Pi-DON: Physics-Informed Deep Operator Network for Control-Oriented Modeling of Thermal Systems in Cluster of Buildings

We propose a novel physics-informed Deep Operator Network (DON), termed Pi-DON, for modeling the thermal dynamics of building clusters. Unlike conventional approaches requiring extensive metadata or separate models per structure, Pi-DON learns a unified operator that solves the differential equations of resistance–capacitance (RC) models representing three single-zone buildings with two-state thermal dynamics, directly from simulated data.

This enables accurate predictions of indoor and envelope temperatures across varying thermal inertia. Moreover, Pi-DON provides rapid inference and enhanced sample efficiency, reducing the costly real-world interactions needed in model-free reinforcement learning (RL), making it well-suited for model-based control strategies such as model-predictive control (MPC) and model-based RL. Experimental results show Pi-DON learns the RC model’s solution operator with 99\% accuracy, outperforming both a purely data-driven DON and an LSTM-based deep neural network model.