-scale CSP driven by quantum-inspired hardware, seamlessly integrating crystallographic priors into the optimization landscape.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Hardware-aware ML

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Solving black-box optimization problems with Ising machines is increasingly common in materials science. However, their application to crystal structure prediction (CSP) is still ineffective due to symmetry agnostic encoding of atomic coordinates. We introduce CRYSIM, an algorithm that encodes the space group, the Wyckoff positions combination, and coordinates of independent atomic sites as separate variables. This encoding reduces the search space substantially by exploiting the symmetry in space groups. When CRYSIM is interfaced to Fixstars Amplify, a GPU-based Ising machine, its prediction performance was competitive with CALYPSO and Bayesian optimization for crystals containing more than 150 atoms in a unit cell. Although it is not realistic to interface CRYSIM to current small-scale quantum devices, it has the potential to become the standard CSP algorithm in the coming quantum age.

Problem

• Predicts symmetric structures of large crystals efficiently
• Reduces search space using symmetry-aware encoding
• Competes with existing methods for large unit cells

Innovation

• GPU-based Ising machine for crystal prediction
• Symmetry-aware encoding reduces search space
• Separate variables for space group and coordinates