  In kinetic equations, external fields play a significant role, particularly
when their strength is sufficient to balance collision effects, leading to the
so-called high-field regime. Two typical examples are the
Vlasov-Poisson-Fokker-Planck (VPFP) system in plasma physics and the Boltzmann
equation in semiconductor physics. In this paper, we propose a generic
asymptotic-preserving multiple-input DeepONet (AP-MIONet) method for solving
these two kinetic equations with variable parameters in the high-field regime.
Our method aims to tackle two major challenges in this regime: the additional
variable parameters introduced by electric fields, and the absence of an
explicit local equilibrium, which is a key component of asymptotic-preserving
(AP) schemes. We leverage the multiple-input DeepONet (MIONet) architecture to
accommodate additional parameters, and formulate the AP loss function by
incorporating both the mass conservation law and the original kinetic system.
This strategy can avoid reliance on the explicit local equilibrium, preserve
the mass and adapt to non-equilibrium states. We demonstrate the effectiveness
and efficiency of the proposed method through extensive numerical examples.
