## 3 Results and Discussion
### Optimizing Thermal Load Predictions: Best Hybrid IFS-ML Models  
In pursuing accurate and efficient thermal load predictions for LEBs, integrating Integral Feature Selection (IFS) with machine learning (ML) models has emerged as a promising avenue. This section unveils the culmination of our research efforts--the identification and validation of the best-performing hybrid IFS-ML models. While traditional input variable  
Figure 9: A comparative analysis of ML models in predicting thermal loads within a hot climate (Marrakech City). selection (IVS) methods often provide only a single \"optimal\" combination of predictors, the IFS methodology systematically explores all possible combinations (in our case study there are \(2^{10}-1=1023\) possible combinations) to identify multiple high-performing feature subsets, ensuring robustness and generalizability. The primary objective of this section is to showcase the prowess of hybrid models in discerning the most influential predictors for robust heating and cooling load predictions. By strategically applying IFS to exhaustively search the predictor space and subsequently integrating these refined variables into the top-performing model obtained in the previous subsection, we aim to achieve a high accuracy yet interpretable modeling framework. The optimal combinations of predictors for heating and cooling loads across the three Moroccan climates are illustrated in Figures 10 and 11. Only the combinations achieving R\({}^{2}\geq 0.99\) were retained as optimal. In a Mediterranean climate (Meknes), 63 optimal combinations were found for heating load prediction. For the cold climate (Ifrane), there were 93 combinations, and for the semi-arid climate (Marrakech), 64 combinations were identified. Remarkably, the best combination across all climates included variables X1, X2, X6, and X7, indicating a core set of features critical to accurate load estimation. For cooling loads, 12 optimal combinations were identified for Meknes and Ifrane, and 11 for Marrakech. While Mediterranean and cold climates shared the same best combinations, the semi-arid climate slightly differed in its top-ranked set. Specifically, for Meknes and Ifrane, the best predictor combination included X2, X3, X4, X6, X7, X8, and X9, while for Marrakech it included X1, X2, X4, X6, X7, X8, and X9. A statistical validation of the top-ranked combinations was performed (Figures 12 and 13). The results show that the R\({}^{2}\) consistently exceeded 0.998, while MAPE and \(\sigma\) values were exceptionally low, confirming the reliability and superiority of the proposed approach compared to benchmarks in the literature. Figure 10: The best combinations of input for predicting heating loads. Figure 11: The best combinations of input for predicting cooling loads. Figure 12: A statistical examination of the best combinations of input for predicting heating loads. For heating load, the top-ranked combination was 955 for Meknes and Ifrane and 1001 for Marrakech, achieving R\({}^{2}\) = 0.998, MAPE = 0.284 kWh/m\({}^{2}\)/year, and \(\sigma\) = 1.115 kWh/m\({}^{2}\)/year. For cooling load, the best-performing combinations were 1013 for Meknes and Ifrane, and 1023 for Marrakech, with R\({}^{2}\) = 0.998, MAPE = 0.263 kWh/m\({}^{2}\)/year, and \(\sigma\) = 1.131 kWh/m\({}^{2}\)/year. Interestingly, the first-best combination for all climates includes X1, X2, X6, and X7. These findings affirm the effectiveness of the IFS-ML hybrid model in accurately identifying the most relevant variable combinations for thermal load prediction across diverse climates. Additionally, Figures 12 and 13 present a comprehensive statistical analysis of all optimal input combinations used for predicting heating and cooling thermal loads. The results highlight that the employed performance metrics--R\({}^{2}\), MAPE, and \(\sigma\)--consistently approach their ideal values (with R\({}^{2}\) nearing 1, and MAPE and \(\sigma\) approaching zero).