  In this paper we present an adaptive deep density approximation strategy
based on KRnet (ADDA-KR) for solving the steady-state Fokker-Planck (F-P)
equations. F-P equations are usually high-dimensional and defined on an
unbounded domain, which limits the application of traditional grid based
numerical methods. With the Knothe-Rosenblatt rearrangement, our newly proposed
flow-based generative model, called KRnet, provides a family of probability
density functions to serve as effective solution candidates for the
Fokker-Planck equations, which has a weaker dependence on dimensionality than
traditional computational approaches and can efficiently estimate general
high-dimensional density functions. To obtain effective stochastic collocation
points for the approximation of the F-P equation, we develop an adaptive
sampling procedure, where samples are generated iteratively using the
approximate density function at each iteration. We present a general framework
of ADDA-KR, validate its accuracy and demonstrate its efficiency with numerical
experiments.
