# Efficient Machine Learning-Based Prediction of Solar Irradiance Using Multi-Site Data
## 3 Results and Discussion
### Results from Each Station  
For each station, tree-based algorithms and ensemble learners were trained for the prediction of GHI, and then a thorough analysis of the importance of the characteristics considered by the top-performing model was conducted. Different combinations of standalone models were used in an ensemble framework and tested to gain insight into the collaborative performance and the possibility that it surpasses standalone models. 1. NELHA: This station is characterized by the presence of 19 features, of which several were found to be correlated with the target variable, as shown earlier. Moreover, a study was conducted on the correlations that can be found between features with the consideration of the past time shift. This is visualized in the correlation heatmap in Figure 8(a). The correlations exceed 90% for the shifted GHI values with the global PAR. In addition, the shifted HST values also demonstrate strong correlations, reaching 88%. This indicates that a possible construction of a feature model could enclose these shifted values. The results from the models trained on this station are depicted in Table 6. It can be seen that the best results are obtained when using the Gradient-Boosting regressor, achieving an \(R^{2}\) of 0.96 and an RMSE of 63.61, followed by the MLP and the RandomForest regressor. Overall, all the models performed well, except the decision tree. As for the residual analysis at the NELHA station in Figure 9(a), it indicates that the errors are centered around 0, predominantly ranging between \(-\)200 and 200. However, errors can occasionally reach values between \(-\)400 and 400. Points outside these intervals suggest the presence of outliers or potential overfitting of the model. 2. ULL: The correlation heatmap in Figure 8(b) and performance table in Table 6 provide a comprehensive view of the relationships between various time-shifted irradiance measurements and their impacts on model performance. The high correlation between ghi_t1_30 min and ghi_t2_30 min at 0.96 indicates a strong temporal autocorrelation, which is also reflected in the significant correlation of 0.91 with other features such as dni_t1_30 min (0.86) and ghi_t3_30 min. This suggests that GHI measurements are closely related to direct normal irradiance (DNI) over short time intervals. Furthermore, the moderate correlation between dni_t1_30 min and dhi_t1_30 min at 0.70 highlights the partial dependency between direct and diffuse horizontal irradiance (DHI). The models' performance metrics, with \(R^{2}\) values ranging from 0.89 to 0.95, demonstrate that models like the MLPRegressor and CatBoostRegressor can capture these intricate relationships effectively. The low RMSE and MAE values further underscore the models' accuracy in predicting irradiance values, with MLPRegressor showing the best overall performance. This indicates that leveraging these correlations can significantly enhance predictive modeling in solar irradiance forecasting. Residual analysis at the ULL station in Figure 10b demonstrates a generally good performance by the MLP regressor. The errors are centered around 0, with most falling within the range [\(-\)200, 200]. However, some data points exhibit errors reaching up to 600. 3. HSU: In this case, 12 features were considered, with those directly associated with GHI--namely, DNI, DHI, and GHI itself--being excluded. The remaining 12 features were retained due to their high correlation with the target variable, as presented in Figure 9c. The correlation heatmap observations highlight significant relationships among various features over 30 min intervals. Notably, the correlation between ghi_t-1_30 min and ghi_t2_30 min is high at 0.97, indicating strong temporal autocorrelation in GHI measurements. Moreover, ghi_t1_30 min shows strong correlations with CR510 Battery [VDC1_t1_30 min0.82 and ghi_t3_30 min at 0.92, suggesting consistent patterns in GHI over time.