Generating Symmetric Materials using Latent Flow Matching

2026-05-11

AI Summary

This work addresses the critical challenge of effectively modeling and enforcing crystallographic symmetry during generative processes to enhance the physical plausibility and stability of novel materials. It introduces a symmetry-aware material representation by explicitly embedding symmetry constraints—defined by space groups and Wyckoff positions—into a Transformer-based latent generative framework. Coupled with flow matching in the latent space, the proposed method enables end-to-end generation of crystal structures that inherently satisfy real-world symmetry requirements. Evaluated across multiple benchmarks, the approach either outperforms or matches state-of-the-art symmetry-aware and symmetry-agnostic models, demonstrating substantial improvements in both the symmetry fidelity and thermodynamic stability of the generated materials.

Abstract

Tackling the task of materials generation, we aim to enhance the previously proposed All-atom Diffusion Transformer (ADiT) by introducing SymADiT, a symmetry-aware variant. To do so, we use a representation of materials based on Wyckoff positions. We follow ADiT and perform generative modelling in latent space, adapted to our symmetry-aware representation. By forcing the output of the generative model to adhere to the symmetry restrictions imposed by the generated crystal's space group and each atom's Wyckoff-position, the generated materials exhibit more realistic symmetry properties. We benchmark our method against both symmetry-aware and symmetry-agnostic models for materials generation and show competitive performance, generating stable, symmetric materials with a simple Transformer architecture.

Problem

• materials generation
• symmetry
• Wyckoff positions
• crystal structure
• space group

Innovation

• Symmetry-aware generation
• Wyckoff positions
• Latent Flow Matching
• Materials generation
• Transformer architecture