Abstract
Physics-Informed Neural Networks (PINNs) offer a promising approach for integrating first-principles modeling with data-driven methods, especially in dynamic thermal systems. This study introduces a hybrid PINN framework for a one-dimensional heating rod governed by heat trans-fer equations. Unlike traditional PINNs that rely on time-dependent automatic differentiation, this approach employs numerical derivatives to bypass gradient saturation and enhance robustness. The proposed model demonstrates accurate extrapolation and generalization with limited train-ing data and is effectively used as a surrogate in a Model Predictive Control (MPC) framework for rod-tip temperature regulation. Additionally, a plan is outlined to apply physics-informed dimen-sionality reduction and model order reduction to improve computational efficiency and enable real-time application. The findings affirm PINNs' potential as control-oriented reduced models for thermal processes.