Comparing Traditional and Physics-Informed Neural Network Solvers for Electron Kinetics in Low-Temperature Plasma

Physics-informed neural networks (PINNs) have recently emerged as alternative methods for solving Partial Differential Equations. Using Pytorch, we have developed a deep neural network for solving kinetic equations for electrons in gas discharge plasma. The 1d2v Boltzmann equation and a Fokker-Planck kinetic equation for electron distribution function are solved using a PINN solver, a finite-volume solver with adaptive mesh in phase space (Basilisk), and a COMSOL finite element solver for comparison. We investigate the effects of network depth and the number of neurons on the accuracy and efficiency of the PINN solution. We also study the feasibility of hybrid solvers using asymptotic preserving schemes and stacked decomposition methods for two- and three-dimensional kinetic equations with a Lorentz model for elastic scattering and inelastic collisions of electrons with atoms.

This work was supported by the NSF project OIA-1655280.