Source-linked AI summary
Generating 3D structures from a 2D slice with GAN-based dimensionality expansion
Steve Kench, Samuel J. Cooper
TL;DR
The paper addresses the difficulty of obtaining 3D training data for volumetric material modelling despite the accessibility and resolution advantages of 2D micrographs. It introduces SliceGAN, which trains 3D generators from 2D slices while using uniform information density to support consistent-quality and variable-size volumes. SliceGAN reconstructs diverse microstructures, including statistically similar battery-electrode volumes, and generates 10^8-voxel instances in seconds, although anisotropy within a given plane remains constrained.
Problem
3D microstructural data are needed for volumetric simulations, but 2D micrographs are easier to obtain, higher resolution, and can contain more representative feature distributions.
Method
SliceGAN generates 3D volumes, slices them along relevant orientations, and feeds the resulting 2D datasets to discriminators, with uniform information density enabling variable-size generation.
Results
SliceGAN produces visually indistinguishable cross sections across seven example training sets and statistically similar battery-electrode volumes across three key microstructural metrics.
Takeaways & Limitations
The tool supports 3D material characterisation, electrochemical simulation, and rapid exploration of 3D microstructures for materials optimisation.
Takeaways & Limitations
The generator cannot learn anisotropy within a given plane, such as graded density, because every 32nd plane uses the same combination of kernel elements.
Abstract
from arXiv · showhide
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.
1 Introduction
The paper addresses the challenge of generating useful 3D material microstructures from more accessible 2D micrographs. It introduces SliceGAN to resolve the incompatibility between 3D generation and 2D training data, with applications across diverse materials.
- Motivation: 3D microstructural data are needed for volumetric simulations, but 2D micrographs are often easier to obtain, higher resolution, and more representative of features.Examples include modelling deformation under stress and fluid flow through porous media.
- Motivation: GANs are proposed for dimensionality expansion, but a 3D generator must be made compatible with 2D training data.The architecture uses a generator to synthesise fake samples and a discriminator to distinguish them from real data.
- Contributions: SliceGAN generates 3D volumetric data from 2D slices of an isotropic material and can be extended to statistically reconstruct anisotropic microstructures.The method is introduced as a novel GAN architecture for this purpose.
- Contributions: SliceGAN addresses low-quality outer regions in GAN-generated images by associating them with non-uniform information density and defining transpose-convolution requirements.The contribution concerns parameter requirements intended to avoid this issue.
- Contributions: Across seven example training sets, SliceGAN produces visually indistinguishable cross sections, while battery-electrode volumes are further compared using three key microstructural metrics.The examples include crystalline, anisotropic polymer-membrane, and three-phase battery-electrode materials.
2 Background
Prior microstructural reconstruction methods include GANs, geometric simulations, and correlation-based stochastic algorithms. Their scope or computational cost motivates a flexible GAN approach that generates large volumes rapidly after training.
- Existing approaches: GANs have been used to generate material microstructures and support material design, including 3D energy-storage volumes and semiconductor surfaces.Generated instances can be evaluated for properties such as absorption coefficient.
- Existing approaches: Geometric reconstruction methods use measurements such as particle size, grain size, and orientation, but are limited to particular material classes including powders and polycrystals.Examples include simulated annealing with ellipsoid packing and tessellation-based grain-growth tools.
- Existing approaches: Two-point correlation functions can be equivalent between 2D and 3D datasets for isotropic materials, enabling stochastic reconstruction algorithms.The correlation function describes the probability that two pixels separated by distance r belong to the same phase.
- Limitations: 106 voxel samples can require hours to synthesise with state-of-the-art methods, making those approaches unsuitable for materials optimisation.The cited benchmark uses a 2.8 GHz, 16GB RAM computer.
- SliceGAN advantages: After approximately 4 hours of training, the proposed GAN generates 108 voxel instances in seconds, a 105-fold acceleration compared with the cited alternative.The authors link this speed to high-throughput optimisation and large-scale modelling.
3 SliceGAN
SliceGAN trains a 3D generator using 2D slices of generated volumes and real 2D images presented to a 2D discriminator. The basic procedure supports isotropic materials, while separate orientation-specific training extends it to anisotropic materials.
- Isotropic SliceGAN: Generated cubic volumes are sliced along x, y, and z before the slices are supplied to a 2D discriminator.A volume with edge length l yields 3l 2D slices at one-voxel increments.
- Isotropic SliceGAN: During discriminator training, each fake slice is paired with a sampled real 2D image, while generator training uses a larger batch size, typically mG = 2mD.The larger generator batch rebalances discriminator training over many slices from each generated volume.
- Anisotropic extension: The basic architecture is suitable only for isotropic materials because one 2D image must represent slices from all three volume orientations.Anisotropic materials require an architectural extension.
- Anisotropic extension: For anisotropic materials, training images and fake slices are divided by orientation, and separate discriminators learn feature distributions along the different axes.The generator is trained to match the appropriate perpendicular and parallel views.
- Training procedure: Figure 1 summarizes the training procedure by showing real-image sampling, fake-volume generation, three-axis slicing, and joint use of compatible datasets by a 2D discriminator.The figure presents the dimensionality-matching step visually.
4 Generator information density
SliceGAN addresses poor edge quality in generated microstructures by enforcing uniform information density throughout the generator. The required transpose-convolution parameters constrain practical architectures, while the design supports variable-size volume generation but cannot capture within-plane anisotropy.
- Motivation: Edge quality is especially consequential for microstructures because boundary features can influence measured physical properties as strongly as central features.Unlike some image-generation applications, microstructural feature locations are often arbitrary, making edges equally important to the center.
- Information-density gradients: A 3 × 3 input with k = 4, s = 2 and p = 0 produces uniform central information density but lower information content near edges and corners.Across multiple transpose-convolution layers, central pixels can receive contributions from 3 orders of magnitude more parameters than edge pixels.
- Design rules: Uniform information density requires transpose-convolution parameters satisfying s < k, k mod s = 0, and p ≥ k −s.These rules ensure kernel overlap, flush output regions, and removal of low-density edge voxels.
- Architectural constraints: Prime kernel sizes and generally k > 6 are impractical under these constraints, while resize-convolution requires trading training time or image quality for its higher memory demand in 3D.Zero-padding in resize-convolution also produces undesirable information gradients.
- Variable-size generation: Training the first generator layer with an input vector of spatial size 4 enables different-size volumes during inference without the overlap distortion associated with changing a spatially single latent vector.The motivation is that standard training volumes are often too small for multiphysics simulations.
- Limitation: The generator’s 32-plane periodicity prevents it from learning anisotropy within an individual plane, such as a graded density.This periodicity does not make the synthetic volume itself periodic because each plane corresponds to a different input-seed region.
5 Empirical results
SliceGAN was applied to diverse microstructures, including anisotropic materials, colour images, and a three-phase battery electrode. Generated volumes generally reproduced visual and statistical features of the training data, while specific limitations arose for continuous labels and unconstrained interfaces.
- Application to microstructures: SliceGAN generated 3D statistical reconstructions from diverse 2D microstructures, including fibre composites, polymer separators, steel, and battery materials.Figure 3 presents the training data, generated volumes, and slices at different orientations.
- Application to microstructures: Anisotropic fibre composites and polymer battery separators demonstrated SliceGAN's ability to synthesise structures across perpendicular views.The anisotropic extension uses discriminators associated with different orientations.
- Application to microstructures: Colour-image synthesis for polycrystalline steel produced somewhat lower image quality than segmented-material examples.The authors attribute this likely to a 12 GB GPU-memory constraint limiting network size for continuous label spaces.
- Application to microstructures: Two discriminators were insufficient to constrain a synthetic interface fully, producing long particle ridges at 45° to the trained orientations.The authors suggest adding discriminated slices at 45° as a possible resolution.
- Statistical validation: Both GAN architectures reproduced conventional microstructural metrics well, while SliceGAN also reproduced effective diffusivity, an emergent property unavailable from individual 2D slices.Medians corresponded closely, although distributions—especially relative diffusivity—were not identical to the training set.
6 Conclusions
The study concludes that SliceGAN can faithfully synthesise 3D n-phase media from 2D micrographs. The authors identify applications in material characterisation, electrochemical simulation, and rapid materials optimisation.
- Conclusions: SliceGAN faithfully synthesises 3D n-phase media from 2D micrographs.The conclusion presents this as the central result of the study.
- Conclusions: The method can visualise statistically realistic 3D instances while addressing limitations of direct 3D imaging in resolution and field of view.The authors identify material characterisation as one use.
- Conclusions: The generated 3D structures support electrochemical and mechanical simulations for which 2D micrographs are insufficient.The conclusion specifically identifies electrochemical simulation as an application.
- Conclusions: Fast generation enables rapid exploration of possible 3D microstructures for materials optimisation.The authors propose future combinations with conditional GANs and transfer learning.
Data Availability
The study used open-access training data from sources covering ceramic, carbon-fibre, battery-separator, steel, and NMC battery-cathode datasets.
- Data Availability: Open-access training data were obtained from ceramic and carbon fibre rod datasets.
- Data Availability: Additional open-access datasets covered battery separators, steel, and NMC battery cathodes.
Authorship
SK led the technical development, experimentation, analysis, and manuscript drafting, while SJC contributed to concept development, interpretation, and revisions.
- Authorship: SK designed and developed SliceGAN, trained the models, performed statistical analysis, and drafted the manuscript.
- Authorship: SJC contributed concepts across the paper, interpreted section 5 data, and substantially revised and edited the manuscript.
Supplementary Information
The supplementary material specifies SliceGAN’s anisotropic algorithm and examines information-density issues in convolutional generators. It also notes a resize-convolution trade-off between uniform gradients and computationally practical architectures.
- Algorithm 1 uses different real data and a different discriminator for each axis when generating anisotropic materials.
- The anisotropic algorithm requires three perpendicular discriminators with trainable parameters w1, w2, w3 and θ.
- The training procedure samples latent vectors, generates 3D volumes, extracts 2D slices along each axis, and compares them with real images.
- Transpose convolutions with kernel size not divisible by stride produce checkerboard, non-uniform information density and can create unrealistic periodic features.
- Resize convolutions with padding produce low-information edge gradients, while avoiding padding requires a minimum 8 × 8 × 8 input and limits early-layer filters.For a 12GB GPU, the first layer can have approximately 64 filters versus 512 for a transpose convolution, leading to poorer-quality microstructures.
D Information overlap during post-training generation
The supplementary examples illustrate how information overlaps during generation and how channel encoding produces probabilistic phase outputs. They also show periodic behavior arising from repeated kernel-element sequences.
- A transpose convolution spreads an input stripe across the output, with a linearly decreasing contribution from the stripe’s position.RGB channels are calculated separately, then concatenated and normalised.
- A striped kernel produces periodic generator behavior, with identical darkness recurring every 32nd slice.
- One-hot coding maps segmented grayscale phase values to channels, while the generator’s softmax output assigns phase probabilities between 0 and 1.
G Metric comparison of real and synthetic datasets
Figure S6 compares real and synthetic microstructures using triple phase boundary density and two-point correlation functions. Both metrics’ distributions match well across the 100 tested samples.
- 100 samples show well-matched medians and distributions for triple phase boundary density between real and synthetic microstructures.Triple phase boundary density counts voxel vertices shared by all three phases.
- The two-point correlation function compares the probability of finding the same phase at voxels separated by distance r in real and synthetic structures.