# Physics-aware Deep Generative Models for Creating Synthetic Microstructures

arXiv: https://arxiv.org/abs/1811.09669 · HTML: https://mlsanity.com/paper/1811.09669/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2018.

## Built on by (most cited first, 6 of 6)

- [Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties](https://mlsanity.com/paper/2302.12881/) (2023)
- [A review of Generative Adversarial Networks (GANs) and its applications in a wide variety of disciplines -- From Medical to Remote Sensing](https://mlsanity.com/paper/2110.01442/) (2021)
- [Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanics](https://mlsanity.com/paper/2206.01693/) (2022)
- [Physics-Informed Deep Learning: A Promising Technique for System Reliability Assessment](https://mlsanity.com/paper/2108.10828/) (2021)
- [A Survey on Evaluation Metrics for Synthetic Material Micro-Structure Images from Generative Models](https://mlsanity.com/paper/2211.09727/) (2022)
- [A Generative Model for Accelerated Inverse Modelling Using a Novel Embedding for Continuous Variables](https://mlsanity.com/paper/2311.11343/) (2023)

## Abstract (arXiv)

A key problem in computational material science deals with understanding the effect of material distribution (i.e., microstructure) on material performance. The challenge is to synthesize microstructures, given a finite number of microstructure images, and/or some physical invariances that the microstructure exhibits. Conventional approaches are based on stochastic optimization and are computationally intensive. We introduce three generative models for the fast synthesis of binary microstructure images. The first model is a WGAN model that uses a finite number of training images to synthesize new microstructures that weakly satisfy the physical invariances respected by the original data. The second model explicitly enforces known physical invariances by replacing the traditional discriminator in a GAN with an invariance checker. Our third model combines the first two models to reconstruct microstructures that respect both explicit physics invariances as well as implicit constraints learned from the image data. We illustrate these models by reconstructing two-phase microstructures that exhibit coarsening behavior. The trained models also exhibit interesting latent variable interpolation behavior, and the results indicate considerable promise for enforcing user-defined physics constraints during microstructure synthesis.