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The study of matter at extreme densities and temperatures as they occur inastrophysical objects and state-of-the art experiments with high-intensitylasers is of high current interest for many applications. While no overarchingtheory for this regime exists, accurate data for the density response ofcorrelated 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-correlationeffects. In this work, we present extensive new path integral Monte Carlo(PIMC) results for the static LFC of the uniform electron gas, which aresubsequently used to train a fully connected deep neural network. This allowsus to present a continuous representation of the LFC with respect towave-vector, density, and temperature covering the entire warm dense matterregime. Both the PIMC data and neural-net results are available online.Moreover, we expect the presented combination of ab initio calculations withmachine-learning methods to be a promising strategy for many applications.

The Static Local Field Correction of the Warm Dense Electron Gas: An ab Initio Path Integral Monte Carlo Study and Machine Learning Representation