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The Vlasov-Poisson-Fokker-Planck (VPFP) system is a fundamental model inplasma physics that describes the Brownian motion of a large ensemble ofparticles within a surrounding bath. Under the high-field scaling, bothcollision and field are dominant. This paper introduces twoAsymptotic-Preserving Neural Network (APNN) methods within a physics-informedneural network (PINN) framework for solving the VPFP system in the high-fieldregime. These methods aim to overcome the computational challenges posed byhigh dimensionality and multiple scales of the system. The first APNN methodleverages the micro-macro decomposition model of the original VPFP system,while the second is based on the mass conservation law. Both methods ensurethat the loss function of the neural networks transitions naturally from thekinetic model to the high-field limit model, thereby preserving the correctasymptotic behavior. Through extensive numerical experiments, these APNNmethods demonstrate their effectiveness in solving multiscale and highdimensional uncertain problems, as well as their broader applicability forproblems with long time duration and non-equilibrium initial data.

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