## 4 Discussion
### Evaluation of the Models
In contrast, fs_cv, Rf_mean and Rf_cv show negligible influence on Vs, as observed from their flat PDP curves. These parameters were excluded from both the XGBoost and Bayesian GLMs to optimize performance. As a result, the final optimized XGBoost model was trained using \(\sigma\),\(\
u\), qc_mean, fs_mean, depth, qc_cv, and Ic_mean, while Bayesian GLM was fitted using \(\sigma\),\(\
u\), qc_mean, fs_mean, depth, and qc_cv. Figure 4: Hyperparameter importance of XGBoost algorithm. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Hyperparameters** & **Search Span** & **Optimized Values** \\ \hline Number of trees (n\_estimators) & 50–600 & 444 \\ Learning rate & 0.001–0.5 & 0.0094 \\ Maximum depth of trees & 1–10 & 10 \\ Subsampling ratio & 0.05–1 & 0.640 \\ L1 Regularization term on weights (reg\_alpha) & 0.01–1 & 0.208 \\ L2 Regularization term on weights (reg\_lambda) & 0.01–1 & 0.603 \\ Column subsampling ratio per tree & 0.5–1 & 0.707 \\ (colsample\_bytree) & & 0.707 \\ Minimum loss reduction required to make a & 0–10 & 8.79 \\ further split (gamma) & & \\ Maximum number of bins for feature & 128–512 & 499 \\ quantization (max\_bin) & & \\ Balancing weight for positive and negative & 0.1–10 & 6.09 \\ classes (scale\_pos\_weight) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimized hyperparameters values of XGBoost model. The predictive performance of the optimized XGBoost model is presented in Figure 6. In Figure 6a, the Vs values predicted by XGBoost model for both the training and testing dataset are plotted against measured Vs values. The diagonal dashed green line (y = x) represents perfect prediction (i.e., the predicted Vs values match the measured Vs values). A good agreement is observed between predicted and measured Vs values. The residual (the difference between predicted and measured Vs) plots for the predictions are illustrated in Figure 6b. It can be observed that random scatters of residuals around zero (horizontal dashed green line) for both training and testing dataset, indicating unbiased predictions. On the right side of the scatter plots, histograms of the residuals are presented. These histograms offer a visual summary of the distribution of residuals. For the training dataset, the residuals appear to be symmetrically distributed around zero, with a relatively narrow spread, indicating strong predictive performance and minimal bias. In contrast, for the testing dataset, the residuals exhibit a slightly wider spread, reflecting the model's reduced performance on unseen data. However, the residuals are still centered around zero, suggesting that the model generalizes reasonably well without significant overfitting. The results demonstrate the robustness of the XGBoost model and emphasize the importance of data preprocessing, feature selection, and hyperparameter optimization in improving model performance. Figure 5: Partial dependence plots. The predictive performance of the model across various performance metrics (\(R^{2}\), IA, KGE) and error metrics are summarized in Table 4 for both the training and testing dataset. For instance, the model achieved an \(R^{2}\) of 0.54, an IA of 0.84 and KGE of 0.65 on the test dataset. For the training dataset, the model achieved an \(R^{2}\) of 0.91, an IA of 0.97 and KGE of 0.82. The difference in performance between the training and testing datasets can be attributed to the complexity and variability inherent in the test data, which were not fully captured during model training. This difference is a common occurrence in ML models, particularly when the training data does not encompass all the potential variations present in the test set. Additionally, while the model was designed to generalize well and hyperparameter optimization techniques were employed to mitigate overfitting, the relatively lower performance on the test dataset reflects the challenges in accurately modeling highly complex or non-linear relationships between input features and the target variable Vs. However, these results are superior to those reported in [20].