Wenzhong Zhang: FBSDE based deep neural network methods for solving high-dimensional quasilinear parabolic PDEs

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.