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

## TL;DR

This paper provides new ab initio PIMC data for the static local field correction of the warm dense electron gas and trains a neural network to offer a continuous, accessible representation across various parameters.

## Contribution

It introduces a comprehensive machine learning model trained on PIMC data to accurately represent the static local field correction in warm dense matter.

## Key findings

- Extensive PIMC results for the static LFC are presented.
- A neural network model successfully represents the LFC across parameters.
- The data and model are publicly available online.

## Abstract

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.