Latent Representation of Microstructures Using Variational Autoencoders with Spatial Statistics-Space Loss

We propose the use of Cross-Entropy on 2-point spatial statistics (CESS) as a reconstruction loss term for a variational autoencoder, creating a small latent-space representation of microstructures from which microstructures can be reconstructed. A prospective application of small reversible microstructure representations is more efficient optimization for materials properties in latent space. In Materials Science, 2-point spatial statistics have been shown to be good representations of microstructure properties, and have many desirable invariances (translation, phase label, inversion). To our knowledge, we are the first to demonstrate a system that successfully creates latent representations of realistic simulations of microstructures by using an error term that minimizes the distance between input and reconstruction in spatial statistics space. We also demonstrate some promising preliminary qualitative results that show improved quality of reconstructions using CESS loss. We demonstrate compression from 224×224 binary microstructure images to 14×14 latent representations.