Deep Reinforcement Learning implementation with Physics-Informed Neural Network for Heat Conduction Control

                                
==Abstract==

As modern systems become more complex, their control strategy can no longer solely rely on measurement data gathered by instrumentation. Instead, it must also incorporate information derived from mathematical models. The complexity of system models can result in excessively long computation times, making the control process impractical. As a solution, surrogate models are implemented to provide estimates within an acceptable timeframe for decision-making purposes. The surrogate model can be a Physics-Informed Neural Network that is used to obtain the system state on the next time step; such information can be used with a Deep Reinforcement Learning algorithm to train a control strategy based on simulations, replacing the need for running direct numerical simulations. On this work, we explore a Deep Q-Learning strategy on 1D heat conduction problem in which temperature distribution feeds a control system to activate a heat source, aiming to obtain a constant, previously defined temperature value. The main goal is to stabilize the bar temperature at the middle point of it without recurring to numerical simulations.