Numerical strategy for solving the Boltzmann equation with variable E/N using physics-informed neural networks

Abstract

A novel strategy to solve the Boltzmann equation with variable reduced electric field by using an artificial neural network (ANN) is introduced, where is the electric field and is the gas number density. In this method, the ANN learns the electron velocity distribution function (EVDF) for arbitrary in the Boltzmann equation. Thus, the ANN can calculate the EVDFs in the training range of without additional training. For validation of the ANN, the EVDFs in each Ar and SF6 gas were calculated with the trained ANN. The electron energy distribution function and electron transport coefficients calculated from the EVDF quantitatively agree with those from another ANN for a single and those from a Monte Carlo simulation, proving the validity of the present method.