Physics-informed neural networks for solving the Boltzmann equation of the electron velocity distribution function in weakly ionized plasmas

Abstract

The equilibrium electron velocity distribution function (EVDF) and electron transport coefficient in weakly ionized plasmas under crossed DC uniform electric and magnetic fields are calculated via the Boltzmann equation (BE) using physics-informed neural networks (PINNs). The latent solution of the BE is represented by an artificial neural network, and then the neural network is trained to respect the BE. By leveraging automatic differentiation, no mesh generation in velocity space is required, allowing us to calculate the three-dimensional EVDF properly with 0.01% of memory capacity required for the conventional mesh-based method. The EVDF and electron transport coefficients in SF6 calculated from the PINNs are benchmarked by comparing with those calculated from the Monte Carlo simulation (MCS). In most cases, the relative difference between the electron transport coefficient calculated from the PINNs and MCS is found to be within 1%.