Events for 04/19/2021 from all calendars

Industrial and Applied Math

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Yufei Zhang, University of Oxford

Title: Deep Neural Networks for High-Dimensional PDEs in Stochastic Control and Games

Abstract: In this talk, we discuss the feasibility of algorithms based on deep artificial neural networks (DNN) for the solution of high-dimensional PDEs, such as those arising from stochastic control and games. In the first part, we show that in certain cases, DNNs can break the curse of dimensionality in representing high-dimensional value functions of stochastic control problems. We then exploit policy iteration to reduce the nonlinear PDEs into a sequence of linear PDEs, which are then further approximated via a multilayer feedforward neural network ansatz. We establish that in suitable settings the numerical solutions and their derivatives converge globally, and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration. Moreover, we construct the optimal feedback controls based on the superlinear convergence of the numerical solutions. Numerical experiments are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method. This is joint work with Christoph Reisinger and Kazufumi Ito.

Panel Discussion: Grant Writing

Time: 4:00PM - 5:00PM

Location: Zoom