## 6 Conclusions  
Pile bearing capacity values were estimated in this paper using five models. The prediction model was built with ten input parameters and one output parameter. The modeling results show that the XGBoost model has the best capability for accurate prediction of \(Pu\) when compared to other models such as AdaBoost, RF, DT and SVM. The following are some of the major findings of this study:  
1. In testing phase, the XGBoost model (\(R^{2}\) = 0.955, \(MAE\) = 59.929, \(RMSE\) = 80.653, \(MAE\) = 6.6, \(NSE\) = 0.950, and \(RSR\) = 0.225) has the highest performance capability as compared to other soft computing techniques considered in this study i.e., AdaBoost, RF, DT and SVM as well as the models used in the literature.
2. Sensitivity analysis results show that SPT blow count at pile shaft (\(\text{N}_{\text{S}}\)) was the most important parameter in predicting pile bearing capacity.
3. Taylor diagram also verified that all the models are good but the predictive power of the XGBoost algorithm had a higher correlation and lower \(RMSE\).
4. Based on the results and analysis the XGBoost model can also be applied to solve a variety of geotechnical engineering problems.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Author** & **Model** & **Foundation Type** & **Number of Samples** & \(\mathbf{R^{2}}\) & \(RMSE\) \\ \hline \multirow{2}{*}{[PERSON] et al. [71]} & ANFS & & & 0.875 & 0.048 \\ \cline{2-6}  & ANN & Thin-walls & 150 & 0.71 & 0.529 \\ \hline \multirow{2}{*}{[PERSON] et al. [72]} & GPR & Files & 296 & 0.84 & - \\ \cline{2-6}  & GA-ANN & & & 0.86 & 0.0093 \\ \cline{2-6}  & ANN & Rock-socked piles & 132 & 0.808 & 0.135 \\ \cline{2-6}  & PSO-ANN & & & 0.918 & 0.063 \\ \hline \multirow{2}{*}{[PERSON] et al. [38]} & GA-DLNN & Files & 472 & 0.882 & 109.965 \\ \cline{2-6}  & XGBoost & Files & 200 & 0.955 & 80.653 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison with other studies.  
Figure 11: Taylor diagram of the models.  
Furthermore, the XGBoost technique has the advantage of being easily updated, it is obvious that the proposed model is open to further development, and that the collection of more data will result in significantly stronger prediction capability, avoiding the requirement for expertise and time to update an existing design aid or equation.  
Conceptualization, M.A. ([PERSON]) and M.A. ([PERSON]); methodology, M.A. ([PERSON]), M.A. ([PERSON]) and I.A.; software, M.A. ([PERSON]) and M.A. ([PERSON]); validation, P.W., P.K., M.A. ([PERSON]) and U.A.; formal analysis, M.A. ([PERSON]) and I.A.; investigation, P.W., P.K., U.A. and M.A. ([PERSON]); resources, P.K.; data curation, M.A. ([PERSON]) and I.A.; writing--original draft preparation, M.A. ([PERSON]); writing--review and editing, M.A. ([PERSON]), I.A., M.A. ([PERSON]) and U.A.; supervision, M.A. ([PERSON]), P.W. and P.K.; project administration, M.A. ([PERSON]) and P.W.; funding acquisition, P.W. and P.K. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data used to support the findings of this study are included within the article.  
The writers gratefully acknowledge [PERSON] from the University of Transport Technology in Vietnam, who provided pile load test results conducted on 200 reinforced concrete piles at the test site in Ha Nam province-Vietnam for this study.  
The authors declare no conflict of interest.