## 4 Discussion  
In the current study, a very important contribution in the geotechnical community has been introduced for the sake of enhancing the performance of the pile-bearing capacity model. It is worth mentioning here that the model quality is influenced by the method utilized. Hence, other unused advanced machine-learning methods demonstrated efficient results in other areas. Consequently, in the current study, we examined the usage of twelve advanced machine-learning methods, such as Deep Neural Network (_DNN_), Extreme Learning Machine (_ELM_), Support Vector Regression (_SVR_), LASSO regression (_LASSO_), Random Forest (_RF_), Ridge Regression (_Ridge_), Partial Least Square Regression (_PLS_), Stepwise Regression (Stepwise), Kernel Ridge (_KRidge_), Genetic Programming (_GP_), and Least Square Regression (_LSR_), to predict the pile-bearing capacity. According to the authors' knowledge, the use of the aforementioned machine-learning methods in predicting  
Figure 5: BeaCa2021 interface. the pile-bearing capacity is very rare. Therefore, this study began with collecting a wide range of data consisting of 100 static load-bearing tests on the _UBC_ of both steel- and concrete-driven piles from different countries, such as Iran, Mexico, and India. Afterward, we selected eight relevant factors based on the literature recommendations, such as average cohesion (\(\rm{kN/m^{2}}\)), average friction angle (\(\rm{{}^{\circ}}\)), average soil-specific weight (\(\rm{kN/m^{3}}\)), average pile-soil friction angle (\(\rm{{}^{\circ}}\)), flap number, pile area (\(\rm{m^{2}}\)), and pile length (\(\rm{m}\)). Based on that, eleven advanced machine-learning methods (_DNN_, _ELM_, _SVR_, _LASSO_, _RF_, _Ridge_, _PLS_, _Stepwise_, _KRidge_, _GP_, and _LS_) were applied for modeling the selected optimal input set for the first time. The findings clearly indicate that the Deep Neural Network (_DNN_) presents the most appropriate model, which yielded the minimum values of error metrics (_MEA_, _RMSE_, and _IOS_) and the higher values of \(R^{2}\), \(R\), and _IOA_ compared to other models. Furthermore, the newly developed model was assessed by the _K_-fold cross-validation method and compared to other proposed models from the literature based on the correlation coefficient. The conclusion drawn is that the optimal _DNN_ model could produce new data without causing over-fitting or under-fitting, plus being much more precise than the other proposed empirical models. Moreover, the last part in the current study consisted of the sensitivity analysis, which provided an overview of the most influential parameters on the pile-bearing capacity according to the proposed model. The findings indicate that the pile area was the most influential factor on the pile-bearing capacity. Pile length also had a considerable effect. In addition, the cohesion and friction angle demonstrated a moderate effect on the pile-bearing capacity, with a sensibility ratio ranging between 9% and 15%. Finally, the proposed optimal model was then used to develop a _GUI_ public interface in order to facilitate its usage in the future. A reliable, easy-to-use, and graphical interface, named \"BeaCa2021, presented in the current study, was programmed via Matlab software. The essential advantage of \"BeaCa2021\" is to help researchers and civil engineers interested in the problem of modeling regardless of their proficiency, by offering them plenty of benefits, such as reliability, easiness, and lowering the budget used for predicting the pile-bearing capacity from relevant and easily obtained parameters without the need to operate expensive in situ tests. The results obtained in the current study also proved that the performance of the pile-bearing capacity model was considerably enhanced by using new machine-learning methods. The model prediction by the _DNN_ was improved by 8.91% with the _ANN_ method proposed by [PERSON] et al. (2015), 3.58% with the _PSO-ANN_ method proposed by [PERSON] et al. (2016), and 0.86% with the _MLP-GWO_ method proposed by [PERSON] et al.