# Data-Driven Pavement Performance: Machine Learning-Based Predictive Models
## 6 Results
Predicted and actual values from LightGBM are shown in Figure 9h. LightGBM shows overall good performance, with slight scatter in data at mid-range and high-range values. At intermediate and higher numbers of passes, some discrepancy between the predicted  
Figure 9: Number of passes to reach rut depth of 6 mm of different models: (**a**) decision tree; (**b**) gradient boosting; (**c**) KNN; (**d**) linear regression; (**e**) random forest; (**f**) SVR; (**g**) CatBoost; (**h**) LightGBM. and actual values can be observed. However, LightGBM yields MSE of 240,337,676.967 and R\({}^{2}\) of 0.997. Comparison of MSE and R\({}^{2}\) values for maximum number of passes to reach rut depth of 6 mm is shown in Table 3. As observed, CatBoost exhibits the least MSE of 5.934 \(\times\) 10\({}^{6}\) among other models and a maximum R\({}^{2}\) of 1.000. Furthermore, the highest MSE exists for SVR, corresponding to a related R\({}^{2}\) of 0.5656. However, gradient boosting, random forest and LightGBM provide significant prediction capabilities, with R\({}^{2}\) of 0.9995, 0.9893 and 0.997, respectively, among other algorithms. Figure 10 shows the prediction performance in terms of rut depth at 1.6 million passes for different models. In Figure 10a, predicted and actual rut depth values based on the number of passes have been shown using the decision tree algorithm. A total of seven folds have been developed, with all folds exhibiting the MSE of 0.02. As observed, predicted values stay closer to the perfect prediction line. In Figure 10b, gradient boosting has been used to evaluate the predicted and actual values for rut depth. A total of 10 folds have been developed, and all folds exhibit the MSE of 0.00. Gradient boosting outperforms the decision tree algorithm in terms of proximity of data points to the perfect prediction line. In Figure 10c, the KNN algorithm has been used to compare the predicted value against the actual values. A total of nine folds have been used for model optimization. Fold 2 and Fold 5 exhibit the least MSE of 0.43. However, the data scatter for predicted values is significantly higher than other models. The data scatter increases at higher rut depth values. In Figure 10d, linear regression has been used to predict the values for rut depth under specified passes and lateral wander type used. Only two folds have been developed for model optimization, and increase in folds did not enhance the model's prediction capability. Fold 2 exhibits the minimum MSE of 0.45. As observed, the predicted values stay closer to the perfect prediction line around intermediate rut depth values; however, the scatter increases at lower and higher rut depth values. This model outperforms the KNN, but the predictive performance is less than that of gradient boosting and decision tree. In Figure 10e, the random forest algorithm has been used to predict the values for rut depth based on the input data. A total of 10 folds have been developed for model optimization. Minimum MSE of 0.01 is obtained. Data scatter for random forest corresponds to that of the gradient boosting and decision tree algorithms. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Machine Learning** & **MSE** & **R\({}^{2}\)** \\
**Algorithm** & **MSE** & **R\({}^{2}\)** \\ \hline Linear Regression & 4.404 \(\times\) 10\({}^{9}\) & 0.9361 \\ Decision Tree & 7.349 \(\times\) 10\({}^{8}\) & 0.9893 \\ Random Forest & 4.163 \(\times\) 10\({}^{8}\) & 0.9940 \\ Gradient Boosting & 3.305 \(\times\) 10\({}^{7}\) & 0.9995 \\ KNN & 6.872 \(\times\) 10\({}^{9}\) & 0.9003 \\ Support Vector Regression & 2.995 \(\times\) 10\({}^{10}\) & 0.5656 \\ LightGBM & 2.403 \(\times\) 10\({}^{9}\) & 0.997 \\ CatBoost & 5.934 \(\times\) 10\({}^{6}\) & 1.000 \\ Linear Regression & 4.404 \(\times\) 10\({}^{9}\) & 0.9361 \\ Decision Tree & 7.349 \(\times\) 10\({}^{8}\) & 0.9893 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: MSE and R\({}^{2}\) values of different models for number of passes to reach rut depth of 6 mm.