## 5 Results and Discussion
indicating that while Random Forest models handle non-linearities better, they may still miss certain data intricacies. Gradient Boosting (see Figure 4c) demonstrates a closer fit to the actual UCS values, reducing the magnitude of prediction errors compared to both Linear Regression and Random Forest. The model's ensemble learning capability enhances its predictive accuracy, although minor deviations are still present. As demonstrated in Figure 4d, XGBoost maintains a robust alignment with actual values across the testing dataset, further validating its efficacy in handling complex data patterns. The minimal deviations observed suggest that XGBoost effectively generalizes the underlying data structure. LightGBM (see Figure 4e) displays performance on par with XGBoost, with predictions closely following the actual UCS values. The model's ability to capture detailed data patterns is evident, though occasional deviations indicate slight overfitting or data-specific challenges. SVM-SVR (see Figure 4f) exhibits reasonable predictive accuracy but with noticeable deviations in several regions of the data index. This suggests that while SVM-SVR is effective in certain scenarios, it may not consistently capture the full complexity of the UCS values as effectively as ensemble methods. As depicted in Figure 4g, MLP-ANN shows a strong predictive performance, with predictions aligning closely with actual values throughout the dataset. The neural network's capability to model complex and non-linear relationships contributes to its high accuracy, although minor deviations suggest room for further optimization. The comparative analysis for both training and testing phases underscores that ensemble methods such as Gradient Boosting, XGBoost, and LightGBM, along with neural network approaches like MLP-ANN, generally outperform simpler models like Linear Regression and SVM-SVR in predicting UCS values. These advanced models demonstrate superior generalization capabilities, making them more reliable for practical applications in predicting complex, real-world phenomena. Figure 4: Comparison between the predicted values of each model and the actual UCS values versus the data index for the testing dataset. (**a**) Linear Regression, (**b**) Random Forest, (**c**) Gradient Boosting, (**d**) XGBoost, (**e**) LightGBM, (**f**) SVM-SVR, and (**g**) MLP-ANN. Figure 5 provides a comparative analysis of the scatter plots illustrating the relationship between predicted and actual UCS values using different modelling techniques. Each subplot displays a series of points representing the actual UCS values on the x-axis and the corresponding predicted UCS values on the y-axis, along with a red dashed line indicating the ideal 1:1 prediction line and a shaded region representing prediction uncertainty. As shown in Figure 5a, the Linear Regression model shows a broad distribution of points around the ideal line, indicating a moderate fit with noticeable variance, particularly for higher UCS values. As depicted in Figure 5b, the Random Forest model demonstrates an improved alignment with the 1:1 line, suggesting better prediction accuracy and less dispersion compared to Linear Regression. As illustrated in Figure 5c,d, the Gradient Boosting and XGBoost (d) models exhibit a closer clustering of points around the ideal prediction line, signifying higher predictive precision and reduced variability. This observation highlights the effectiveness of ensemble techniques in capturing the underlying patterns in the data. Similarly, as shown in Figure 5e, LightGBM also shows a strong correlation between predicted and actual values, though with slightly more dispersion compared to Gradient Boosting and XGBoost. Furthermore, The SVM-SVR model (see Figure 5f) presents a robust performance, with most points lying near the ideal line and within the uncertainty bounds. However, there are a few outliers that deviate significantly, indicating some limitations in the model's generalization capability.