Jiequn Han est instructeur en mathématiques à l'université de Princeton. Il est actuellement de passage en France en tant qu'invité de l'Inria.
Titre : Deep Learning-Based Numerical Methods for High-Dimensional Parabolic PDEs and Forward-Backward SDEs.
Résumé : Developing algorithms for solving high-dimensional partial differential equations (PDEs) and forward-backward stochastic differential equations (FBSDEs) 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", to solve general high-dimensional parabolic PDEs and FBSDEs. Starting from the BSDE formulation, we approximate the unknown $Z$ component by neural networks and design a least squares objective function based on the terminal condition to optimize parameters. Numerical results of a variety of examples 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.