Qiu, JinniaoMolla, Md Hasib Uddin2020-09-112020-09-112020-09-10Molla, Md. H. U. (2020). Numerical approximations of coupled forward-backward SPDEs with applications (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.http://hdl.handle.net/1880/112515We 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.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Stochastic partial differential equationsdeep learningEducation--Mathematicsmaster thesis10.11575/PRISM/38185