Generating 3D structures from a 2D slice with GAN-based dimensionality expansion

TL;DR

The paper tackles the problem of obtaining volumetric microstructure data for simulations when only 2D imaging is readily available. It introduces SliceGAN, a 3D generator paired with a 2D discriminator that receives $3l$ slices along the $x$, $y$, and $z$ axes, trained with a Wasserstein loss and a batch-size rule $m_G = 2 m_D$ to achieve stable learning; it also addresses edge artifacts via uniform information density constraints on transpose convolutions, including parameter choices such as $s<k$, $k \bmod s = 0$, and $p \ge k-s$. The approach is demonstrated across diverse isotropic and anisotropic microstructures, showing quantitative alignment with real data on metrics like two-point correlations and effective diffusivity, and enabling rapid generation of large volumes ($10^8$ voxels) in seconds. This work enables high-throughput microstructure design and simulation using 2D data, with potential extensions to conditional GANs and transfer learning to broaden applicability and control over anisotropy and features.

Abstract

Generative adversarial networks (GANs) can be trained to generate 3D image data, which is useful for design optimisation. However, this conventionally requires 3D training data, which is challenging to obtain. 2D imaging techniques tend to be faster, higher resolution, better at phase identification and more widely available. Here, we introduce a generative adversarial network architecture, SliceGAN, which is able to synthesise 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 both ensures 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 $10^8$ voxel volume is on the order of a few seconds, yielding a path for future studies into high-throughput microstructural optimisation.

Figures (4)

• Figure 1: SliceGAN training procedure. First, real images are sampled from a 2D training sample. Second, a fake volume $\textbf{f}$ is generated and sliced along $x$, $y$ and $z$. This yields a compatible pair of datasets, which can both be fed to a 2D discriminator.
• Figure 2: a) An example of how information density is calculated for a single transpose convolution with input size = $3 \times 3$, $k$ = 4, $s$ = 2 and $p$ = 0. The overlap from the outputs of individual pixels is depicted, showing a information density gradient at the edges of the final image. b) Illustration of how information density gradients propagate and are exacerbated in a full neural net as an input is passed through multiple transpose convolutional layers.
• Figure 3: Application of SliceGAN to a variety of microstructures, with details specified in Table \ref{['Tab:EmpDetails']}. From left to right, the original training dataset, a 3D statistical reconstruction and 2 examples of slices through an example volume taken at different angles.
• Figure 4: Statistical analysis of three electrochemical and general materials properties, showing that the real properties of the dataset are captured well by both a 3D to 3D GAN and SliceGAN. Boxes depict the interquartile range (IQR) from the lower quartile, Q1 to the upper quartile, Q3). Each box contains a horizontal line and a small square to indicate the median and mean respectively. The upper and lower whiskers show the last datum greater than $\text{Q3} + (1.5 \times \text{IQR})$ and less than $\text{Q1} - (1.5 \times \text{IQR})$ respectively. Outlier data points beyond this range are represented by solid black diamonds.