# Efficient Machine Learning-Based Prediction of Solar Irradiance Using Multi-Site Data
## 3 Results and Discussion
### Results from Each Station
This analysis underscores the critical role of temporal shifts in understanding irradiance patterns and their predictive modeling. The performance analysis in Table 6 reveals that the GradientBoostingRegressor and RandomForestRegressor models exhibit the highest \(R^{2}\) values (0.8903 and 0.8897, respectively), indicating strong predictive accuracy. RandomForestRegressor slightly outperforms the other models in terms of MAE, with a value of 28.47 compared to GradientBoostingRegressor's 30.93, suggesting it has lower average prediction errors. ExtraTreesRegressor shows similar performance to RandomForestRegressor but with slightly higher RMSE and MAE. MLPRegressor has a significantly higher MAE (56.59) and RMSE (108.05), indicating poorer performance. CatBoostRegressor also performs well, though not as effectively as GradientBoosting or RandomForest, with an \(R^{2}\) of 0.8650 and higher RMSE and MAE. DecisionTreeRegressor shows the lowest performance, with the lowest \(R^{2}\) of 0.8238 and the highest RMSE of 131.79, indicating higher prediction errors and less accuracy compared to the other models. In this comparison, RandomForestRegressor and GradientBoostingRegressor are the most effective models. 6. NWTC: The NWTC station is characterized by the presence of more than 20 features, from the ambient to the operating conditions and the GHI, DHI, and DNI values. In this station, as shown in Figure 9f, all features exhibit a strong correlation with values shifted by 30 min, except for the monthly series, which displays weak correlations. This is expected, given that the PACF and ACF functions are designed to capture dependencies in lagged values up to 30 min. The model's performance, shown in Table 6, reveals that GradientBoosting stands out, with the highest \(R^{2}\) value of 0.9942, demonstrating superior predictive accuracy and the best fit to the data. It also has the lowest RMSE of 71.26 and a low MAE of 34.00, indicating minimal average prediction errors and superior precision. In contrast, the MLP, with the lowest \(R^{2}\) of 0.9744 and the highest RMSE of 149.92, shows the weakest performance, reflecting higher prediction errors and less accuracy. RandomForest and CatBoost also perform well, with high \(R^{2}\) values of 0.9893 and 0.9868, respectively, and relatively low error metrics, though slightly less favorable than GradientBoosting. Notably, ExtraTrees exhibits higher errors compared to these top models, while DecisionTree, though strong, has a slightly higher RMSE and MAE than the top performers. Residual analysis at the NWTC station in Figure 10d demonstrates generally good performance by the GradientBoosting regressor. The errors are centered around 0, with most falling within the range [\(-\)250, 25]. However, some data points exhibit errors reaching up to 982. Figure 9: Time-shifted correlated features for (**a**) NELHA, (**b**) ULL, (**c**) HSU, (**d**) UNLV, (**e**) RAZON, and (**f**) NWTC. Figure 10: Residual analysis for the different stations: (**a**) NELHA, (**b**) ULL, (**c**) HSU, and (**d**) NWTC. It is important to highlight that for the training set consisting of 10,000 samples, selected to maintain a balanced trade-off between model performance and computational complexity, the standalone regressors (including RandomForest, XGBoost, CatBoost, and MLP) required on average approximately 0.6 s to complete training. This corresponds to roughly \(6\times 10^{-5}\) seconds per sample, illustrating the high efficiency of these models in both the training and inference phases. Moreover, the models demonstrated rapid convergence on the testing set due to the adopted feature engineering strategy. In particular, when using only lagged GHI features, specifically the current and one-prior time step, the decision-making process becomes significantly simplified. This reduction in input dimensionality enables the models to focus on the most temporally relevant information, minimizing redundancy while preserving forecasting accuracy.