A neural network closure for the Euler-Poisson system based on kinetic simulations

TL;DR

This paper introduces a neural network-based closure for the Euler-Poisson system in plasma modeling, trained on kinetic simulation data, to accurately predict heat flux across various collision regimes.

Contribution

It presents a novel neural network closure using a V-net architecture, trained on kinetic simulations, for the Euler-Poisson system across different collision regimes.

Findings

The neural network closure achieves uniform accuracy over a range of Knudsen numbers.

Numerical tests validate the model's flexibility and predictive capability.

The approach improves plasma modeling by integrating machine learning with kinetic data.

Abstract

This work deals with the modeling of plasmas, which are charged-particle fluids. Thanks to machine leaning, we construct a closure for the one-dimensional Euler-Poisson system valid for a wide range of collision regimes. This closure, based on a fully convolutional neural network called V-net, takes as input the whole spatial density, mean velocity and temperature and predicts as output the whole heat flux. It is learned from data coming from kinetic simulations of the Vlasov-Poisson equations. Data generation and preprocessings are designed to ensure an almost uniform accuracy over the chosen range of Knudsen numbers (which parametrize collision regimes). Finally, several numerical tests are carried out to assess validity and flexibility of the whole pipeline.