A key problem in computational material science deals with understanding the effect of material distribution (i.e., microstructure) on material performance. The challenge we consider here is to synthesize microstructures with desired physical and chemical properties, given a finite number of microstructure images, evaluated based on the physical invariances that the microstructure exhibits.
We introduce Machine learning based generative models for the fast synthesis of binary microstructure images. The first approach uses a standard GAN architecture trained with a Wasserstein metric. We show that the generated images respect the distribution of certain physical invariances — specifically, the one-point and two-point correlations — of the training data. In this approach, we effectively let the discriminator learn the features of the data. For the training of our model, we curated a dataset of Binary 2D microstructural images of polymer phase separation. We made our dataset available publically.
While the typical GAN model learns the implicit features of training dataset to generate images resambling the training data, it doesn't incorporate the explicitly known physics-based or statistical rules into the generation process. Thus we propose the second approach replaces the traditional discriminator with a checker function. This checker function is defined by the user and identifies the most physically informed features of the microstructures. There is no discriminator training involved and thus the issue of mode collapse can be averted. Here, the data requirements are minimal, and data is only used to calibrate the checker. We demonstrate how the generated images are diverse and mimic the supplied invariance metric (two point correlation curve).