## 5 Results and Discussion
### Driving Physical Meaning of AI Results
#### 5.3.1 Effects of \(e/D\) on \(V_{H}^{*}\)  
Figure 8 illustrates the variations of \(V_{H}^{*}\) as a function of \(e/D\). In fact, this type of variation was assessed for all the considered AI models at various levels of \(KC\) and \(\alpha\).  
Figure 8a shows that the experimental values of \(V_{H}^{*}\), for \(KC=8.7\) and \(\alpha=0^{\circ}\) increase from 2.77 at \(e/D=0.1\) to 3.81 at \(e/D=0.2\) and then descend towards 1.51 at \(e/D=0.4\). This non-monotonic trend is well captured by the MARS model, the results of which are more in harmony with the observations in comparison to the remaining models. All the AI models show underprediction at \(e/D=0.2\). Quantitatively, the EPR model exhibits significant underprediction with SSE = 0.843 in comparison to GEP (SSE = 0.435), MSMT (SSE = 0.300), and MARS (SSE = 0.161). According to Figure 8b, all the AI models were in satisfying agreement with the observations in the case of \(KC=15.8\) and \(\alpha=0^{\circ}\). Generally, AI models predict a linear downward trend between \(V_{H}^{*}\) and \(e/D\), as observed experimentally. Similarly, Figure 8c, which relates to the case of \(KC=18.0\) and \(\alpha=0^{\circ}\), shows an even more pronounced linear decreasing trend between \(V_{H}^{*}\) and \(e/D\), quite well captured by all the AI models. EPR had the most satisfying performance (SSE = 0.018), while the GEP model showed a significant overprediction at \(e/D=0.4\). Figure 8d, which relates to the case \(KC=15.8\) and \(\alpha=30^{\circ}\), exhibiting more alleviated values of \(V_{H}^{*}\) when compared to those in Figure 8b. This is due to the higher value of \(\alpha\) (equal to \(30^{\circ}\) here while equal to \(0^{\circ}\) in Figure 8b); it remains the observed downward trend between \(V_{H}^{*}\) and \(e/D\). Moreover, in this case, the considered AI models perform satisfactorily by assessing the effect of the angle \(\alpha\) properly, though the MARS model appears more resilient for \(e/D\) from 0.1 to 0.2. Moreover, MARS and GEP models indicated marginal underestimations at \(e/D=0.1\) and 0.4. More specifically, EPR with SSE of 0.003 shows the most compromising efficiency compared to M5 MT (SSE = 0.011), GEP (SSE = 0.0468), and MARS (SSE = 0.0631). Figure 8e, which relates to the case \(KC=18.0\) and \(\alpha=30^{\circ}\), clearly shows the effect of the angle \(\alpha\) when compared to Figure 8c, while it is less significant in realizing the effect of \(KC\) when compared to Figure 8d (on the other hand, \(KC\) in Figure 8d is equal to 15.8 and slightly differs from \(KC=18.0\) in Figure 8e). It is confirmed that \(V_{H}^{*}\) decreases with increasing \(\alpha\) as well as decreasing with increasing normalized embedment depth \(e/D\) (especially for the highest values of \(KC\)). AI models are still in harmony with these observed trends. Quantitatively, EPR with an SSE of 0.028 had the most compromising efficiency compared to MSMT (SSE = 0.031), MARS (SSE = 0.040), and GEP (SSE = 0.054). Further effects of the wave angle of attack \(\alpha\) on \(V_{H}^{*}\) are highlighted in Figure 8g, which relates to the case \(KC=15.8\) and \(\alpha=45^{\circ}\), when Figure 8b,d is considered for comparison. In this analysis, significant underpredictions were found for the MARS model (SSE = 0.054) at \(e/D=0.1\) and for GEP (SSE = 0.035) and MARS (SSE = 0.054) at \(e/D=0.4\). For the sake of completeness, Table 5 below shows the performance index SSE for all AI models by varying the normalized embedment depth \(e/D\). Overall, it appears that the M5 MT model had the best performance compared to the other AI models, though it is not always quite so straightforward.