## 3 Results and Discussion
### Machine Learning to Predict \(q_{u}\) and \(E_{t}\)
#### 3.4.1 Comparison of Machine Learning Models
Random forest regression (RFR) consistently produces robust results but shows slightly higher error metrics, indicating some constraints in its predictive capacity. Gradient boosting regression (GBR) maintains remarkable performance with acceptable generalization ability, while XGBoost outshines others with exceptional performance and robust generalization. Artificial neural networks (ANNs) and support vector regression (SVR) exhibit commendable performance, with ANN-GMDH emerging as a top performer, boasting high R\({}^{2}\) values and low error metrics. It should be noted that an ML model's capacity for generalization is assessed by its performance on unseen (testing) data. Metric scores during testing typically indicate a slight decrease in performance across all models compared to the training stage due to the unfamiliar data. To quantify this decline in performance, the degradation rate, or \(r_{d}\), is defined in Equation (5) [76]:  
\[r_{d}=\left|\frac{m_{train}-m_{test}}{m_{train}}\right|\times 100\% \tag{5}\]  
where \(m_{test}\) and \(m_{train}\) stand for a particular measure's values during the testing and training stages, respectively. Notably, the K-fold technique produces the least amount of performance decay and outperforms the TVT technique, except for ANN, where the TVT technique outperforms the ANN technique in terms of consistency for \(E_{t}\) prediction. All performance metrics show that the ANN-GMDH and ANN produce the least amount of performance decay among all models, with only the \(r_{d}\) of RMSE exceeding 10% for \(E_{t}\) predictions. The SVR follows. The performance of the other models significantly declined, particularly when it came to the MAE and RMSE for DTR using TVT technique for \(q_{u}\) predictions, where the rd values were 1544% and 4969%, respectively. Throughout both \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Metrics**} & \multicolumn{4}{c}{\(E_{t}\)} & \multicolumn{4}{c}{\(q_{u}\)} \\ \cline{3-8}  & & **Training** & **Testing** & **r\({}_{d}\) (\%)** & **Training** & **Testing** & **r\({}_{d}\) (\%)** \\ \hline \multirow{4}{*}{DTR} & R\({}^{2}\) & 0.99492 & 0.8766 & 11.89 & 0.9835 & 0.9042 & 8.06 \\  & RMSE & 145.52 & 681.11 & 368.05 & 51.083 & 114.465 & 124.08 \\  & MAE & 66.272 & 546.266 & 724.28 & 27.73 & 80.778 & 191.30 \\ \hline \multirow{4}{*}{RFR} & R\({}^{2}\) & 0.9854 & 0.9388 & 4.73 & 0.9828 & 0.9007 & 8.35 \\  & RMSE & 241.62 & 521.71 & 115.92 & 52.17 & 116.51 & 123.33 \\  & MAE & 189.75 & 408.33 & 115.19 & 33.3 & 76.91 & 130.96 \\ \hline \multirow{4}{*}{GBR} & R\({}^{2}\) & 0.999694 & 0.9861 & 1.36 & 0.99755 & 0.9591 & 3.85 \\  & RMSE & 35.72 & 228.93 & 540.90 & 19.694 & 74.827 & 279.95 \\  & MAE & 29.35 & 167.56 & 470.90 & 14.83 & 48.52 & 227.17 \\ \hline \multirow{4}{*}{XGBoost} & R\({}^{2}\) & 0.99803 & 0.9906 & 0.74 & 0.99995 & 0.9652 & 3.48 \\  & RMSE & 90.51 & 187.53 & 107.19 & 2.7669 & 69.011 & 2394.16 \\  & MAE & 69.5 & 148.97 & 114.35 & 2.08 & 40.92 & 1867.31 \\ \hline \multirow{4}{*}{SVR} & R\({}^{2}\) & 0.99394 & 0.99323 & 0.07 & 0.9958 & 0.98926 & 0.66 \\  & RMSE & 158.865 & 159.557 & 0.44 & 26.203 & 35.051 & 33.77 \\  & MAE & 97.77 & 121.494 & 24.27 & 13.409 & 23.053 & 71.92 \\ \hline \multirow{4}{*}{ANN} & R\({}^{2}\) & 0.99487 & 0.9901 & 0.48 & 0.9914 & 0.9903 & 0.11 \\  & RMSE & 147.19 & 187.71 & 27.53 & 36.971 & 36.0973 & 2.36 \\ \cline{1-1}  & MAE & 107.69 & 145.744 & 35.34 & 23.58 & 24.35 & 3.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The study’s metrics for the various models using (k-fold) cross-validation technique. training and testing phases, the ANN-GMDH and ANN models demonstrated remarkable consistency in their performance, with ANN-GMDH, ANN and SVR delivering the most accurate predictions. However, because of the widespread use of ANN in geotechnical engineering [50; 51; 52; 54; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72] and consistently superior performance in achieving better metrics.