## 5 Results and Discussion
### Driving Physical Meaning of AI Results
#### 5.3.3 Effects of \(e/D\) and \(Kc\) on \(V_{L}^{*}\)  
Figure 11a-d shows the variations of \(V_{L}^{*}\) against \(e/D\) at given values of \(KC\), and for \(\alpha=0^{\circ}\), according to AI models. All AI models exhibit a downward trend when interpreting the variations of \(V_{L}^{*}\) with \(e/D\) increasing from 0.1 to 0.4. For example, M5 MT simulates that \(V_{L}^{*}\) decreases linearly with increasing \(e/D\), as shown in Figure 11a. In addition, for a constant value of \(e/D\), \(V_{L}^{*}\) increases with increasing \(KC\), with a tendency towards an asymptotic value. For example, \(V_{L}^{*}\) increases sharply from 2.776 for \(KC=8.7\) to 4.482 for \(KC=18\), at \(e/D=0.2\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**AI Models**} & \multicolumn{3}{c}{**SSE Values for \(e/D\) Varying**} \\ \cline{2-4}  & **KC=8.7** & **KC=15.8** & **KC=18.0** \\ \hline M5 MT & 0.0388 & 0.2038 & 0.0271 \\ GEP & 0.0622 & 0.2602 & 0.0827 \\ MARS & 0.0483 & 0.0844 & 0.1490 \\ EPR & 0.0168 & 0.0132 & 0.0969 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**AI Models**} & \multicolumn{3}{c}{**SSE Values for \(KC\) Varying**} \\ \cline{2-4}  & _e/D=0.1_ & _e/D=0.2_ & _e/D=0.3_ & _e/D=0.4_ \\ \hline M5 MT & 0.0480 & 0.0948 & 0.0244 & 0.1924 \\ GEP & 0.0349 & 0.1298 & 0.0416 & 0.3338 \\ MARS & 0.0629 & 0.1662 & 0.0544 & 0.0920 \\ EPR & 0.0355 & 0.0106 & 0.0035 & 0.1197 \\ \hline \hline \end{tabular}
\end{table}
Table 6: SSE values for the considered AI models when predicting \(V_{R}^{*}\) at various \(e/D\) ratios and \(KC\) values.  
Analogously, Figure 12a-d shows the variations of \(V_{L}^{*}\) against \(KC\) at given values of \(e/D\), according to AI models. All AI models exhibit an upward trend when interpreting the variations of \(V_{L}^{*}\) with \(KC\) increasing from 8.7 to 18. For example, GEP simulates that \(V_{L}^{*}\) increases from 2.83 for \(KC=8.7\) to 4.207 for \(KC=18\), at \(e/D=0.1\). However, in general, the trend is not linear but approximately asymptotic. In addition, for a constant value of \(KC\), \(V_{L}^{*}\) decreases with \(e/D\) increasing. For example, \(V_{L}^{*}\) plummets from 4.168 for \(e/D=0.1\) to 3.047 for \(e/D=0.4\), at \(KC=15.8\), as shown in Figure 12b.  
According to Table 7, the GEP model had the best performance (SSE = 0.0502) at \(KC=8.7\) while all other AI models indicated the most accurate prediction of \(V_{L}^{*}\) values for \(KC=18\). The EPR technique predicted variations of \(V_{L}^{*}\) versus \(e/D\) with highly satisfying performance at \(KC=15.8\) (SSE = 0.0494) and \(KC=18\) (SSE = 0.0272). Table 7 also indicates that M5 MT (SSE = 0.0658), EPR (SSE = 0.0207), and GEP (SSE = 0.0188) had the most favorable performance at \(e/D=0.3\) while MARS (SSE = 0.00633) stood at the highest level of efficiency at \(e/D=0.4\). EPR model indicated more successful efficiency for \(e/D=0.1\) (SSE = 0.0720) and \(e/D=0.2\) (SSE = 0.0617) than the remaining AI models. What is more, GEP raised the most well-matched predictions for the variations of \(V_{L}^{*}\) versus \(KC\) with SSE = 0.0188 at \(e/D=0.2\), while EPR had the best performance (SSE = 0.00633) at \(e/D=0.4\).  
Figure 12: Variations of \(V_{L}^{*}\) against \(KC\) at \(e/D\) from 0.1 to 0.4 and \(\alpha=0^{\circ}\) for: (**a**) M5 MT, (**b**) GEP, (**c**) EPR, and (**d**) MARS.