## 3 Results and Discussion
### Machine Learning Results and Discussion
#### 3.2.2 Models Results  
DTR Model Results  
Figure 18 provides a comprehensive analysis of the DTR model's predictive performance for \(\sigma_{min}\) and \(\gamma_{max}\) across both training and test datasets. The training set exhibits exceptional accuracy, as indicated by a coefficient of determination (R-squared) of 0.995 and 1 for \(\sigma_{min}\) and \(\gamma_{max}\), respectively, along with low RMSE and MAE values (5.79 and 3.65 for \(\sigma_{min}\), 0 for \(\gamma_{max}\)). This suggests robust capturing of training data variance and minimal prediction errors. However, in the test set, performance diminished, with R-squared values of 0.9372 and 0.9845 for \(\sigma_{min}\) and \(\gamma_{max}\), respectively, and higher RMSE and MAE values (21.79 and 16.414 for \(\sigma_{min}\), 0.158 and 0.0965 for \(\gamma_{max}\)). This confirms a notable degradation in predictions for unseen data. The combined assessment of metrics and visualization highlights the DTR model's limited ability to align predictions with actual values, particularly evident in the deviation of certain unseen data points from the best-fit trend line in specific contexts. Figure 18: Comparing the actual and predicted values for the training and test datasets in the DTR model for (**A**) \(\sigma_{min}\) and (**B**) \(\gamma_{max}\). RFR Model Result  
Figure 19 presents a visualization of the RFR model's predictive performance for \(\sigma_{min}\) and \(\gamma_{max}\) across both training and test datasets. The training set showcased exceptional accuracy, with a coefficient of determination (R-squared) of 0.9946 and 0.999 for \(\sigma_{min}\) and \(\gamma_{max}\), respectively. Additionally, the model exhibited low RMSE and MAE values (5.975 and 4.728 for \(\sigma_{min}\), 0.0374 and 0.244 for \(\gamma_{max}\)), indicating robust capturing of training data variance and minimal prediction errors, akin to DTR but with a slight advantage favoring DTR. In the test set, RFR outperformed DTR, with R-squared values of 0.9636 and 0.9924 for \(\sigma_{min}\) and \(\gamma_{max}\), respectively, along with lower RMSE and MAE values (16.6 and 12.954 for \(\sigma_{min}\), 0.111 and 0.0696 for \(\gamma_{max}\)). While there was still a degradation in predictions for unseen data, it is notably better than DTR. The combined assessment of metrics and visualization indicates that the RFR model had a strong ability to align predictions with actual values. Clear evidence suggests that the RFR model surpassed the DTR model, showcasing enhanced predictive capabilities. However, it is essential to note that although the number of data points deviating from the best-fit trend line had significantly been reduced compared to the DTR model, some instances still exist, particularly for lower stress values. These deviations indicate ongoing challenges in specific situations, emphasizing the need to explore other models to address these discrepancies. GBR Model Results  
Figure 20 provides a visualization of the \(GBR\) model's predictive abilities for \(\sigma_{min}\) and \(\gamma_{max}\) across both training and test datasets. In the training set, the model demonstrated exceptional accuracy with a coefficient of determination (R-squared) of 0.9997 and 0.999 for \(\sigma_{min}\) and \(\gamma_{max}\), respectively. The low RMSE and MAE values (1.385 and 1.017 for \(\sigma_{min}\), 0.01 and 0.0081 for \(\gamma_{max}\)) underscored the robust capturing of training data variance and minimal prediction errors, although slightly better than RFR. However, in the test set, GBR  
Figure 19: Comparing the actual and predicted values for the training and test datasets in the RFR model for (**A**) \(\sigma_{min}\) and (**B**) \(\gamma_{max}\). outperformed RFR with R-squared values of 0.9789 and 0.9954 for \(\sigma_{min}\) and \(\gamma_{max}\), respectively. The RMSE and MAE values (12.64 and 9.172 for \(\sigma_{min}\), 0.087 and 0.0463 for \(\gamma_{max}\)) indicate a degradation in predictions on unseen data compared to the training set.