## 3 Results and Discussion
### Artificial-Intelligence-Based Modeling  
The SVM algorithm was implemented on the training and testing datasets to predict the UCS variation for the studied limestone. Figure 5 provides the predicted values of the UCS values from the SVM model against the measured values, which were correlated by using R2, representing the dependency of the measured and predicted variables. R2 is the link between the actual outcomes and the predicted values that normally range from 0 to 1, where if it is closer to 1, a higher accuracy of the data overlap appears. According to Figure 5, the estimated R2 for the UCS results was 0.967, which was considerable for a shallow learning classifier. In addition, Figure 6 provides information about the overlap of the actual and predicted values of the UCS. As seen in this figure, there were good agreements between the actual and predicted data. In addition, the loss rate calculated for the model was reduced to 0.2 in the training set. So, the model was appropriately  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **Max** & **Min** & **Mean** & **Std.Dev.** & **Variance** & **Skewness** \\ \hline UCS & 190 & 43 & 109.93 & 39.754 & 158.044 & 0.214 \\ \hline \hline \end{tabular} Max = maximum value, Min = minimum value, and Std.Dev. = standard deviation.  
\end{table}
Table 2: Statistical analysis for Maragheh limestone UCS results.  
Figure 4: The normal distribution envelope of UCS results.  
Figure 3: The Q–Q chart for normality tests of UCS results.  
Figure 8: Demonstration of index values for the case of overprediction.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Analysis Set** & **MAE** & **Score** & **MSE** & **Score** & **RMSE** & **Score** & **R2** & **Score** & **A10-Index** & **Score** & **Rank** \\ \hline Training & 0.23746 & 2 & 0.21054 & 2 & 0.20067 & 2 & 0.967 & 2 & 0.9317 & 2 & 10 \\ \hline Testing & 0.45108 & 1 & 0.43598 & 1 & 0.41045 & 1 & 0.955 & 1 & 0.9148 & 1 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of SVM model performance for Maragheh limestone UCS results.  
Figure 7: (a) Scattered and (b) [PERSON]’s index for error variations for UCS results.  
Figure 10: The estimated loss function for the SVM model.  
Figure 9: The evaluation criteria estimated for SVM model.  
Figure 11: Statistical specifications of the SVM model’s results: (**a**) [PERSON]’s correlation coefficient, (**b**) heat map, (**c**) frequency distribution, and (**d**) boxplot diagram.  
Figure 12: The corresponding (**a**) predicted and measured values and (**b**) prediction error variations.  
The application of the SVM algorithm is appropriate for different types of geo-material behavioral predictions, and researchers in future scientific projects can consider this. However, it should be noted that the SVM algorithm is unsuitable for large datasets and when facing datasets with noise. So, users must be notified when they attempt to utilize the SVM or SVP models in the prediction process. In addition, if a probabilistic analysis needs to be conducted, SVM classifiers are not capable of using a probabilistic explanation for the classification. Although these limitations are general aspects of SVM and provide sufficient coverage and accuracy for the analyses of intact rocks, they have to be considered in analyses such as when analyzing the anisotropy of rocks.