  The study of matter at extreme densities and temperatures as they occur in
astrophysical objects and state-of-the art experiments with high-intensity
lasers is of high current interest for many applications. While no overarching
theory for this regime exists, accurate data for the density response of
correlated electrons to an external perturbation are of paramount importance.
In this context, the key quantity is given by the local field correction (LFC),
which provides a wave-vector resolved description of exchange-correlation
effects. In this work, we present extensive new path integral Monte Carlo
(PIMC) results for the static LFC of the uniform electron gas, which are
subsequently used to train a fully connected deep neural network. This allows
us to present a continuous representation of the LFC with respect to
wave-vector, density, and temperature covering the entire warm dense matter
regime. Both the PIMC data and neural-net results are available online.
Moreover, we expect the presented combination of ab initio calculations with
machine-learning methods to be a promising strategy for many applications.
