  We employ variational autoencoders to extract physical insight from a dataset
of one-particle Anderson impurity model spectral functions. Autoencoders are
trained to find a low-dimensional, latent space representation that faithfully
characterizes each element of the training set, as measured by a reconstruction
error. Variational autoencoders, a probabilistic generalization of standard
autoencoders, further condition the learned latent space to promote highly
interpretable features. In our study, we find that the learned latent variables
strongly correlate with well known, but nontrivial, parameters that
characterize emergent behaviors in the Anderson impurity model. In particular,
one latent variable correlates with particle-hole asymmetry, while another is
in near one-to-one correspondence with the Kondo temperature, a dynamically
generated low-energy scale in the impurity model. Using symbolic regression, we
model this variable as a function of the known bare physical input parameters
and "rediscover" the non-perturbative formula for the Kondo temperature. The
machine learning pipeline we develop suggests a general purpose approach which
opens opportunities to discover new domain knowledge in other physical systems.
