  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.
