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Generating three-dimensional structures from a two-dimensional slice with generative adversarial network-based dimensionality expansion

Matters Arising to this article was published on 11 October 2021

A preprint version of the article is available at arXiv.


Generative adversarial networks (GANs) can be trained to generate three-dimensional (3D) image data, which are useful for design optimization. However, this conventionally requires 3D training data, which are challenging to obtain. Two-dimensional (2D) imaging techniques tend to be faster, higher resolution, better at phase identification and more widely available. Here we introduce a GAN architecture, SliceGAN, that is able to synthesize high-fidelity 3D datasets using a single representative 2D image. This is especially relevant for the task of material microstructure generation, as a cross-sectional micrograph can contain sufficient information to statistically reconstruct 3D samples. Our architecture implements the concept of uniform information density, which ensures both that generated volumes are equally high quality at all points in space and that arbitrarily large volumes can be generated. SliceGAN has been successfully trained on a diverse set of materials, demonstrating the widespread applicability of this tool. The quality of generated micrographs is shown through a statistical comparison of synthetic and real datasets of a battery electrode in terms of key microstructural metrics. Finally, we find that the generation time for a 108 voxel volume is on the order of a few seconds, yielding a path for future studies into high-throughput microstructural optimization.

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Fig. 1: SliceGAN training procedure.
Fig. 2: Information density in a generator neural network.
Fig. 3: Application of SliceGAN to a variety of microstructures.
Fig. 4: Statistical analysis of three electrochemical and general materials properties.

Data availability

The study used open-access training data available from the following sources: ceramic21, carbon fibre rods22, battery separator23,24, steel25 and NMC battery cathode26. All generated data used are available from the authors on request.

Code availability

The codes used in this manuscript are available at


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Authors and Affiliations



S.K. designed and developed the code for SliceGAN, trained the models, performed the statistical analysis and drafted the manuscript. S.J.C. contributed to the development of the concepts presented in all sections of this work, helped with data interpretation in the ‘Empirical results’ section and made substantial revisions and edits to all sections of the draft manuscript.

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Correspondence to Steve Kench or Samuel J. Cooper.

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The authors declare no competing interests.

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Peer review informationNature Machine Intelligence thanks Jong Chul Ye and Alejandro Franco for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Algorithm 1 and Figs. 1–6.

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Kench, S., Cooper, S.J. Generating three-dimensional structures from a two-dimensional slice with generative adversarial network-based dimensionality expansion. Nat Mach Intell 3, 299–305 (2021).

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