## 3 Results and Discussion
### Model Performance and Comparative Analysis  
The IFI was predicted by three models that used the COF and MPD as input variables. Overall, the logarithmic model performed the best, with the lowest testing RMSE (0.049) and the greatest testing R\({}^{2}\) (0.821). The four parameters of this model's simplicity improve interpretability and lower the possibility of overfitting. The power law model performed nearly as well as the logarithmic model (testing R\({}^{2}\) = 0.813) and the testing RMSE (0.050). The polynomial model showed slightly better training performance (R\({}^{2}\) = 0.776), but its testing metrics were marginally lower (testing R\({}^{2}\) = 0.802). The ability of each model to capture the IFI values from experimental measurements throughout training and testing datasets is demonstrated by Figure 9, which shows the actual vs. predicted values for each model. With little departure from the parity line (y = x), each model exhibits good predictive power and high accuracy during both the training and testing stages. The  
Figure 8: Pair plot of DFT and CTM test data. Figure 7: Scatter plot matrix of key surface and friction parameters. original IFI model defined by PIARC (ASTM E1960) achieved a test R\({}^{2}\) of 0.7940 and RMSE of 0.0534. These results demonstrate that the proposed models better capture the nonlinear relationship between texture (MPD) and friction (COF), particularly in HFST contexts with extended MPD ranges. The Surface Response Plots for various models are shown in Figure 10, which shows the relationship between the target response, IFI, and two independent variables, COF and MPD. The IFI value's reaction to changes in COF and MPD is depicted by the colored surface. The experimental data points are represented by red dots, which show how well the modeled surface matches the measured data. It is found that IFI rises when COF and MPD rise across all models. The sensitivity of IFI to variations in friction is reflected in the gradient or steepness of the surface along the COF axis; steeper slopes suggest a stronger impact. Likewise, the effect of macrotexture depth on the IFI is shown by the tilt along the MPD axis [41]. Table 3 presents the coefficients and corresponding equations for each evaluated model. Among them, the logarithmic model emerges as the most suitable for HFST applications. This model demonstrates the highest level of reliability, with performance metrics indicating strong agreement between predicted and observed values (R\({}^{2}\) Test = 0.821, R\({}^{2}\) Train = 0.760, RMSE = 0.049). The clear physical meaning of its coefficients further supports its applicability in practical scenarios. Figure 9: Actual vs. predicted data points for different models. A local derivative-based sensitivity analysis was used, in which partial derivatives of the IFI with respect to the input variables, specifically the COF and MPD, were calculated. This strategy enabled a precise measurement of how minor changes in input values propagate across each model. This was performed by perturbing COF and MPD by \(\pm\)20% and determining the resulting IFI (\(\Delta\)IFI). Each model's biggest percentage change in IFI was extracted and used as a sensitivity metric. Across all three models, the projected IFI is often more sensitive to changes in the COF than to MPD, according to the sensitivity analysis findings, which are shown in Table 4. A 20% variance in COF resulted in a change in IFI (\(\Delta\)IFI) that varied from 14.3% to 17.7%, but a similar level of variation in MPD produced a significantly lower \(\Delta\)IFI that ranged from 1.5% to 6.0%. The polynomial model was the most sensitive of the three models to both COF (17.7%) and MPD (6.0%), indicating that changes in input parameters within the tested range had a greater impact on the model's output. This increased sensitivity is due in part to the model's use of squared and interaction components, which can exaggerate output variation, particularly outside of the calibration range.