## 5 Results and Discussion
### Performance of Data-Driven Models under Study
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**AI Models**} & \multicolumn{5}{c}{**Training Stage**} \\ \cline{2-6}  & **IOA** & **SSE** & **MAE** & **SI** & **ADR** \\ \hline M5 MT & 0.9468 & 0.0612 & 0.0886 & 0.0974 & 1.0090 \\ GEP & 0.9244 & 0.0111 & 0.1056 & 0.1158 & 1.0039 \\ EPR & 0.9799 & 0.0030 & 0.0550 & 0.0599 & 1.0026 \\ MARS & 0.9468 & 0.0068 & 0.0826 & 0.1016 & 1.0068 \\ \hline \multicolumn{6}{c}{**Testing Stage**} \\ \cline{2-6}  & **IOA** & **SSE** & **MAE** & **SI** & **ADR** \\ \hline M5 MT & 0.9430 & 0.1323 & 0.0644 & 0.0644 & 0.9682 \\ GEP & 0.9084 & 0.2143 & 0.0893 & 0.0893 & 0.9621 \\ EPR & 0.8237 & 0.4124 & 0.1254 & 0.1988 & 0.9260 \\ MARS & 0.9506 & 0.1156 & 0.0912 & 0.1048 & 0.9476 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical performances of the AI models in the estimation of \(V_{H}^{*}\). Figure 5: Performance of AI models in the prediction of \(V_{H}^{*}\) for: (**a**) Training and (**b**) testing stage. (IOA = 0.9896, SSE = 0.0449, and MAE = 0.0644), and MARS (IOA = 0.9828, SSE = 0.0738, and MAE = 0.0870) stood at the second and third place in terms of precision level, respectively. Ultimately, EPR (i.e., Equation (A5)) provided \(V_{L}^{*}\) predictions with the lowest level of accuracy in terms of SSE (0.1322) and MAE (0.0944). SI values confirm an unconvincing performance associated with EPR (SI = 0.1502). ADR values indicated a very marginal under estimation (ADR < 1) for the GEP model. For the sake of qualitative comparisons, Figure 6 illustrates the comparison between predicted and observed values of \(V_{L}^{*}\). In the case of the training stage, Figure 6a shows very compromising efficiency with almost all predictions inside \(\pm\)25% error lines. In the case of the testing stage, the EPR model remarkably overpredicted with the observed value of \(V_{L}^{*}=4.52\) (Figure 6b). Table 4 shows statistical benchmarks associated with the training and testing phases for prediction of \(V_{R}^{*}\). In the training phase, statistical criteria demonstrated that the EPR-base relationship [Equation (A6)] predicted \(V_{R}^{*}\) values with the highest level of accuracy (i.e., IOA = 0.9913, SSE = 0.0345, and MAE = 0.1030) than those obtained by other AI models. Furthermore, SI values given by Table 4 indicate superiority of EPR model over other AI techniques. According to IOA, SSE, and SI criteria, the MARS-based formulation (Equation (A9)) placed second in precision (IOA = 0.9831, SSE = 0.0670, and SI = 0.103), followed by M5 MT (IOA = 0.9801, SSE = 0.0788, and SI = 0.1046) and GEP (IOA = 0.976, SSE = 0.0953, and SI = 0.0964). In addition to this, ADR values \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**AI Models**} & \multicolumn{6}{c}{**Training Stage**} \\ \cline{2-6}  & **IOA** & **SSE** & **MAE** & **SI** & **ADR** \\ \hline M5 MT & 0.9877 & 0.0387 & 0.0672 & 0.0772 & 1.0277 \\ GEP & 0.9680 & 0.1001 & 0.1027 & 0.1274 & 1.0242 \\ EPR & 0.9883 & 0.0369 & 0.0754 & 0.0771 & 1.0085 \\ MARS & 0.9950 & 0.0157 & 0.0374 & 0.0504 & 0.9993 \\ \hline \hline \multirow{2}{*}{**AI Models**} & \multicolumn{6}{c}{**Testing Stage**} \\ \cline{2-6}  & **IOA** & **SSE** & **MAE** & **SI** & **ADR** \\ \hline M5 MT & 0.9896 & 0.0449 & 0.0644 & 0.0481 & 1.0520 \\ GEP & 0.9911 & 0.0384 & 0.0544 & 0.0611 & 0.9987 \\ EPR & 0.9693 & 0.1322 & 0.0944 & 0.1052 & 1.0624 \\ MARS & 0.9828 & 0.0738 & 0.0870 & 0.0680 & 1.0729 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical performances of the AI models in the estimation of \(V_{L}^{*}\). Figure 6: Performance of AI models in the prediction of \(V_{L}^{*}\) for: (**a**) training and (**b**) testing stage. models had compromising performance with values of ADR roughly close to 1. These values are also indicative of very small overpredictions. The assessment of performance for the testing phase indicated that the MARS model (Equation (A9)) had the most accurate prediction in terms of IOA (0.9670), SSE (0.0855), and MAE (0.1086) in comparison to other AI models.