Deep learning for solving the Boltzmann equation of electrons in weakly ionized plasma

A novel direct numerical method to calculate the electron velocity distribution function (EVDF) in hydrodynamic equilibrium under a uniform DC electric field is presented. In the present method, an artificial feedforward neural network learns the EVDF governed by both the Boltzmann equation and boundary conditions. The present method dost not require the expansion of the EVDF in the Legendre polynomials and the discretization of both the EVDF and the Boltzmann equation. As a benchmark, the EVDF in Reid's ramp model gas and Ar gas was calculated by the present method, and then the validity of the present method was demonstrated by comparing electron energy distributions and electron transport coefficients deduced from the EVDF with those calculated by Monte Carlo simulation.