## 5 Discussion  
### Comparison of Different Models  
Table 9 compares the results of three artificial intelligence (AI) models, namely artificial neural network (ANN), support vector machine (SVM), and genetic programming (GP), in predicting the California bearing ratio (CBR), using different performance metrics, for both the training and testing databases. The performance metrics used to evaluate the models' performance include, mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), mean squared logarithmic error (MSLE), root mean squared logarithmic error (RMSLE), and coefficient of determination (\(R^{2}\)).  
In addition, Table 10 shows the ranking of the different AI models. The SVM model was the first AI model examined in this study, and is known as a black-box model. The ANN method, another black-box model, was subsequently employed, to explore another black-box model's performance. The GP method was utilized to examine grey-box AI methods.  
The results demonstrate, that the SVM model exhibits the lowest accuracy for both the training and test datasets, but still, it shows a good performance. In contrast, the ANN method performs significantly better, and predicts CBR values with high accuracy, achieving an \(R^{2}\) of 0.989 and 0.980 for the training and test databases, respectively. The  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Performance** & \multicolumn{2}{c}{**SVM**} & \multicolumn{2}{c}{**ANN**} & \multicolumn{2}{c}{**GP**} \\ \cline{2-6}
**Parameters** & **TR** & **TS** & **TR** & **TS** & **TR** & **TS** \\ \hline MAE & 3 & 3 & 1 & 1 & 2 & 2 \\ \hline MSE & 3 & 3 & 1 & 1 & 2 & 2 \\ \hline RMSE & 3 & 3 & 1 & 1 & 2 & 2 \\ \hline MSLE & 3 & 3 & 1 & 1 & 2 & 2 \\ \hline RMSLE & 3 & 3 & 1 & 1 & 2 & 2 \\ \hline R\({}^{2}\) & 3 & 3 & 1 & 1 & 2 & 2 \\ \hline Subtotal & 18 & 18 & 6 & 6 & 12 & 12 \\ \hline Total score & 36 & & 12 & & 24 \\ \hline Overall rank & 3 & & 1 & & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Overall rank analysis of different performance parameters for different machine learning techniques.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Performance Metrics**} & \multicolumn{4}{c}{**Training**} & \multicolumn{4}{c}{**Testing**} \\ \cline{2-6}  & **SVM** & **ANN** & **GP** & **SVM** & **ANN** & **GP** \\ \hline MAE & 0.497 & 0.392 & 0.459 & 0.512 & 0.302 & 0.475 \\ MSE & 0.409 & 0.200 & 0.358 & 0.357 & 0.116 & 0.304 \\ RMSE & 0.640 & 0.447 & 0.598 & 0.598 & 0.341 & 0.552 \\ MSLE & 0.017 & 0.005 & 0.010 & 0.011 & 0.002 & 0.009 \\ RMSLE & 0.129 & 0.074 & 0.100 & 0.103 & 0.046 & 0.097 \\ R\({}^{2}\) & 0.978 & 0.989 & 0.980 & 0.939 & 0.980 & 0.948 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Results of all three AI models in predicting CBR for both training and testing databases.  
GP method, a grey-box model, achieves slightly lower accuracy than the ANN method but still performs well, with an \(R^{2}\) of 0.98 and 0.948 for the training and testing databases, respectively. Notably, the GP method offers the benefit of producing an equation as output, which can be used for other datasets.  
The reason for the observed results, is that the SVM and GP models are known to be better suited for problems with a small number of inputs and a large number of data points, whereas ANN models are better suited for problems with a large number of inputs and a small number of data points. These findings contribute to a better understanding of the performance of different AI models for predicting CBR, which may have implications for future research and practical applications in the field of civil engineering and transportation planning.