Physics-Informed Sparse Gaussian Processes for Model Predictive Control in Building Energy Systems

Efficient energy management in building energy systems (BES) is essential for reducing energy consumption while maintaining thermal comfort. One effective approach is Model Predictive Control (MPC), which optimizes control actions based on a model of the building; however, deriving such models can be costly and time-consuming. This paper combines Gaussian Processes (GP) with parametric mean functions which can be viewed as Physics Informed Gaussian Processes (PIGP). The PIGP is evaluated against other approaches to identify the thermal dynamics of BES, showing that the PIGP provides the best predictive accuracy. Furthermore, these models are integrated into a nonlinear MPC to compare energy demand and constraint violations in a sample BES, with simulations indicating that the PIGP results in lower energy demand.