  In this paper we present a novel adaptive deep density approximation strategy
based on KRnet (ADDA-KR) for solving the steady-state Fokker-Planck equation.
It is known that this equation typically has high-dimensional spatial variables
posed on unbounded domains, which limit 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 of the
Fokker-Planck equation, which have weaker dependence on dimensionality than
traditional computational approaches. To result in effective stochastic
collocation points for training KRnet, we develop an adaptive sampling
procedure, where samples are generated iteratively using KRnet at each
iteration. In addition, we give a detailed discussion of KRnet and show that it
can efficiently estimate general high-dimensional density functions. We present
a general mathematical framework of ADDA-KR, validate its accuracy and
demonstrate its efficiency with numerical experiments.
