  The electronic structure in matter under extreme conditions is a challenging
complex system prevalent in astrophysical objects and highly relevant for
technological applications. We show how machine-learning surrogates in terms of
neural networks have a profound impact on the efficient modeling of matter
under extreme conditions. We demonstrate the utility of a surrogate model that
is trained on \emph{ab initio} quantum Monte Carlo data for various
applications in the emerging field of warm dense matter research.
