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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.

Abstract

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.

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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 https://github.com/stke9/SliceGAN.

References

  1. Goodfellow, I. et al. Generative adversarial nets. In Advances in Neural Information Processing Systems Vol. 27, 2672–2680 (NIPS, 2014).

  2. Creswell, A. et al. Generative adversarial networks: an overview. IEEE Signal Process. Mag. 35, 53–65 (2018).

    Article  Google Scholar 

  3. Odena, A. Semi-supervised learning with generative adversarial networks. Preprint at https://arxiv.org/abs/1606.01583 (2016).

  4. Arjovsky, M., Chintala, S., Bottou, L. Wasserstein generative adversarial networks. In Proc. 34th International Conference on Machine Learning Vol. 70, 214–223 (PMLR, 2017).

  5. Gulrajani, I., Ahmed, F., Arjovsky, M., Dumoulin, V. & Courville, A. C. Improved training of Wasserstein GANs. Preprint at http://arxiv.org/abs/1704.00028 (2017).

  6. Mirza, M. & Osindero, S. Conditional generative adversarial nets. Preprint at https://arxiv.org/abs/1411.1784 (2014).

  7. Wu, J., Zhang, C., Xue, T., Freeman, W. T. & Tenenbaum, J. B. Learning a probabilistic latent space of object shapes via 3D generative-adversarial modeling. Preprint at http://arxiv.org/abs/1610.07584 (2016).

  8. Mosser, L., Dubrule, O. & Blunt, M. J. Reconstruction of three-dimensional porous media using generative adversarial neural networks. Phys. Rev. E 96, 043309 (2017).

    Article  Google Scholar 

  9. Gayon-Lombardo, A. et al. Pores for thought: generative adversarial networks for stochastic reconstruction of 3D multi-phase electrode microstructures with periodic boundaries. npj Comput. Mater. 6, 82 (2020).

    Article  Google Scholar 

  10. Yang, Z. et al. Microstructural materials design via deep adversarial learning methodology. J. Mech. Des. 140, 111416 (2018).

    Article  Google Scholar 

  11. Xu, H., Dikin, D. A., Burkhart, C. & Chen, W. Descriptor-based methodology for statistical characterization and 3D reconstruction of microstructural materials. Comput. Mater. Sci. 85, 206–216 (2014).

    Article  Google Scholar 

  12. Groeber, M. A. & Jackson, M. A. DREAM.3D: a digital representation environment for the analysis of microstructure in 3D. Integr. Mater. Manuf. Innov. 3, 56–72 (2014).

    Article  Google Scholar 

  13. Torquato, S. & Stell, G. Microstructure of two-phase random media. I. The n-point probability functions. J. Chem. Phys. 77, 2071–2077 (1982).

    Article  MathSciNet  Google Scholar 

  14. Torquato, S. & Haslach Jr, H. Random heterogeneous materials: microstructure and macroscopic properties. Appl. Mech. Rev. 55, B62–B63 (2002).

    Article  Google Scholar 

  15. Hasanabadi, A., Baniassadi, M., Abrinia, K., Safdari, M. & Garmestani, H. 3D microstructural reconstruction of heterogeneous materials from 2D cross sections: a modified phase-recovery algorithm. Comput. Mater. Sci. 111, 107–115 (2016).

    Article  Google Scholar 

  16. Izadi, H. et al. Application of full set of two point correlation functions from a pair of 2D cut sections for 3D porous media reconstruction. J. Pet. Sci. Eng. 149, 789–800 (2017).

    Article  Google Scholar 

  17. Gommes, C. J., Jiao, Y. & Torquato, S. Microstructural degeneracy associated with a two-point correlation function and its information content. Phys. Rev. E 85, 051140 (2012).

    Article  Google Scholar 

  18. Zhang, Y. et al. High-throughput 3D reconstruction of stochastic heterogeneous microstructures in energy storage materials. npj Comput. Mater. 5, 11 (2019).

    Article  Google Scholar 

  19. Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. Preprint at https://arxiv.org/abs/1412.6980 (2017).

  20. Odena, A., Dumoulin, V. & Olah, C. Deconvolution and checkerboard artifacts. Distill http://distill.pub/2016/deconv-checkerboard (2016).

  21. Gratia, P. et al. The many faces of mixed ion perovskites: unraveling and understanding the crystallization process. ACS Energy Lett. 2, 2686–2693 (2017).

    Article  Google Scholar 

  22. Armentrout, D., Kumosa, M. & Mcquarrie, T. Boron-free fibers for prevention of acid induced brittle fracture of composite insulator grp rods. IEEE Trans. Power Deliv. 18, 684–693 (2003).

    Article  Google Scholar 

  23. Finegan, D. et al. Microstructure reconstruction of battery polymer separators by fusing 2D and 3D image data for transport property analysis. J. Power Sources 333, 184–192 (2016).

    Article  Google Scholar 

  24. Xu, H., Usseglio-Viretta, F., Kench, S., Cooper, S. J. & Finegan, D. P. Microstructure reconstruction of battery polymer separators by fusing 2D and 3D image data for transport property analysis. J. Power Sources 480, 229101 (2020).

    Article  Google Scholar 

  25. Oxford instruments grain size and grain boundary characterisation in SEM. EBSD http://www.ebsd.com/solving-problems-with-ebsd/grain-size-and-grain-boundary-characterisation-in-sem (2020).

  26. Hsu, T. et al. Mesoscale characterization of local property distributions in heterogeneous electrodes. J. Power Sources 386, 1–9 (2018).

    Article  Google Scholar 

  27. Cooper, S., Bertei, A., Shearing, P., Kilner, J. & Brandon, N. TauFactor: an open-source application for calculating tortuosity factors from tomographic data. SoftwareX 5, 203–210 (2016).

    Article  Google Scholar 

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Authors and Affiliations

Authors

Contributions

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). https://doi.org/10.1038/s42256-021-00322-1

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