Symmetry-Aware Bayesian Flow Networks for Crystal Generation

TL;DR

This work addresses the challenge of discovering crystalline materials by introducing SymmBFN, a symmetry-aware Bayesian Flow Network that jointly models fractional coordinates, atom types, lattice parameters, and site symmetries within a unified framework. By explicitly encoding space-group symmetries and using a graph-based neural network, the method accurately reproduces real-world space-group distributions while achieving substantial speedups over diffusion-based generators, reported up to two orders of magnitude in efficiency. The model also supports property-conditioned generation, enabling design of crystals with targeted formation energies and other properties, demonstrated on the MP-20 dataset with robust conditioning performance. Overall, SymmBFN offers a fast, symmetry-consistent, and versatile approach to crystalline material generation, with significant potential to accelerate computational materials discovery and design.

Abstract

The discovery of new crystalline materials is essential to scientific and technological progress. However, traditional trial-and-error approaches are inefficient due to the vast search space. Recent advancements in machine learning have enabled generative models to predict new stable materials by incorporating structural symmetries and to condition the generation on desired properties. In this work, we introduce SymmBFN, a novel symmetry-aware Bayesian Flow Network (BFN) for crystalline material generation that accurately reproduces the distribution of space groups found in experimentally observed crystals. SymmBFN substantially improves efficiency, generating stable structures at least 50 times faster than the next-best method. Furthermore, we demonstrate its capability for property-conditioned generation, enabling the design of materials with tailored properties. Our findings establish BFNs as an effective tool for accelerating the discovery of crystalline materials.

Figures (4)

• Figure 1: Visualisation of the 2D crystallographic point group 4mm. The symbols indicate different Wyckoff positions and the dashed lines show the symmetry axes. The light blue triangle is the asymmetric unit.
• Figure 2: Bayesian Flow Network. Illustration of BFN training procedure at the upper panel (A) and of the sampling procedure at the lower panel (B).
• Figure 3: Results for the property-conditioned generation for three different target values. The histograms show the distributions of the formation energy per atom of the generated structures in blue and of the training set in orange. The dashed red line represents the target of the generation while the blue line is the mean formation energy per atom of the generated structures.
• Figure 4: Structures generated by SymmBFN with the corresponding space group. Visualisations created with Crystal Toolkit crystaltoolkit.