# Efficient Machine Learning-Based Prediction of Solar Irradiance Using Multi-Site Data
## 3 Results and Discussion
### Ensemble Learners in Different Stations  
Training ensemble learners is a key factor in many classes of problems in machine learning, especially those related to the energy domain, as proven in [29]. Thus, a particular \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Site** & **Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** & **Median AE** & \(\mathbf{D^{2}}\) \\ \hline \multirow{8}{*}{ULL} & MLP & 0.95 & 62.09 & 26.63 & 3.21 & 0.86 \\  & CatBoost & 0.95 & 63.93 & 26.99 & 2.77 & 0.86 \\  & GradientBoosting & 0.95 & 64.33 & 28.60 & 4.19 & 0.85 \\  & RandomForest & 0.95 & 64.68 & 26.64 & 1.42 & 0.86 \\  & ExtraTrees & 0.95 & 65.58 & 27.07 & 1.36 & 0.86 \\  & Decision Tree & 0.89 & 93.62 & 38.56 & 1.64 & 0.80 \\ \hline \multirow{8}{*}{HSU} & CatBoost & 0.97 & 45.87 & 18.94 & 1.56 & 0.88 \\  & GradientBoosting & 0.97 & 46.60 & 20.35 & 3.92 & 0.87 \\  & RandomForest & 0.97 & 46.61 & 18.97 & 1.17 & 0.88 \\  & ExtraTrees & 0.97 & 46.64 & 18.94 & 1.12 & 0.88 \\  & MLP & 0.97 & 47.22 & 21.13 & 3.29 & 0.87 \\  & Decision Tree & 0.93 & 66.30 & 26.95 & 1.67 & 0.83 \\ \hline \multirow{8}{*}{UNLV} & MLP & 0.98 & 42.82 & 15.46 & 1.92 & 0.93 \\  & CatBoost & 0.98 & 43.62 & 15.35 & 1.60 & 0.94 \\  & RandomForest & 0.98 & 43.66 & 14.67 & 0.81 & 0.94 \\  & GradientBoosting & 0.98 & 43.88 & 17.17 & 4.07 & 0.93 \\  & ExtraTrees & 0.98 & 43.98 & 14.67 & 0.77 & 0.94 \\  & Decision Tree & 0.96 & 60.30 & 20.23 & 1.07 & 0.91 \\ \hline \multirow{8}{*}{RAZON} & GradientBoosting & 0.89 & 103.98 & 30.93 & 6.35 & 0.84 \\  & RandomForest & 0.89 & 104.26 & 28.47 & 0.60 & 0.85 \\  & ExtraTrees & 0.88 & 106.78 & 28.94 & 0.59 & 0.85 \\  & MLP & 0.88 & 108.05 & 56.59 & 33.04 & 0.71 \\  & CatBoost & 0.87 & 115.36 & 30.37 & 2.73 & 0.84 \\  & Decision Tree & 0.82 & 131.79 & 38.42 & 0.67 & 0.80 \\ \hline \multirow{8}{*}{NWTC} & GradientBoosting & 0.99 & 71.26 & 34.00 & 11.85 & 0.89 \\  & Decision Tree & 0.99 & 95.11 & 38.07 & 1.77 & 0.87 \\ \cline{1-1}  & RandomForest & 0.99 & 96.66 & 29.62 & 1.80 & 0.90 \\ \cline{1-1}  & CatBoost & 0.99 & 107.49 & 32.93 & 5.14 & 0.89 \\ \cline{1-1}  & ExtraTrees & 0.98 & 126.01 & 31.28 & 1.74 & 0.90 \\ \cline{1-1}  & MLP & 0.97 & 149.92 & 103.40 & 64.56 & 0.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Model performance comparison across different stations. step was taken to combine the best learners in the first step of training to explore the possibility of building a powerful ensemble model that can be used across all stations. Table 7 depicts the obtained best combination in each station. Several combinations of tree-based models were tested using the Optuna framework (Appendix A), aiming to develop a robust model that can be generalized across all stations. Despite these efforts, it was observed that the best results for each station did not surpass those obtained with single models, as presented in Table 7 and Figure 11. However, what is particularly intriguing is the superiority of the stacking ensemble over other ensemble techniques, such as voting and bagging, across all stations, even when the composing learners differed. This finding suggests that a potential general model could benefit significantly from the stacking technique. Furthermore, it was observed that, for all stations, the GradientBoosting framework was essential for the composition of the models. Typically, this framework could be complemented with an MLP or a RandomForest model. This suggests that a stacking-based general model could leverage the strengths of these models, combined with other powerful techniques, to achieve optimal performance. The power of stacking lies in its ability to combine the predictions of multiple models, thereby improving accuracy and robustness. This ensemble method outperformed others by effectively capturing the strengths of its individual learners, indicating its potential to create a generalized high-performance model applicable to various stations. This assumption forced the expansion of the obtained results shown in Table 7 for a 30-min shift to verify the performance under a 1-h shift.