## 4 Simulations
### Reasonableness of Factor Importance Ranking Obtained by NC-RBF-DNN
This is because with current technology, the solar radiation-power output conversion efficiency of different panel models is similar; only their minimum operating radiation and maximum power output differ somewhat, and these do not have a significant impact on the overall prediction results. Finally, we look at the five factors with the lowest importance scores: _surface pressure, relative humidity at 1000 mbar, surface thermal rad down, two-meter temperature, total precipitation._ Generally, the relative humidity at 1000 mbar and the two-meter temperature are considered to provide redundant information in relation to surface solar radiation, such that the scores assigned by NC-RBF-DNN were lower. The other three factors only affect the power output of the solar panel under special circumstances and do not have a long-term impact on power output. Thus, it is not surprising that they were assigned the lowest importance scores. The second phenomenon that we observed in the solid line of Figure 10 was that, although the NC-RBF-DNN divided the 16 factors into four groups, the differences among the scores in each group were small and within error range. This shows that if methods from past studies [52,53] were to be directly applied to the target problem, using the ranking to select factors for modeling may not necessarily result in the optimal solution. For instance,  
Figure 10: Importance ranking of 16 factors obtained by NC-RBF-DNN and Pearson correlation. if we only needed eight factors for modeling, then pairing the first seven factors with the eighth or the ninth may both seem reasonable. In this case, the factor combination search algorithm becomes necessary to aid the algorithm in selecting the most suitable factors for modeling. The trends of the solid and dotted lines in Figure 10 revealed two phenomena. First, the scores for the top 12 factors of the solid line were similar to those of the dotted line. This provides strong evidence that NC-RBF-DNN succeeded in determining the importance of the input-output relationship. Second, among the bottom four factors identified by NC-RBF-DNN, the Pearson coefficients of relative humidity at 1000 mbar and 2 m temperature were unexpectedly very high, ranked third and fourth, respectively. The exclusion of a factor despite a high Pearson coefficient can be attributed to the fact that NC-RBF-DNN assigns lower importance scores to dimensions with redundant information, as mentioned previously. In the target dataset, the variation patterns of relative humidity at 1000 mbar and 2 m temperature were similar to those of surface solar radiation (see Figure 11), and NC-RBF-DNN prioritized the surface solar radiation variable that was most relevant to the output in constructing its model. These findings demonstrate that the NC-RBF-DNN can indeed give reasonable importance scores to the 16 factors of the target problem. We next discuss the quantitative reasonableness using Figures 12 and 13. Figure 12 presents the results of modeling using the first \(n\) factors (solid curve) and the last \(n\) factors (dashed curve) selected by the NC-RBF-DNN. For instance, the location of the solid curve where \(x\) equals 4 is the output error when the top four factors are used for modeling. The location of the dashed curve where \(x\) equals 3 is the output error when the 14 th, 15 th, and 16 th factors are used for modeling. Figure 12 is divided into two sub-graphs, respectively presenting the modeling results of the lightweight NC-RBF-DNN and a random forest. Both sub-graphs clearly show that whichever model is used, using the top factors for modeling will always be superior to using the last factors for modeling (the errors of the former are only about one-half of those of the latter). This means that most important factors identified by the NC-RBF-DNN are indeed more important than the least important factors, thus demonstrating the reasonableness of the NC-RBF-DNN designed in this study.