Asymptotic-preserving neural networks for multiscale Vlasov-Poisson-Fokker-Planck system in the high-field regime

TL;DR

This paper develops two asymptotic-preserving neural network methods within a physics-informed framework to efficiently solve the multiscale, high-dimensional Vlasov-Poisson-Fokker-Planck system in the high-field regime, ensuring correct asymptotic behavior.

Contribution

It introduces two novel APNN approaches that preserve asymptotic limits in solving the VPFP system, addressing high-dimensional and multiscale computational challenges.

Findings

Effective in multiscale, high-dimensional problems

Preserve asymptotic behavior from kinetic to limit models

Suitable for long-time and non-equilibrium simulations

Abstract

The Vlasov-Poisson-Fokker-Planck (VPFP) system is a fundamental model in plasma physics that describes the Brownian motion of a large ensemble of particles within a surrounding bath. Under the high-field scaling, both collision and field are dominant. This paper introduces two Asymptotic-Preserving Neural Network (APNN) methods within a physics-informed neural network (PINN) framework for solving the VPFP system in the high-field regime. These methods aim to overcome the computational challenges posed by high dimensionality and multiple scales of the system. The first APNN method leverages the micro-macro decomposition model of the original VPFP system, while the second is based on the mass conservation law. Both methods ensure that the loss function of the neural networks transitions naturally from the kinetic model to the high-field limit model, thereby preserving the correct asymptotic behavior. Through extensive numerical experiments, these APNN methods demonstrate their effectiveness in solving multiscale and high dimensional uncertain problems, as well as their broader applicability for problems with long time duration and non-equilibrium initial data.