  Emission from the interstellar medium can be a significant contaminant of
measurements of the intensity and polarization of the cosmic microwave
background (CMB). For planning CMB observations, and for optimizing
foreground-cleaning algorithms, a description of the statistical properties of
such emission can be helpful. Here we examine a machine learning approach to
inferring the statistical properties of dust from either observational data or
physics-based simulations. In particular, we apply a type of neural network
called a Variational Auto Encoder (VAE) to maps of the intensity of emission
from interstellar dust as inferred from Planck sky maps and demonstrate its
ability to a) simulate new samples with similar summary statistics as the
training set, b) provide fits to emission maps withheld from the training set,
and c) produce constrained realizations. We find VAEs are easier to train than
another popular architecture: that of Generative Adversarial Networks (GANs),
and are better-suited for use in Bayesian inference.
