Approximation of Optimal Feedback Controls for Stochastic Reaction-Diffusion Equations

TL;DR

This paper develops a method to approximate optimal feedback controls for stochastic reaction-diffusion equations, providing theoretical error estimates and demonstrating neural network approximations with numerical examples.

Contribution

It introduces a new approximation framework with explicit error bounds for stochastic PDE control problems, including neural network applications.

Findings

Theoretical approximation results with explicit error estimates.

Neural network-based approximation of feedback controls.

Numerical examples illustrating the effectiveness of the approach.

Abstract

In this paper we present a method to approximate optimal feedback controls for stochastic reaction-diffusion equations. We derive two approximation results providing the theoretical foundation of our approach and allowing for explicit error estimates. The approximation of optimal feedback controls by neural networks is discussed as an explicit application of our method. Finally we provide a numerical examples to illustrate our findings.