Model‐based reinforcement learning control of reaction‐diffusion problems

Abstract

Mathematical and computational tools have proven to be reliable in decision‐making processes. In recent times, in particular, machine learning‐based methods are becoming increasingly popular as advanced support tools. When dealing with control problems, reinforcement learning has been applied to decision‐making in several applications, most notably in games. The success of these methods in finding solutions to complex problems motivates the exploration of new areas where they can be employed to overcome current difficulties. In this article, we explore the use of automatic control strategies to initial boundary value problems in thermal and disease transport. Specifically, in this work, we adapt an existing reinforcement learning algorithm using a stochastic policy gradient method and we introduce two novel reward functions to drive the flow of the transported field. The new model‐based framework exploits the interactions between a reaction‐diffusion model and the modified agent. The results show that certain controls can be implemented successfully in these applications, although model simplifications had to be assumed.