Deep BSDE: A Unified Framework for Solving High-Dimensional PDEs, FBSDEs, and Control Problems
Date/Time:03 Jan 2020 16:00Venue: S17 #04-06 SR1Speaker: HAN Jiequn, Princeton UniversityDeep BSDE: A Unified Framework for Solving High-Dimensional PDEs, FBSDEs, and Control ProblemsDeveloping algorithms for solving high-dimensional partial differential equations (PDEs), forward-backward stochastic differential equations (FBSDEs), and control problems has been an exceedingly difficult task for a long time, due to the notorious difficulty known as the curse of dimensionality. In this talk we introduce the “deep BSDE method” as a unified framework to solve general high-dimensional PDEs and FBSDEs. Starting from the BSDE formulation, we approximate the unknown component by neural networks and design a proper loss function to optimize parameters. Numerical results of a variety of examples, including applications in game theory and eigenvalue problem, demonstrate that the proposed algorithm is quite effective in high- dimensions, in terms of both accuracy and speed. We furthermore provide a theoretical error analysis to illustrate the validity and property of the objective function.Add to calendar:
