# Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanics

arXiv: https://arxiv.org/abs/2206.01693 · HTML: https://mlsanity.com/paper/2206.01693/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 81 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 30 of 32)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2001.06937/) (2020)
- [NVIDIA Tensor Core Programmability, Performance & Precision](https://mlsanity.com/paper/1803.04014/) (2018)
- [CubeNet: Equivariance to 3D Rotation and Translation](https://mlsanity.com/paper/1804.04458/) (2018)
- [Physics informed neural networks for continuum micromechanics](https://mlsanity.com/paper/2110.07374/) (2021)
- [Reconstruction of three-dimensional porous media using generative adversarial neural networks](https://mlsanity.com/paper/1704.03225/) (2017)
- [3D G-CNNs for Pulmonary Nodule Detection](https://mlsanity.com/paper/1804.04656/) (2018)
- [3D-StyleGAN: A Style-Based Generative Adversarial Network for Generative Modeling of Three-Dimensional Medical Images](https://mlsanity.com/paper/2107.09700/) (2021)
- [Generative Adversarial Registration for Improved Conditional Deformable Templates](https://mlsanity.com/paper/2105.04349/) (2021)
- [Deep Learning Based 3D Segmentation: A Survey](https://mlsanity.com/paper/2103.05423/) (2021)
- [Megapixel Size Image Creation using Generative Adversarial Networks](https://mlsanity.com/paper/1706.00082/) (2017)
- [Three-dimensional convolutional neural network (3D-CNN) for heterogeneous material homogenization](https://mlsanity.com/paper/2002.07600/) (2020)
- [Group Equivariant Generative Adversarial Networks](https://mlsanity.com/paper/2005.01683/) (2020)
- [Pores for thought: The use of generative adversarial networks for the stochastic reconstruction of 3D multi-phase electrode microstructures with periodic boundaries](https://mlsanity.com/paper/2003.11632/) (2020)
- [Microstructure Generation via Generative Adversarial Network for Heterogeneous, Topologically Complex 3D Materials](https://mlsanity.com/paper/2006.13886/) (2020)
- [What machine learning can do for computational solid mechanics](https://mlsanity.com/paper/2109.08419/) (2021)
- [Microstructure synthesis using style-based generative adversarial network](https://mlsanity.com/paper/1909.07042/) (2019)
- [Physics-aware Deep Generative Models for Creating Synthetic Microstructures](https://mlsanity.com/paper/1811.09669/) (2018)

## Built on by (most cited first, 11 of 11)

- [Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties](https://mlsanity.com/paper/2302.12881/) (2023)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Spiking neural networks for nonlinear regression](https://mlsanity.com/paper/2210.03515/) (2022)
- [DA-VEGAN: Differentiably Augmenting VAE-GAN for microstructure reconstruction from extremely small data sets](https://mlsanity.com/paper/2303.03403/) (2023)
- [Artificial Intelligence in Materials Science and Engineering: Current Landscape, Key Challenges, and Future Trajectorie](https://mlsanity.com/paper/2601.12554/) (2026)
- [Synthesizing realistic sand assemblies with denoising diffusion in latent space](https://mlsanity.com/paper/2306.04411/) (2023)
- [Position Paper on Materials Design -- A Modern Approach](https://mlsanity.com/paper/2312.10996/) (2023)
- [FluxGAN: A Physics-Aware Generative Adversarial Network Model for Generating Microstructures That Maintain Target Heat Flux](https://mlsanity.com/paper/2310.04622/) (2023)
- [Denoising diffusion-based synthetic generation of three-dimensional (3D) anisotropic microstructures from two-dimensional (2D) micrographs](https://mlsanity.com/paper/2312.07832/) (2023)
- [MicroLad: 2D-to-3D Microstructure Reconstruction and Generation via Latent Diffusion and Score Distillation](https://mlsanity.com/paper/2508.20138/) (2025)
- [Training Variation of Physically-Informed Deep Learning Models](https://mlsanity.com/paper/2510.03416/) (2025)

## Abstract (arXiv)

Multiscale simulations are demanding in terms of computational resources. In the context of continuum micromechanics, the multiscale problem arises from the need of inferring macroscopic material parameters from the microscale. If the underlying microstructure is explicitly given by means of microCT-scans, convolutional neural networks can be used to learn the microstructure-property mapping, which is usually obtained from computational homogenization. The CNN approach provides a significant speedup, especially in the context of heterogeneous or functionally graded materials. Another application is uncertainty quantification, where many expansive evaluations are required. However, one bottleneck of this approach is the large number of training microstructures needed. This work closes this gap by proposing a generative adversarial network tailored towards three-dimensional microstructure generation. The lightweight algorithm is able to learn the underlying properties of the material from a single microCT-scan without the need of explicit descriptors. During prediction time, the network can produce unique three-dimensional microstructures with the same properties of the original data in a fraction of seconds and at consistently high quality.