Deep BSDE approach for high dimensional PDE problems

主讲人 Speaker:Mo Zhou (UCLA)
时间 Time:11:30-13:30, Nov. 9th, 2023
地点 Venue:Tencent Meeting ID: 677-1805-8331

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Solving high-dimensional problems is a challenging task, particularly in the realm of partial differential equations (PDEs). Neural networks have emerged as powerful tools for addressing such complexities. In this presentation, I will provide an overview of deep learning techniques commonly used to tackle PDE problems.

Specifically, I will delve into the innovative DeepBSDE method, presenting its theoretical foundations and detailing its application in two scenarios. The first application centers on solving the eigenvalue problem, creatively transformed into a fixed-point formulation reminiscent of a diffusion Monte Carlo approach. In the second application, we harness the actor-critic framework from reinforcement learning to address the Hamilton—Jacobi—Bellman (HJB) equation. To enhance the accuracy of our approach, we introduce a variance-reduced temporal difference method for the critic and implement an adaptive step size algorithm for the actor.

Short bio:

Mo Zhou (周默) is an assistant adjunct Professor at UCLA, where he conducts cutting-edge research at the intersection of optimal control, mean-field game problems and deep learning. Currently, he is in Prof. Stan Osher's and Prof. Hayden Schaeffer's research groups. Before joining UCLA, Mo earned his Ph.D. at Duke University, where he was mentored by Prof. Jianfeng Lu. Prior to that, he was an undergraduate at Tsinghua University.