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MatterGen: a generative model for inorganic materials design

Claudio Zeni, Robert Pinsler, Daniel Zügner, Andrew Fowler, Matthew Horton, Xiang Fu, Sasha Shysheya, Jonathan Crabbé, Lixin Sun, Jake Smith, Bichlien Nguyen, Hannes Schulz, Sarah Lewis, Chin-Wei Huang, Ziheng Lu, Yichi Zhou, Han Yang, Hongxia Hao, Jielan Li, Ryota Tomioka, Tian Xie

TL;DR

MatterGen tackles inverse design of inorganic materials with a diffusion-based model that jointly denoises atom types, fractional coordinates, and lattice, augmented by adapter modules for property-guided fine-tuning. The approach achieves higher stability, novelty, and proximity to local energy minima than prior methods and demonstrates versatile conditional generation across chemistry, symmetry, and scalar properties using classifier-free guidance. It shows effectiveness in designing materials with targeted chemistry, symmetry, magnetic density, band gap, bulk modulus, and even multi-constraint magnets with low supply-chain risk, with notable efficiency gains over traditional search or substitution methods. While promising, the work notes limitations such as symmetry bias and the need for experimental validation, pointing toward future extension to broader material classes and non-scalar objectives.

Abstract

The design of functional materials with desired properties is essential in driving technological advances in areas like energy storage, catalysis, and carbon capture. Generative models provide a new paradigm for materials design by directly generating entirely novel materials given desired property constraints. Despite recent progress, current generative models have low success rate in proposing stable crystals, or can only satisfy a very limited set of property constraints. Here, we present MatterGen, a model that generates stable, diverse inorganic materials across the periodic table and can further be fine-tuned to steer the generation towards a broad range of property constraints. To enable this, we introduce a new diffusion-based generative process that produces crystalline structures by gradually refining atom types, coordinates, and the periodic lattice. We further introduce adapter modules to enable fine-tuning towards any given property constraints with a labeled dataset. Compared to prior generative models, structures produced by MatterGen are more than twice as likely to be novel and stable, and more than 15 times closer to the local energy minimum. After fine-tuning, MatterGen successfully generates stable, novel materials with desired chemistry, symmetry, as well as mechanical, electronic and magnetic properties. Finally, we demonstrate multi-property materials design capabilities by proposing structures that have both high magnetic density and a chemical composition with low supply-chain risk. We believe that the quality of generated materials and the breadth of MatterGen's capabilities represent a major advancement towards creating a universal generative model for materials design.

MatterGen: a generative model for inorganic materials design

TL;DR

MatterGen tackles inverse design of inorganic materials with a diffusion-based model that jointly denoises atom types, fractional coordinates, and lattice, augmented by adapter modules for property-guided fine-tuning. The approach achieves higher stability, novelty, and proximity to local energy minima than prior methods and demonstrates versatile conditional generation across chemistry, symmetry, and scalar properties using classifier-free guidance. It shows effectiveness in designing materials with targeted chemistry, symmetry, magnetic density, band gap, bulk modulus, and even multi-constraint magnets with low supply-chain risk, with notable efficiency gains over traditional search or substitution methods. While promising, the work notes limitations such as symmetry bias and the need for experimental validation, pointing toward future extension to broader material classes and non-scalar objectives.

Abstract

The design of functional materials with desired properties is essential in driving technological advances in areas like energy storage, catalysis, and carbon capture. Generative models provide a new paradigm for materials design by directly generating entirely novel materials given desired property constraints. Despite recent progress, current generative models have low success rate in proposing stable crystals, or can only satisfy a very limited set of property constraints. Here, we present MatterGen, a model that generates stable, diverse inorganic materials across the periodic table and can further be fine-tuned to steer the generation towards a broad range of property constraints. To enable this, we introduce a new diffusion-based generative process that produces crystalline structures by gradually refining atom types, coordinates, and the periodic lattice. We further introduce adapter modules to enable fine-tuning towards any given property constraints with a labeled dataset. Compared to prior generative models, structures produced by MatterGen are more than twice as likely to be novel and stable, and more than 15 times closer to the local energy minimum. After fine-tuning, MatterGen successfully generates stable, novel materials with desired chemistry, symmetry, as well as mechanical, electronic and magnetic properties. Finally, we demonstrate multi-property materials design capabilities by proposing structures that have both high magnetic density and a chemical composition with low supply-chain risk. We believe that the quality of generated materials and the breadth of MatterGen's capabilities represent a major advancement towards creating a universal generative model for materials design.
Paper Structure (62 sections, 48 equations, 10 figures, 3 tables)

This paper contains 62 sections, 48 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Results
  3. Diffusion process for crystalline material generation
  4. Generating stable, diverse materials
  5. Generating materials with target chemistry
  6. Designing materials with target symmetry
  7. Designing materials with target magnetic, electronic, and mechanical properties
  8. Designing low-supply-chain-risk magnets
  9. Discussion
  10. Appendix
  11. Diffusion model for periodic materials
  12. Representation of periodic materials
  13. Invariance and equivariance in periodic materials
  14. Diffusion model background and notation
  15. Joint diffusion process
  16. ...and 47 more sections

Figures (10)

  • Figure 1: Inorganic materials design with MatterGen.(a) MatterGen generates stable materials by reversing a corruption process through iteratively denoising an initially random structure. The forward diffusion process is designed to independently corrupt atom types ${\bm{A}}$, coordinates ${\bm{X}}$, and the lattice ${\bm{L}}$ to approach a physically motivated distribution of random materials. (b) An equivariant score network is pre-trained on a large dataset of stable material structures to jointly denoise atom types, coordinates, and the lattice. The score network is then fine-tuned with a labeled dataset through an adapter module that alters the model using the encoded property $\bm{c}$. (c) MatterGen can be fine-tuned to steer the generation towards materials with desired chemistry, symmetry, and scalar property constraints.
  • Figure 2: Generating stable, unique and novel inorganic materials.(a) Visualization of four randomly selected crystals generated by MatterGen, with corresponding chemical formula and space group symbols. (b) Distribution of energy above the hull using and dataset as energy references, respectively. (c) Distribution of between initial generated structures and relaxed structures. (d) Percentage of unique, novel structures as a function of number of generated structures. Novelty is defined with respect to . (e-f) Percentage of structures (e) and average between initial and -relaxed structures (f) for MatterGen, MatterGen-MP, and several baseline models, including CDVAE cdvae, P-G-SchNet, G-SchNet gebauer2019symmetry, and FTCP ren2022invertible.
  • Figure 3: Generating materials in target chemical system.(a-b) Mean percentage of structures generated by MatterGen and baselines for 27 chemical systems, grouped by system type (a) and number of elements (b). Vertical black lines indicate maximum and minimum values. (c-d) Number of structures on the combined convex hull found by each method and in the dataset, grouped by system type (c) and number of elements (d). (e) Convex hull diagram for V-Sr-O, a well-explored ternary system. The dots represent structures on the hull, their coordinates represent the element ratio of their composition, and their color indicates by which method they were discovered. (f-i) Four of the five structures MatterGen discovered on the V-Sr-O hull depicted in (e), along with their composition and space group.
  • Figure 4: Generating materials with target symmetry.(a) Fraction of generated structures that belong to the target space group for 14 randomly chosen space groups spanning the seven lattice types. (b) Four randomly selected structures generated by MatterGen, along with their chemical formula and space group.
  • Figure 5: Generating materials with target magnetic, electronic, and mechanical properties.(a-c) Density of property values among (1) generated samples by MatterGen, and (2) structures in the labeled fine-tuning dataset for a magnetic, electronic, and mechanical property, respectively. The property target for MatterGen is shown as a black dashed line. Magnetic density values $< 10^{-3}~\text{\AA}^{-3}$ in (a) are excluded from the labeled data to improve readability. (d-f) Visualization of structures with the best property values generated by MatterGen for magnetic density (d), band gap (e), and bulk modulus (f). Alongside each structure, the chemical formula, space group and property value is shown. (g-h) Number of structures that satisfy target constraints found MatterGen compared to number of structures found by baselines across a range of property calculation budgets.
  • ...and 5 more figures