## 6 Conclusions  
This study aimed to explore 3D scouring patterns around subsea pipelines under wave-only conditions. To this purpose, the experimental work by [PERSON] et al. [9] was considered. Experimental data were collected in a wave flume 50 m long, 4 m wide, and 2.5 m deep. A total of 60 wave-only tests were considered, though some of these tests (i.e., 22 tests) have proved to be of no use. An almost uniform siliceous sand with \(d_{50}\) equal to 0.37 mm and specific gravity of 2.70 was used for the mobile bed. Experiments were conducted under live-bed conditions with the Shields' parameter \(\theta_{w}\) ranging from 0.18 to 0.30, the Keulegan-Carpenter number \(KC\) from 8.7 to 18.0, the initial pipeline embedment depth, \(e\), from 0.1\(D\) to 0.5\(D\), and the flow incident angle, \(\alpha\), relative to the pipeline varying from 0\({}^{\circ}\) to 45\({}^{\circ}\). Four robust data-driven models were applied to predict the 3D scour propagation around undersea pipelines, namely Gene-Expression Programming (GEP), Evolutionary Polynomial Regression (EPR), Multivariate Adaptive Regression Spline (MARS), and M5 Model Tree (M5 MT). Generally, the following conclusions can be drawn from the current investigation:  
1. The considered predictive methodologies indicated two main potentialities: (i) Providing non-linear regression equations with a high degree of complexity (as naturally seen in the scouring process around submarine pipelines) when developed by a limit volume of datasets; (ii) selecting the effective variables (i.e., \(e/D\), \(KC\), \(\alpha\), \(\theta_{w}\)) on the scour rates estimation under a full automated manner. 2. All AI models applied in this study provided explicit relationships with satisfying performance for the prediction of 3D scour rates. However, the performance indices in the training and testing phases overall revealed that the MARS technique is most the eligible one. Therefore, the scour Equations (A7)-(A9), given in Appendix B, associated with the Basis Functions (BFs) explicitly stated in Table 10, are recommended in the prediction of \(V_{H}^{*}\), \(V_{L}^{*}\), and \(V_{R}^{*}\), respectively. 3. The physical consistency of the AI models was controlled by analyzing 3D scour propagation rates versus the normalized embedment depth \(e/D\), the flow incident angle \(\alpha\), and Keulegan-Carpenter number \(KC\). It was confirmed that scour propagation rates decrease with increasing \(e/D\), decrease with increasing the angle of attack \(\alpha\), and increase with \(KC\) number. Conversely, it was ascertained the Shields' parameter does not control, at least significantly, the scour rate propagation at the right- and left-hand pipeline shoulders. 4. A comparison with the conventional approach by [9] for the prediction of \(V_{H}^{*}\) would prove the superiority of the proposed scour equations. For example, by applying Equation (8) in [9], the performance index IOA is 0.842, significantly lower than the values of IOA for all the considered AI techniques (i.e., 0.9670 for MARS, 0.9435 for M5 MT, 0.9356 for EPR, and 0.9329 for GEP). \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 MSMT & 0.0874 & 0.0958 & 0.0488 \\ GEP & 0.0502 & 0.1037 & 0.1627 \\ MARS & 0.0618 & 0.1847 & 0.0563 \\ EPR & 0.0606 & 0.0494 & 0.0272 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: SSE values for the considered AI models when predicting \(V_{L}^{*}\) at various \(e\)/\(D\) ratios and \(KC\) values. **Author Contributions:** Conceptualization, M.N. and G.O. ; methodology, M.N. ; software, M.N. ; validation, M.N. and G.O. ; formal analysis, M.N. and G.O. ; investigation, M.N. and G.O. ; data curation, M.N. and G.O. ; writing--original draft preparation, M.N. and G.O. ; writing--review and editing, M.N. and G.O. ; visualization, M.N. and G.O. ; supervision, M.N. and G.O.