Evaluation of a Hybrid Physical–LSTM Model for Air-to-Air Heat Pump Control: Insights from Multi-Day Closed-Loop Simulations in Mediterranean Climate

Air-to-air heat pumps are a key technology for improving energy efficiency and reducing carbon emissions in residential buildings, yet their optimal control remains challenging under real-world conditions. This study evaluates the performance of a hybrid physical–LSTM model for controlling an air-to-air heat pump in a residential building in Zadar, Croatia. The hybrid framework integrates a first-order energy balance model of the building envelope with LSTM-based temperature correction using adaptive weighting. The physical model was calibrated and validated against 52,128 real IoT measurements collected during the 2024/2025 heating season, achieving high accuracy (RMSE ≈ 0.076 °C). Rolling one-day and continuous multi-day closed-loop simulations (up to 15 days) show that the hybrid model yields slightly lower RMSE in long-term runs compared to the pure physical model. However, this apparent statistical improvement is accompanied by systematic underestimation of indoor temperature and significantly higher simulated energy consumption. The results indicate that the observed effect originates from an implicit virtual heat flux introduced by the LSTM correction, which affects thermodynamic consistency in closed-loop operation. The findings highlight that short-term error metrics such as RMSE alone are insufficient for evaluating hybrid models intended for model predictive control (MPC). The main contribution of this study is the explicit demonstration and quantification of an implicit virtual heat flux generated by the LSTM correction in closed-loop multi-day operation, which leads to misleading statistical improvements while causing significant thermodynamic inconsistency and energy overconsumption. In 15-day continuous simulations the hybrid model (ω = 0.05–0.10) caused an indoor temperature underestimation of 1.25–1.31 °C and increased simulated electricity consumption by more than 300% (316 kWh vs. 72 kWh) compared to the physical model. These results have direct implications for the development of reliable digital twins and model predictive control strategies in residential HVAC systems.