## 2 Materials and Methods
### First Scenario: Relative Energy Dissipation  
In the first scenario, a total of seven different combinations was used. The dimensionless parameters were \(Fr_{0}\), D/H and \(y_{c}\)/H. These parameters were entered into the support vector machine in the form presented in Table 4, the results of which are presented in Table 5. The combination with the smallest RMSE and the highest coefficient of determination was optimal. According to Figure 4, the results obtained from SVM show that in the first scenario, combination number 3 with input parameter \(Fr_{0}\) had the lowest RMSE, and the highest coefficient of determination and Kling-Gupta value. These values were 0.00565, 0.991 and 0.998, respectively for the training mode. The corresponding results for the testing mode were 0.00489, 0.996 and 0.991, respectively. These settings were selected as the best combination for predicting energy dissipation. To improve visibility, values of RMSE have been multiplied by 100 in the figure. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Input Parameters** & **Model** & **Input Parameters** \\ \hline \multicolumn{5}{c}{First scenario: Relative Energy Dissipation (\(\Delta E/E_{0}\))} \\ Model 1 & D/H & Model 5 & \(\text{Fr}_{0}\), \(\text{y}_{\text{c}}/\text{H}\) \\ Model 2 & \(\text{y}_{\text{c}}/\text{H}\) & Model 6 & \(\text{Fr}_{0}\), D/H \\ Model 3 & \(\text{Fr}_{0}\) & Model 7 & \(\text{Fr}_{0}\), D/H, \(\text{y}_{\text{c}}/\text{H}\) \\ Model 4 & \(\text{D}/\text{H},\text{y}_{\text{c}}/\text{H}\) & \\ \hline \multicolumn{5}{c}{Second scenario: Relative Pool Depth (\(y_{p}\)/H)} \\ Model 1 & D/H & Model 3 & \(\text{D}/\text{H},\text{y}_{\text{c}}/\text{H}\) \\ Model 2 & \(\text{y}_{\text{c}}/\text{H}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Different input combinations applied in the present study. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \begin{tabular}{c} **Criteria** \\ **Evaluation** \\ \end{tabular} & **60–40\%** & **70–30\%** & **75–25\%** & **80–20\%** \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} First scenario \\ (\(\Delta E/E_{0}\)) \\ \end{tabular} } & RMSE & 0.0429 & 0.0386 & 0.0243 & 0.0395 \\ \cline{2-6}  & R\({}^{2}\) & 0.942 & 0.961 & 0.963 & 0.952 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Second scenario \\ (\(y_{p}\)/H) \\ \end{tabular} } & RMSE & 0.0531 & 0.0461 & 0.0328 & 0.0584 \\ \cline{2-6}  & R\({}^{2}\) & 0.952 & 0.966 & 0.972 & 0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Criteria for evaluating different percentages of training and testing in general (training-testing). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \begin{tabular}{c} **Training** \\ **Training** \\ \end{tabular}  & \multicolumn{4}{c}{**Testing**} \\ \hline
**Model** & **R\({}^{2}\)** & **RMSE \(\times\) 100** & **KGE** & **R\({}^{2}\)** & **RMSE \(\times\) 100** & **KGE** & \(\gamma\) \\ \hline Model 1 & 0.863 & 5.88 & 0.965 & 0.895 & 6.81 & 0.955 & 5 \\ Model 2 & 0.994 & 0.614 & 0.99 & 0.997 & 0.583 & 0.988 & 8 \\ Model 3 & 0.991 & 0.565 & 0.998 & 0.996 & 0.489 & 0.991 & 5 \\ Model 4 & 0.986 & 0.721 & 0.9 Figure 4: Variation of RMSE and R\({}^{2}\) vs. Gamma values for best model in the first scenario; (**a**) training, (**b**) testing. First Scenario SVM Results  
Figure 5 shows the experimental and predicted data for the best model in the first scenario. Figure 5 shows the measured and predicted results for the best composition in the first scenario for the training phase. It was inferred from the figure that the laboratory data were less dispersed than the predicted data, which means that the output data from the SVM were very well matched with a maximum relative error of \(\pm\)1.67%. Figure 5 compares the laboratory data with the predicted results obtained from the best model in the training phase. The figure shows that there was a very good correlation in this scenario between the laboratory data and the predicted energy consumption.