A NEURAL NETWORK CLOSURE FOR THE EULER-POISSON SYSTEM BASED ON KINETIC SIMULATIONS

Abstract

This work deals with the modeling of plasmas, which are ionized gases. Thanks to machine learning, we construct a closure for the onedimensional Euler-Poisson system valid for a wide range of collisional 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 collisional regimes). Finally, several numerical tests are carried out to assess validity and flexibility of the whole pipeline