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  • Perspective
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Leveraging generative models with periodicity-aware, invertible and invariant representations for crystalline materials design

Nature Computational Science volume 5, pages 365–376 (2025)Cite this article

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Abstract

Designing periodicity-aware, invariant and invertible representations provides an opportunity for the inverse design of crystalline materials with desired properties by generative models. This objective requires optimizing representations and refining the architecture of generative models, yet its feasibility remains uncertain, given current progress in molecular inverse generation. In this Perspective, we highlight the progress of various methods for designing representations and generative schemes for crystalline materials, discuss the challenges in the field and propose a roadmap for future developments.

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Fig. 1: Computational strategies for materials generation.
Fig. 2: Typical invertible representations for crystalline materials.
Fig. 3: Text-based representations for crystalline materials.
Fig. 4: Generative architecture with diffusion models and flow-based models.
Fig. 5: Future research directions.

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Acknowledgements

This project is partially supported by the Eric and Wendy Schmidt AI in Science Postdoctoral Fellowship, a program of Schmidt Sciences, LLC.

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Authors and Affiliations

  1. Cornell University AI for Science Institute, Cornell University, Ithaca, NY, USA

    Zhilong Wang & Fengqi You

  2. College of Engineering, Cornell University, Ithaca, NY, USA

    Zhilong Wang & Fengqi You

  3. Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY, USA

    Zhilong Wang & Fengqi You

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  1. Zhilong Wang
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Contributions

Z.W.: conceptualization, methodology, visualization, data curation, writing—original draft. F.Y.: conceptualization, methodology, supervision, resources, writing—review and editing.

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Correspondence to Fengqi You.

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Nature Computational Science thanks Ming Hu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Kaitlin McCardle, in collaboration with the Nature Computational Science team.

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Supplementary Table 1

An overview of generative models of crystalline materials design. This table summarizes the representative studies from this Perspective, highlighting their main representations, artificial intelligence architectures, materials applications, properties and access links.

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Wang, Z., You, F. Leveraging generative models with periodicity-aware, invertible and invariant representations for crystalline materials design. Nat Comput Sci 5, 365–376 (2025). https://doi.org/10.1038/s43588-025-00797-7

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