PINN-based optimal control for parabolic systems

This paper proposes a novel framework that integrates physics-informed neural networks with deep deterministic policy gradient for the optimal control of partial differential equations. The proposed methodology enables the automatic tuning of control parameters by leveraging a closed-loop approach that combines physics-constrained learning with reinforcement learning. Specifically, the PINN is used to model the system dynamics, while DDPG is employed to optimize the control inputs. The effectiveness of the proposed framework is demonstrated through the numerical simulation of a parabolic PDE system, highlighting its capability to accurately solve the control problem while ensuring robust parameter optimization.