## 5 Results and Discussion
(**a**) Linear Regression, (**b**) Random Forest, (**c**) Gradient Boosting, (**d**) XGBoost, (**e**) LightGBM, (**f**) SVM-SVR, and (**g**) MLP-ANN. The comparative analysis reveals that ensemble methods, particularly Gradient Boosting and XGBoost, deliver superior predictive accuracy and reliability, minimizing residuals and reducing extreme prediction errors for UCS prediction. Random Forest and LightGBM also perform well, albeit with slightly more variance. Linear Regression and MLP-ANN show moderate predictive capabilities with higher variability and wider residual distributions, indicating less precise predictions, and SVM-SVR, while generally accurate, shows better error handling than Linear Regression but not as refined as the boosting methods and is prone to occasional significant errors. Figure 10 depicts the relationship between actual UCS data and the predictions made by the Golubev and Rabinovitch [9] model. The red triangles represent the data points, which generally align with the blue linear fit line, indicating a strong positive correlation. The \(R^{2}\) value of 0.7761 suggests a moderate fit, implying that the model explains approximately 77.61% of the variance in the actual UCS data. This degree of correlation indicates that the Golubev and Rabinovitch [9] model is capable of predicting UCS values with average accuracy. However, the spread of data points around the fit line also suggests the presence of some deviations and potential outliers, which may be due to various factors such as heterogeneity or model limitations. Figure 11 illustrates the comparison between real UCS data and the estimates produced by the Rzhevsky and Novick [41] model. The coefficient of determination, \(R^{2}\), is 0.7656, signifying that the model accounts for approximately 76.56% of the variability in the UCS data. This \(R^{2}\) value suggests that the Rzhevsky and Novick [41] model is a moderate predictor of UCS. Nonetheless, the dispersion of data points around the regression line points to some discrepancies and outliers, potentially arising from inherent model limitations. Figure 10: Scatter plot of estimated and measured UCS via the Golubev and Rabinovich model [9]. Figure 12 presents a comparative analysis of the measured UCS data against predictions made by [PERSON] et al. 's [10] model. The \(R^{2}\) value of 0.7674 suggests a moderately positive correlation between the model's predictions and the actual UCS values. However, some scatter around the line indicates that while the model captures the general trend of the data, there are discrepancies and potential outliers that could be attributed to variances in measurement conditions or inherent limitations of the model. The alignment of a majority of the data points along the line of best fit implies that [PERSON] et al. 's [10] model can moderately estimate UCS values within a specific range, although the spread of the data suggests that further refinement of the model could enhance its predictive accuracy. Figure 11: Scatter plot of estimated and measured UCS via the Rzhevsky and Novick model [41]. Figure 12: Scatter plot of estimated and measured UCS via [PERSON] et al.’s [10] model. Table 3 compares the outputs of different machine learning models in terms of statistical indicators such R\({}^{2}\), RMSE, MAE, MAE, and MPE. Linear Regression exhibited the lowest RMSE of 4.72 and MSE of 22.27, indicating its effectiveness in minimizing prediction errors. Additionally, it showed the lowest MAPE (3.38) and MPE (\(-0.0002\)), implying minimal percentage error. XGBoost and MLP-ANN also demonstrated competitive performance in terms of MAPE and MPE. In terms of MAE, XGBoost achieved the lowest value (2.578), followed closely by Linear Regression (2.993) and SVM-SVR (3.337). Linear Regression exhibited the highest \(R^{2}\) value of 0.8849, indicating its ability to explain approximately 88.49% of the variance in the UCS values. SVM-SVR also demonstrated a high \(R^{2}\) (0.8660), followed by XGBoost (0.8542).