  In this paper, we propose forward and backward stochastic differential
equations (FBSDEs) based deep neural network (DNN) learning algorithms for the
solution of high dimensional quasilinear parabolic partial differential
equations (PDEs). The algorithms relies on a learning process by minimizing the
path-wise difference of two discrete stochastic processes, which are defined by
the time discretization of the FBSDEs and the DNN representation of the PDE
solutions, respectively. The proposed algorithms demonstrate a convergence for
a 100-dimensional Black--Scholes--Barenblatt equation at a rate similar to that
of the Euler--Maruyama discretization of the FBSDEs.
