Controlled SPDEs: Peng’s Maximum Principle and Numerical Methods

SIAM Student Seminar
Friday, November 17, 2023 - 11:00am for 1 hour (actually 50 minutes)
Skiles 005
Lukas Wessels – Georgia Tech – lwessels3@gatech.edu
Biraj Dahal

In this talk, we consider a finite-horizon optimal control problem of stochastic reaction-diffusion equations. First, we apply the spike variation method which relies on introducing the first and second order adjoint state. We give a novel characterization of the second order adjoint state as the solution to a backward SPDE. Using this representation, we prove the maximum principle for controlled SPDEs.

In the second part, we present a numerical algorithm that allows the efficient approximation of optimal controls in the case of stochastic reaction-diffusion equations with additive noise by first reducing the problem to controls of feedback form and then approximating the feedback function using finitely based approximations. Numerical experiments using artificial neural networks as well as radial basis function networks illustrate the performance of our algorithm.

This talk is based on joint work with Wilhelm Stannat and Alexander Vogler. Talk will also be streamed: