Before revision:  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.
After revision:  The algorithms relies on a learning process by minimizing the pathwise difference between two discrete stochastic processes, which are defined by the time discretization of the FBSDEs and the DNN representation of the PDE solutions, respectively.