Physics-Informed Neural Networks for Predicting Indoor Temperature and Cooling Demand in Historic Buildings

Buildings are complex assets, characterised by evolving uses, variable occupancies, and long-life cycles, which lead to high operational costs and significant energy demands. Globally, buildings are responsible for 30–40 % of greenhouse gas emissions, making accurate energy forecasting essential for reducing both economic and environmental impacts. Despite the growing adoption of Machine Learning (ML) methods, these approaches often require large datasets and struggle to maintain physical consistency, particularly in data-scarce contexts such as historic buildings, where energy efficiency measures must also comply with heritage constraints. To address these challenges, this study proposes a hybrid predictive framework based on Physics-Informed Neural Networks (PINNs), dynamic energy simulations, and energy balance constraints to forecast, 1 h ahead, the indoor operative temperature (To) and cooling electricity consumption (Eel,Cool) of a historic public building in southern Italy. The PINN operates in two stages: first predicting To,t+1 and then estimating Eel,Cool,t+1 by combining data-driven learning with thermodynamic principles. This approach reduces reliance on computationally expensive simulations, shortens prediction times, and provides physically consistent predictions. Results confirm the superiority of the PINN over conventional ML models, achieving an RMSE of 0.091 °C (CVRMSE = 0.34 %, MBE = 0.025 °C, and NMBE = 0.09 %) for To and 2.12 kWh (CVRMSE = 9.95 %, MBE = 0.04 kWh, and NMBE = 0.19 %) for Eel,Cool. Compared to MLP, Random Forest, and Linear Regression, the PINN reduced RMSE by 96.8 %, 96.7 %, and 98.6 % respectively for To, and by 26.1 %, 24.3 %, and 68.4 % for Eel,Cool. These findings highlight the potential of PINNs to bridge the gap between data scarcity and physical interpretability, enabling robust energy forecasting and comfort optimization in heritage contexts.