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

TL;DR

This paper compares traditional finite volume and PINN solvers for various PDEs and discusses their application to electron kinetics in collisional plasmas, highlighting advantages, challenges, and potential ML-based reductions.

Contribution

It introduces a comparative analysis of finite volume and PINN methods for plasma electron kinetics and explores ML-based reduced models in phase space.

Findings

PINNs show promise but have specific challenges compared to traditional solvers.

Discussion of angular moments and ML algorithms for reduced kinetic modeling.

Potential for adaptive closure relations in phase space modeling.

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.