Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Symmetry-aware Conditional Generation of Crystal Structures Using Diffusion Models

Takanori Ishii, Kaoru Hisama, Kohei Shinohara

TL;DR

This work addresses symmetry-aware conditional generation for crystal structure prediction by showing limitations of existing conditional models in maintaining space-group symmetry. It introduces WyckoffDiff-Adaptor, which embeds conditional information into the diffusion process on Wyckoff positions, with protostructures defined as $M = (s, z^∞, z^0)$. The method enables energy-based conditioning ($E_{hull}$) and space-group constraints, and demonstrates formation-energy phase diagrams for Li–O and Ti–O that align with Materials Project data while being significantly faster for CIF generation than prior approaches. Limitations include generation of chemically questionable bonds and loss of internal parameters in generalized Wyckoff positions, suggesting directions for future improvement.

Abstract

The application of generative models in crystal structure prediction (CSP) has gained significant attention. Conditional generation--particularly the generation of crystal structures with specified stability or other physical properties has been actively researched for material discovery purposes. Meanwhile, the generative models capable of symmetry-aware generation are also under active development, because space group symmetry has a strong relationship with the physical properties of materials. In this study, we demonstrate that the symmetry control in the previous conditional crystal generation model may not be sufficiently effective when space group constraints are applied as a condition. To address this problem, we propose the WyckoffDiff-Adaptor, which embeds conditional generation within a WyckoffDiff architecture that effectively diffuses Wyckoff positions to achieve precise symmetry control. We successfully generated formation energy phase diagrams while specifying stable structures of particular combination of elements, such as Li--O and Ti--O systems, while simultaneously preserving the symmetry of the input conditions. The proposed method with symmetry-aware conditional generation demonstrates promising results as an effective approach to achieving the discovery of novel materials with targeted physical properties.

Symmetry-aware Conditional Generation of Crystal Structures Using Diffusion Models

TL;DR

This work addresses symmetry-aware conditional generation for crystal structure prediction by showing limitations of existing conditional models in maintaining space-group symmetry. It introduces WyckoffDiff-Adaptor, which embeds conditional information into the diffusion process on Wyckoff positions, with protostructures defined as . The method enables energy-based conditioning () and space-group constraints, and demonstrates formation-energy phase diagrams for Li–O and Ti–O that align with Materials Project data while being significantly faster for CIF generation than prior approaches. Limitations include generation of chemically questionable bonds and loss of internal parameters in generalized Wyckoff positions, suggesting directions for future improvement.

Abstract

The application of generative models in crystal structure prediction (CSP) has gained significant attention. Conditional generation--particularly the generation of crystal structures with specified stability or other physical properties has been actively researched for material discovery purposes. Meanwhile, the generative models capable of symmetry-aware generation are also under active development, because space group symmetry has a strong relationship with the physical properties of materials. In this study, we demonstrate that the symmetry control in the previous conditional crystal generation model may not be sufficiently effective when space group constraints are applied as a condition. To address this problem, we propose the WyckoffDiff-Adaptor, which embeds conditional generation within a WyckoffDiff architecture that effectively diffuses Wyckoff positions to achieve precise symmetry control. We successfully generated formation energy phase diagrams while specifying stable structures of particular combination of elements, such as Li--O and Ti--O systems, while simultaneously preserving the symmetry of the input conditions. The proposed method with symmetry-aware conditional generation demonstrates promising results as an effective approach to achieving the discovery of novel materials with targeted physical properties.
Paper Structure (6 sections, 5 figures, 1 table)

This paper contains 6 sections, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Computational Methods
  3. WyckoffDiff-Adaptor architecture
  4. Dataset, training and validation setup
  5. Results and Discussion
  6. Conclusion

Figures (5)

  • Figure 1: (a) Schematic diagram of the training and generation process of the WyckoffDiff-Adaptor, and (b) architecture of WyckoffGNN model including the adaptor module.
  • Figure 2: Heatmaps of the numbers of generated structure between input and generated structures, using (a) MatterGen and (b) WyckoffDiff-Adaptor, both conditioned by space group. The rows denote the space group of the input and the columns denote the crystal system of the generated structures after optimization using MatterSim. Note that the number of generated structure by WyckoffDiff-Adaptor for each input space group is less than the generation batch size $64$, because the generated protostructure is duplicated.
  • Figure 3: Predicted phase diagrams of (a) Li–O by MatterGen, (b) Li–O by WyckoffDiff-Adaptor, (c) Ti–O by MatterGen, (d) Ti–O by WyckoffDiff-Adaptor, Red and blue lines represent the convex hull of formation energy drawn by Materials project data and generated structures by the model, respectively.
  • Figure 4: (a) generated stable Li$_2$O structure in Li–O system shown in Figure 3 (b) , (b) generated stable TiO$_2$ structure shown in Figure 4 (b), and (c) stable TiO$_2$ structure in Materials project (mp-390).
  • Figure 5: (a) an example in Ba-Ta-In-O system generated using WyckoffDiff-Adaptor, compared to the (b) structure in the same system in the Materials Project, and (c,d) structures generated by the post processing using PyXtal from the same protostructure (A2BC4$\_$cF56$\_$227$\_$c$\_$b$\_$e:Al-Mg-O)