  In this paper, we present a deep learning-based numerical method for
approximating high dimensional stochastic partial differential equations
(SPDEs). At each time step, our method relies on a predictor-corrector
procedure. More precisely, we decompose the original SPDE into a degenerate
SPDE and a deterministic PDE. Then in the prediction step, we solve the
degenerate SPDE with the Euler scheme, while in the correction step we solve
the second-order deterministic PDE by deep neural networks via its equivalent
backward stochastic differential equation (BSDE). Under standard assumptions,
error estimates and the rate of convergence of the proposed algorithm are
presented. The efficiency and accuracy of the proposed algorithm are
illustrated by numerical examples.
