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

arXiv: https://arxiv.org/abs/2504.06878 · HTML: https://mlsanity.com/paper/2504.06878/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 84 references that are in the map.
- First posted on arXiv 9 Apr 2025.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributions](https://mlsanity.com/paper/2410.23405/) (2024)
- [Shotgun crystal structure prediction using machine-learned formation energies](https://mlsanity.com/paper/2305.02158/) (2023)
- [A novel design update framework for topology optimization with quantum annealing: Application to truss and continuum structures](https://mlsanity.com/paper/2406.18833/) (2024)

## Built on by (most cited first, 1 of 1)

- [Subsampling Factorization Machine Annealing](https://mlsanity.com/paper/2508.08778/) (2025)

## Abstract (arXiv)

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.