Toward Learning Latent-Variable Representations of Microstructures by
  Optimizing in Spatial Statistics Space
Sayed Sajad Hashemi Michael Guerzhoy Noah H. Paulson
In Materials Science, material development involves evaluating and optimizing
the internal structures of the material, generically referred to as
microstructures. Microstructures structure is stochastic, analogously to image
textures. A particular microstructure can be well characterized by its spatial
statistics, analogously to image texture being characterized by the response to
a Fourier-like filter bank. Material design would benefit from low-dimensional
representation of microstructures Paulson et al. (2017).
  In this work, we train a Variational Autoencoders (VAE) to produce
reconstructions of textures that preserve the spatial statistics of the
original texture, while not necessarily reconstructing the same image in data
space. We accomplish this by adding a differentiable term to the cost function
in order to minimize the distance between the original and the reconstruction
in spatial statistics space.
  Our experiments indicate that it is possible to train a VAE that minimizes
the distance in spatial statistics space between the original and the
reconstruction of synthetic images. In future work, we will apply the same
techniques to microstructures, with the goal of obtaining low-dimensional
representations of material microstructures.