Development of grid-based and PINN solvers for electron kinetics in collisional non-thermal plasmas

Abstract

We compare traditional finite volume and Physics Informed Neural Network (PINN) solvers for elliptic (Poisson), hyperbolic (advection), and parabolic (diffusion) equations in 2d settings. We describe the challenges of using traditional and PINN solvers for electron kinetic equations in collisional plasmas. The advantages and drawbacks of PINNs over state-of-the-art traditional solvers are discussed. We also consider angular moments in spherical velocity space and the potential use of ML algorithms for reduced kinetic models in the coordinate-energy phase space based on adaptive closure relations.