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. 2025 Mar;639(8055):624-632.
doi: 10.1038/s41586-025-08628-5. Epub 2025 Jan 16.

A generative model for inorganic materials design

Claudio Zeni #  1 , Robert Pinsler #  1 , Daniel Zügner #  2 , Andrew Fowler #  1 , Matthew Horton #  3 , Xiang Fu  1 , Zilong Wang  4 , Aliaksandra Shysheya  1 , Jonathan Crabbé  1 , Shoko Ueda  1 , Roberto Sordillo  1 , Lixin Sun  1 , Jake Smith  3 , Bichlien Nguyen  3 , Hannes Schulz  2 , Sarah Lewis  1 , Chin-Wei Huang  5 , Ziheng Lu  6 , Yichi Zhou  7 , Han Yang  6 , Hongxia Hao  6 , Jielan Li  6 , Chunlei Yang  4 , Wenjie Li  4 , Ryota Tomioka #  8 , Tian Xie #  9
Affiliations

A generative model for inorganic materials design

Claudio Zeni et al. Nature. 2025 Mar.

Abstract

The design of functional materials with desired properties is essential in driving technological advances in areas such as energy storage, catalysis and carbon capture1-3. Generative models accelerate materials design by directly generating new materials given desired property constraints, but current methods have a low success rate in proposing stable crystals or can satisfy only a limited set of property constraints4-11. 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. Compared with previous generative models4,12, structures produced by MatterGen are more than twice as likely to be new and stable, and more than ten times closer to the local energy minimum. After fine-tuning, MatterGen successfully generates stable, new materials with desired chemistry, symmetry and mechanical, electronic and magnetic properties. As a proof of concept, we synthesize one of the generated structures and measure its property value to be within 20% of our target. We believe that the quality of generated materials and the breadth of abilities of MatterGen represent an important advancement towards creating a foundational generative model for materials design.

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Conflict of interest statement

Competing interests: A.F., M.H., R.P., R.T., T.X., C.Z. and D.Z. are inventors of the pending, non-provisional patent application 18/759,208 in the name of Microsoft Technology Licensing, relating to generative models for the computational design of materials. The other authors declare no competing interests.

Figures

Fig. 1
Fig. 1. Inorganic materials design with MatterGen.
a, MatterGen generates stable materials by reversing a corruption process through iteratively denoising a random structure. The forward diffusion process independently corrupts atom types A, coordinates X and the lattice L towards a physically motivated distribution of random materials. b, An equivariant score network is pretrained 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 labelled dataset through an adapter module that adapts the model using the encoded property c. c, The fine-tuned model generates materials with desired chemistry, symmetry or scalar property constraints. m, magnetic density.
Fig. 2
Fig. 2. Generating stable, unique and new inorganic materials.
a, Visualization of four randomly selected crystals generated by MatterGen, with corresponding reduced formula and space group. b, Distribution of energy above hull values of generated structures using MP and Alex-MP-ICSD datasets as energy references, respectively. c, Distribution of root mean squared displacement (RMSD) between initial generated and DFT-relaxed structures. d, Percentage of unique, new structures as a function of the number of generated structures. e,f, Percentage of SUN structures (e) and average RMSD between initial and DFT-relaxed structures (f) for MatterGen, MatterGen-MP and several baseline models, including DiffCSP, CDVAE, P-G-SchNet, G-SchNet and FTCP. Training datasets are in parentheses. Percentage of SUN structures are computed using 1,024 samples for MatterGen and 1,000 for baseline models.
Fig. 3
Fig. 3. Generating materials in target chemical system.
a,b, Mean percentage of SUN structures generated by MatterGen and baselines for 27 chemical systems, grouped by system type (a) and number of elements (b). Percentages are computed on 100 structures for each of 9 chemical systems. Error bars denote 95% percentile intervals (n = 9). c,d, Number of structures on the combined convex hull found by each method and in the Alex-MP-ICSD dataset, grouped by system type (c) and number of elements (d). e, Convex hull diagram for V–Sr–O, a well-explored ternary system. Dots denote structures on the hull, their coordinates show the element ratio of their composition and their colour indicates by which method they were discovered. f–i, Four structures that MatterGen discovered (rediscovered in the case of f) on the V–Sr–O hull shown in e, along with their reduced formula: Sr2VO4 (f), Sr3(VO4)2 (g), SrV2O4 (h) and SrV2O6 (i).
Fig. 4
Fig. 4. Designing materials with target magnetic, electronic and mechanical properties.
a–c, Density of property values among (1) SUN samples generated by MatterGen and (2) structures in the labelled fine-tuning dataset for magnetic (a), electronic (b) and mechanical (c) properties. The property target for MatterGen is shown as a black dashed line. Magnetic density values  less than 10−3 Å−3 in a are excluded from the labelled data to improve readability. d–f, Visualization of SUN structures with the best property values generated by MatterGen for magnetic density (d), bandgap (e) and bulk modulus (f), along with their reduced formula, space group and property value. g,h, Number of SUN structures that satisfy target constraints found by MatterGen and baselines across DFT property calculation budgets: magnetic density > 0.2 Å–3 (g) and bulk modulus > 400 GPa (h).
Fig. 5
Fig. 5. Designing low-supply-chain-risk magnets.
a, Distribution of SUN structures generated by MatterGen when fine-tuned on magnetic density (single) and on both HHI score and magnetic density (joint), as well as structures from the labelled fine-tuning dataset. The property target of MatterGen is shown as a black cross. b, Occurrence of most frequent elements in SUN structures for the two fine-tuned MatterGen models. c, SUN structures on the Pareto front for the jointly fine-tuned model, along with their reduced formula, space group, magnetic density and HHI score.
Fig. 6
Fig. 6. Experimental validation of generated structures.
a, Rietveld refinement for the experimental sample we synthesize, including the measured X-ray diffraction spectra (yellow dots), the theoretical fit (black line) and the difference between the two (teal line). Vertical ticks (purple) highlight the major peaks of TaCr2O6 and Cr2O3. Inset: a picture of the sample. b, Two views of the TaCr2O6 structure generated by MatterGen that we use as a synthesis target, along with the reduced formula, space group and DFT bulk modulus value. c, Two views of the disordered TaCr2O6 structure we experimentally synthesize. d, DFT bulk modulus values of structures generated by MatterGen that match experimentally verified ICSD structures not present in the training dataset, across four different target bulk modulus values. The yellow triangle indicates the generated structure from b. a.u., arbitrary units.
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