[Paper Review] Towards Symmetry-Aware Generation of Periodic Materials

Youzhi Luo, Chengkai Liu+1 more|arXiv (Cornell University)|Jul 6, 2023

Machine Learning in Materials Science8 citations

TL;DR

SyMat introduces symmetry-aware generation for 3D periodic materials by using a VAE to generate atom types and lattices and a score-based diffusion model to generate coordinates, ensuring invariance to permutation, rotation, translation, and periodic transformations.

ABSTRACT

We consider the problem of generating periodic materials with deep models. While symmetry-aware molecule generation has been studied extensively, periodic materials possess different symmetries, which have not been completely captured by existing methods. In this work, we propose SyMat, a novel material generation approach that can capture physical symmetries of periodic material structures. SyMat generates atom types and lattices of materials through generating atom type sets, lattice lengths and lattice angles with a variational auto-encoder model. In addition, SyMat employs a score-based diffusion model to generate atom coordinates of materials, in which a novel symmetry-aware probabilistic model is used in the coordinate diffusion process. We show that SyMat is theoretically invariant to all symmetry transformations on materials and demonstrate that SyMat achieves promising performance on random generation and property optimization tasks. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Motivation & Objective

• Motivate the need to generate novel periodic materials with target properties while respecting physical symmetry constraints.
• Propose a generative framework that captures symmetry in both unit-cell descriptions and coordinate generation.
• Enable generation of valid, symmetry-consistent material structures suitable for property optimization.

Proposed method

• Represent each periodic material by its unit cell data (A, P, L) and transform A and L into symmetry-invariant targets for generation.
• Use a variational auto-encoder to model distributions of atom-type sets and lattice parameters (c, l, φ).
• Employ a score-based diffusion model to generate coordinates P conditioned on A and L, with a symmetry-aware score formulation.
• Construct a multi-graph of unit-cell atoms to compute edge-distance-based score functions that inherently respect symmetry."
• Train the score model via denoising score matching and Langevin dynamics for sampling; ensure translational, rotational, and periodic invariances.

Experimental results

Research questions

• RQ1 How can periodic materials be generated while preserving symmetry transformations (permutation, rotation, translation, periodicity) beyond traditional molecule generation?
• RQ2 Can a VAE effectively model symmetry-invariant representations of atom types and lattice parameters for periodic materials?
• RQ3 Does a symmetry-aware diffusion process improve coordinate generation and enable reliable property optimization?

Key findings

• SyMat achieves theoretical invariance to all symmetry transformations on periodic materials.
• The framework demonstrates promising performance on random generation tasks and property optimization tasks.
• Atom types and lattices are generated with a VAE on symmetry-invariant targets (atom-type sets and lattice lengths/angles).
• Coordinate generation uses a symmetry-aware score-based diffusion model based on edge-distance scores to ensure invariances.
• The approach shows competitiveness on three benchmark datasets and provides public code in the AIRS library.