A Study for Solving the Boltzmann Equation with Variable E/N using Physics-informed Neural Networks

In this study, we introduce a novel strategy to solve the Boltzmann equation with varying the reduced electric field E/N by using an artificial neural network (ANN), where E is the electric field and N is the gas number density. In the method, the ANN learns the electron velocity distribution function (EVDF) for a range of E/N in the Boltzmann equation. Thus, the ANN can calculate the EVDFs in the training range of E/N without additional training. The trained ANN was used to calculate the EVDFs in both Ar and SF6 gases for validating the ANN. The electron energy distribution function (EEDF), electron transport coefficients calculated from the EVDF quantitively agree with those from another ANN for a single E/N [1, 2]and those from a Monte Carlo simulation [3, 4], proving the validity of the present method.