Numerical approximations of coupled forward-backward SPDEs with applications
We introduce a new scheme combining the finite element method and machine learning techniques for the numerical approximations of coupled forward-backward stochastic partial differential equations (FBSPDEs) with homogeneous Dirichlet boundary conditions. For the FBSPDE, the finite element method in the spatial domain leads to approximations by finite-dimensional forward-backward stochastic differential equations (FBSDEs) in the temporal domain. We then approximate the solution of FBSDE by some existing machine learning schemes. Strong convergence results for spatial discretization of FBSPDEs are addressed.
Stochastic partial differential equations, deep learning
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