## 4 Results and Discussion
### Model Results  
The three selected models were designed for deep training on the measured results of HVTT and ITS under both dry and wet conditions, considering variations in FBC, RAP content, and the number of passes (NP). Linear Regression achieved an R\({}^{2}\) of 0.85, indicating a good linear relationship between prediction values and measured ones, but its moderate MSE suggested a balance between simplicity and accuracy. Random Forest performed the best with an R\({}^{2}\) of 0.91, capturing nonlinear relationships effectively and minimizing errors with the lowest MSE. SVR had an R\({}^{2}\) of 0.91, providing a reasonable fit,  
Figure 4: Comparison of designed models. but its higher MSE showed slightly less accuracy than Random Forest as shown later. The predictions for ITS values (MPa) were made under both wet and dry conditions. The tests were conducted at a temperature of 25 \({}^{\circ}\)C, which corresponds to room temperature. In the analysis of ITS-wet predictions, yellow represents higher predicted ITS values, indicating better tensile strength, while dark blue represents lower predicted ITS values, indicating weaker tensile strength. The optimal configuration for Linear Regression was identified with an FBC ranging from 2.00% to 2.30% and a RAP between 0% and 6%, leading to a predicted ITS of 338.18 MPa. Conversely, Random Forest demonstrated slightly superior performance with an FBC of 1.50% to 1.7% and a RAP of 62% to 68%, resulting in a predicted ITS of 341.67 MPa. Support Vector Regression (SVR) pinpointed its best combination as an FBC of 1.5% to 1.80% and a RAP of 64% to 70%, yielding a predicted ITS of 340.68 MPa, as shown in Figure 5.  
For ITS-dry predictions, the most effective combination for Linear Regression was an FBC of 1.5% to 1.70% with a RAP exceeding 90%, which predicted an ITS of 444.55 MPa. In contrast, Random Forest identified an FBC of 1.50% and a RAP of 64% to 68%, achieving a slightly elevated predicted ITS of 455.46 MPa. SVR also found an optimal combination with an FBC of 1.5% to 1.80% and a RAP of 76% to 80%, resulting in a predicted ITS of 429.80 MPa (Figure 6). Across both wet and dry conditions, the percentages of FBC and RAP are crucial in determining the mechanical properties of the asphalt mixture. Generally, an increase in RAP tends to reduce the ITS due to the aging and inferior quality of the binder in RAP materials; however, the interplay with FBC alters this dynamic. FBC serves as a binder  
Figure 5: ITS-wet predictions using three models. Figure 6: ITS-dry predictions using three models. that enhances the stiffness and performance of the mixture by strengthening the bond between aggregates, especially under dry conditions. The models, especially Random Forest, adeptly capture the intricate nature of these interactions, as Figures 7 and 8 show. The high percentage of RAP with a small one of FBC achieved high ITS results. The color variations in the figures allow us to see how the FBC percentage affects the predicted outcomes. Each FBC percentage is represented by five main colors, showing the influence of FBC on the predicted ITS values. For instance, in Figure 7, the yellow color corresponds to FBC at 4.5%, and for RAP in the range of 0% to 36%, the predicted ITS values fall between 430 and 431 MPa. This pattern indicates how varying FBC percentages influence ITS predictions across different RAP dosages. Additionally, the model predicts ITS values for each RAP percentage in increments of 2%. As a result, within specific RAP dosage intervals, the ITS values remain relatively  
Figure 8: ITS-wet predictions. Figure 7: ITS-dry predictions. constant, which is reflected in the horizontal trends in the figures. Therefore, the horizontal data points indicate that ITS does not change significantly over those specific RAP percentages. Figure 9 illustrates the performance of three models used for HWTT predictions, all achieving a high R\({}^{2}\) value exceeding 0.85, alongside low MSE and MAE.