New closure for Vlasov-Poisson equation using Machine Learning

Emmanuel Franck (INRIA Nancy Grand Est)

In this work we are interested in the modeling of plasmas by macroscopic fluid model. The Navier-Stokes Poisson is the classical model used to describe plasma. The closure (formula which linked the fourth moment to the three others) is obtain by asymptotic expansion on the Knudsen number (which parametrise collision regimes). In this work we construct a closure for 1d equations. This closure, based on a fully convolutional neural network called V-net, takes as input the whole spatial density, mean ve- locity and temperature and predicts as output the whole heat flux. Data generation and preprocessings are designed to ensure an almost uniform accuracy over the chosen range of Knudsen numbers. Finally, several numerical tests are carried out to assess validity and exibility of the whole pipeline.