  Microstructure reconstruction is an important and emerging field of research
and an essential foundation to improving inverse computational materials
engineering (ICME). Much of the recent progress in the field is made based on
generative adversarial networks (GANs). Although excellent results have been
achieved throughout a variety of materials, challenges remain regarding the
interpretability of the model's latent space as well as the applicability to
extremely small data sets. The present work addresses these issues by
introducing DA-VEGAN, a model with two central innovations. First, a
$\beta$-variational autoencoder is incorporated into a hybrid GAN architecture
that allows to penalize strong nonlinearities in the latent space by an
additional parameter, $\beta$. Secondly, a custom differentiable data
augmentation scheme is developed specifically for this architecture. The
differentiability allows the model to learn from extremely small data sets
without mode collapse or deteriorated sample quality. An extensive validation
on a variety of structures demonstrates the potential of the method and future
directions of investigation are discussed.
