Open AccessA neural network closure for the Euler-Poisson system based on kinetic simulations
Author(s) -
L éo Bois,
Emmanuel Franck,
Laurent Navoret,
Vincent Vigon
Publication year - 2022
Publication title -
kinetic and related models
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.987
H-Index - 28
eISSN - 1937-5093
pISSN - 1937-5077
DOI - 10.3934/krm.2021044
Subject(s) - closure (psychology) , artificial neural network , kinetic energy , knudsen number , range (aeronautics) , poisson distribution , computer science , euler equations , euler's formula , statistical physics , mathematics , physics , algorithm , mechanics , mathematical analysis , classical mechanics , artificial intelligence , materials science , statistics , economics , market economy , composite material
This work deals with the modeling of plasmas, which are ionized gases. Thanks to machine learning, we construct a closure for the one-dimensional 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.