## 3 Results
### Bearing Capacity Prediction through AI Models  
To define the optimal machine-learning model, the first step consists of selecting the optimal input parameters that have a high influence on the target value, and the second step is to determine the best machine-learning methods. To begin with, in order to define the suitable input parameters, eight factors have been used following the literature recommendations. Afterward, we attempted to determine the optimal \(ANN\) model for predicting the pile-bearing capacity depending on six statistical measures. The performance of each model for the selected optimal input in both concrete and steel piles is presented in Table 6. Six performance measures have been used to compare the proposed models in order to select the best one, in terms of the mean absolute error (\(MAE\)), root mean square error (\(RMSE\)), index of scattering (\(IOS\)), coefficient of determination (\(R^{2}\)), Pearson correlation coefficient (\(R\)), and index of agreement (\(IOA\)). The data were divided into two parts, i.e., 80% for the training and 20% for the validation. As Table 6 demonstrates, the target values were modeled via the machine-learning methods, where the parameters of the methods have been fixed (as presented in Table 4) and compared using the six performance measures in order to find the best model. The different models produced the values: \(MAE\) (0.1650 \(\times\) 10\({}^{3}\) to 3.0424 \(\times\) 10\({}^{3}\)), \(RMSE\) (0.2140 \(\times\) 10\({}^{3}\) to 4.2390 \(\times\) 10\({}^{3}\)), \(IOS\) (0.0755 to 0.7737), \(R\) (0.9315 to 0.9977), \(R^{2}\) (0.8676 to 0.9954), and \(IOA\) (0.9360 to 0.9988) in concrete piles. Similarly, in the steel piles, we obtained \(MAE\) (0.1870 \(\times\) 10\({}^{3}\) to 3.1064 \(\times\) 10\({}^{3}\)), \(RMSE\) (0.3100 \(\times\) 10\({}^{3}\) to 4.3966 \(\times\) 10\({}^{3}\)), \(IOS\) (0.0448 to 0.9081), \(R\) (0.8478 to 0.9997), \(R^{2}\) (0.7187 to 0.9994), and \(IOA\) (0.9118 to 0.9998). The results indicate that the best performance was obtained from the \(DNN\) model trained by the Tan-Sigmoid function. This model is said to be the most appropriate one because it displays the highest accuracy in terms of \(MAE\) (0.1650 \(\times\) 10\({}^{3}\)/0.1870 \(\times\) 10\({}^{3}\)), \(RMSE\) (0.214 \(\times\) 10\({}^{3}\)/0.31 \(\times\) 10\({}^{3}\)), \(IOS\) (0.0755/0.0448), \(R\) (0.9977/0.9997), \(R^{2}\) (0.9954/0.9994), and \(IOA\) (0.9988/0.9998) in both concrete/steel piles. Finally, the most appropriate \(DNN\) model displayed the higher values of performance measures criteria in both the training and validation phase. Furthermore, this model is closely followed by the \(GP\) model, which shows an acceptable accuracy as it ranked second. Moreover, the results showed the poor performance of the \(ELM\) model in predicting the pile-bearing capacity. With respect to the performance of machine-learning models during the training phase, the performance hierarchy follows the following order: \(DNN\), \(GP\), \(RF\), \(Kridge\), \(SVR\), \(LS\), \(Ridge\), \(Step\), \(PLS\), \(Lasso\), and \(ELM\). Finally, the scatter plots between the target and the output bearing capacity value of each model are presented in Appendix A (Figures A1-A11).