## 6 Experiments and Results
### Combination of the Two Models  
Forecasting temperatures for both the laboratory and the inertia tank is possible by integrating the outputs of two models, using each prediction for the next time instant's temperature. This method relies on the set points for both systems and the exterior temperature, the latter being the only constraint. On the test set, the combined models achieve an R\({}_{avg}^{2}\) of 0.91 for the inertia tank, consistent with previous performance. The fan coil, however, shows an R\({}_{avg}^{2}\) of 0.37, worse than the standalone model. Examining individual test days reveals the highest errors occur on days with the greatest deviations. Excluding these two days improves the R\({}_{avg}^{2}\) to 0.79, confirming the model's robust performance on other days.  
Although this study does not primarily focus on energy consumption forecasting, such an analysis can be conducted by assuming constant power operation at 0.2 kW for the fan coil and 2 kW for the inertia tank. The operational status of the machines, as indicated by tendency variables, allows the determination of total energy consumption. Figures 17 and 18 illustrate the optimal forecast days within the combined model's test set, with blue shaded areas indicating periods of system operation.  
Figure 16: Best forecast temperatures of the inertia tank’s model. (**a**) Best R\({}^{2}\) of the best-performing model. (**b**) Second-best R\({}^{2}\) of the best-performing model.  
Figure 17: Best combined temperature forecasting of the laboratory and the inertia tank with the predicted consumption.  
[PERSON] et al. [47] focused on forecasting room temperature in HVAC systems by leveraging historical data to identify distinct operational scenarios using k-means clustering. These scenarios, representing different modes of operation (e.g., cooling or heating), are used to train separate temperature prediction models via symbolic regression. The methodology was tested in a lecture building in Suita, Osaka, Japan, using data collected at 5 min intervals over a year from multiple indoor and outdoor sensors. The best results achieved were an R\({}^{2}\) of 0.97 for the cooling phase and 0.73 for the heating phase.  
The study described in [47] closely resembles the system under investigation, with the primary difference being the absence of geothermal energy as a power source. Compared to this approach, our proposed methodology achieves superior accuracy in temperature forecasting for complex HVAC systems. While the clustering approach facilitates modeling through operational segmentation, it relies heavily on extensive datasets (over 232,576 data points) and may struggle to generalize in scenarios with limited data availability or unique configurations. In contrast, the proposed approach explicitly integrates domain knowledge, allowing the model to achieve R\({}^{2}\) values of 0.94 for the laboratory and 0.93 for the inertia tank even when using the combination of the two models, independently of the operational mode and with much less training data. The integration of physical principles enhances model reliability, ensuring the forecasts remain grounded in the underlying thermal dynamics. Moreover, the adaptability of our methodology makes it more reliable, demonstrating how it can handle complex HVAC systems and improve accuracy in real world scenarios