Learning Latent-Variable Representations of Microstructure Accounting for Materials Stochasticity

Over the past decade, generative machine learning has found application in the design of materials with tailored properties. Generative latent-variable models represent high-dimensional data in low-dimensional spaces. The original data is n-dimensional, for example, 2-D/3-D image-based representations of materials microstructure with k pixels/voxels. New plausible examples of image-based representations can be generated from points in the low-dimensional space. The variational autoencoder (VAE) is a popular latent-variable model. The VAE is learned by optimizing the L2 distance in data space (2-D/3-D) between real and generated examples (in addition to regularization). This is suboptimal, since materials microstructure is stochastic. Therefore, image-based representations should be considered similar if their statistical properties are similar rather than just if they are close in Euclidean data space. We develop a novel VAE architecture to prioritize statistical representations of materials microstructure and the generation of statistically similar microstructure examples from a single location in the latent space. A successful implementation of this architecture would greatly aid materials development and optimization through iterative materials simulations. This novel capability will be demonstrated on both synthetic and natural microstructure datasets.