## 3 Artificial Neural Network Models
However, both models could be used, as they yielded similar results. On the other hand, significantly worse statistics were observed when using I\({}_{\rm BH}\) instead of I\({}_{\rm GH}\) with the two previously mentioned variables (\(\alpha\), Cc). It can be seen that the selected model (model 9) presented an R\({}^{2}\) of 99.59% with the training dataset, and of 99.61% with the test dataset, and similar values were obtained with the model that used k\({}_{\rm t}\) instead of I\({}_{\rm GH}\). Figure 4 shows the relationship between I\({}_{\rm UV}\) and I\({}_{\rm GH}\) based on the data considered in this study. Both the training and the test datasets showed similar distributions. Figure 5 also shows the relationship between solar height and ultraviolet radiation for both the training and test datasets. These figures are included because solar height will be a variable that will be part of the selected models, as can be seen in Table 3, while Figure 6 represents the ultraviolet radiation vs. cloud cover for both datasets. Figure 7 shows the values predicted with ANN model number 9, where the \"Output\" corresponds to the neural network outputs and \"Target\" to the experimental values for both training and test dataset results. \begin{table}
\begin{tabular}{l l c c c c c c} \hline \hline \multicolumn{3}{c}{**Model Number \& Variables**} & \multicolumn{2}{c}{**Training**} & \multicolumn{3}{c}{**Test**} \\ \hline \# & **Variables** & **nRMSE (\%)** & **nMBE (\%)** & **R\({}^{2}\) (\%)** & **nRMSE (\%)** & **nMBE (\%)** & **R\({}^{2}\) (\%)** \\ \hline
1 & **I\({}_{\rm GH}\)**, **k\({}_{\rm t}\)**, \(\alpha\), I\({}_{\rm BH}\), **D**, \(\varepsilon\), **T**, **Cc** & 3.82 & 0.00 & 99.68\% & 3.77 & \(-\)0.01 & 99.69\% \\
2 & **I\({}_{\rm GH}\)**, \(\alpha\), I\({}_{\rm BH}\), **D**, \(\varepsilon\), **T**, **Cc** & 3.87 & 0.00 & 99.67\% & 3.83 & \(-\)0.01 & 99.68\% \\
3 & **I\({}_{\rm GH}\)**, **I\({}_{\rm BH}\)**, **D**, \(\varepsilon\), **T**, **Cc** & 4.26 & \(-\)0.01 & 99.60\% & 4.21 & \(-\)0.01 & 99.62\% \\
4 & **I\({}_{\rm GH}\)**, \(\alpha\), D, \(\varepsilon\), **T**, **Cc** & 3.89 & 0.00 & 99.67\% & 3.86 & \(-\)0.02 & 99.68\% \\
5 & **I\({}_{\rm GH}\)**, \(\alpha\), \(\varepsilon\), **T**, **Cc** & 3.91 & \(-\)0.02 & 99.66\% & 3.88 & \(-\)0.03 & 99.67\% \\
6 & **I\({}_{\rm GH}\)**, \(\alpha\), T, **Cc** & 4.04 & 0.00 & 99.64\% & 4.01 & \(-\)0.01 & 99.65\% \\
7 & **I\({}_{\rm GH}\)**, \(\alpha\), \(\varepsilon\), **Cc** & 4.15 & 0.00 & 99.62\% & 4.09 & 0.00 & 99.64\% \\
8 & **I\({}_{\rm GH}\)**, \(\alpha\), **T** & 4.85 & 0.00 & 99.48\% & 4.82 & 0.04 & 99.49\% \\
9 & **I\({}_{\rm GH}\)**, \(\alpha\), **Cc** & 4.30 & 0.00 & 99.59\% & 4.24 & 0.00 & 99.61\% \\
10 & **I\({}_{\rm GH}\)**, \(\alpha\), **\(\varepsilon\)** & 4.71 & \(-\)0.01 & 99.51\% & 4.67 & 0.02 & 99.53\% \\
11 & **I\({}_{\rm GH}\)**, \(\alpha\) & 5.13 & 0.01 & 99.42\% & 5.09 & 0.07 & 99.44\% \\
12 & **I\({}_{\rm GH}\)** & 10.30 & 0.00 & 97.66\% & 10.29 & 0.19 & 97.70\% \\
13 & **k\({}_{\rm t}\)**, \(\alpha\), **Cc** & 4.36 & 0.00 & 99.58\% & 4.34 & 0.02 & 99.59\% \\
14 & **k\({}_{\rm t}\)**, \(\alpha\) & 5.13 & 0.00 & 99.42\% & 5.10 & 0.05 & 99.44\% \\
15 & **k\({}_{\rm t}\)** & 39.72 & \(-\)0.05 & 65.26\% & 40.08 & 0.58 & 65.14\% \\
16 & **I\({}_{\rm BH}\)**, \(\alpha\), **Cc** & 8.70 & \(-\)0.01 & 98.33\% & 8.55 & 0.08 & 98.41\% \\
17 & **I\({}_{\rm BH}\)**, \(\alpha\) & 11.94 & 0.00 & 96.86\% & 12.03 & \(-\)0.02 & 96.86\% \\
18 & **I\({}_{\rm BH}\)** & 45.45 & 0.00 & 54.50\% & 46.05 & 0.45 & 53.98\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of I\({}_{\rm UV}\) ANN models.