  The recently proposed numerical algorithm, deep BSDE method, has shown
remarkable performance in solving high-dimensional forward-backward stochastic
differential equations (FBSDEs) and parabolic partial differential equations
(PDEs). This article lays a theoretical foundation for the deep BSDE method in
the general case of coupled FBSDEs. In particular, a posteriori error
estimation of the solution is provided and it is proved that the error
converges to zero given the universal approximation capability of neural
networks. Numerical results are presented to demonstrate the accuracy of the
analyzed algorithm in solving high-dimensional coupled FBSDEs.
