# Artificial Intelligence-Based Model for the Prediction of Dynamic Modulus of Stone Mastic Asphalt
## 5 Results and Discussion
### Validation and Comparison of ANN-TLBO with Single ANN  
The performance of the ANN model, in comparison with the ANN-TLBO algorithm, is presented under regression plots (Figure 7), showing a comparison between the predicted and actual values of the dynamic modulus \(|\)E*\(|\). The ideal regression lines are in discontinuous style, whereas the R\({}^{2}\) between predicted and actual dynamic modulus \(|\)E*\(|\) are given (Table 6). The correlation results analysis showed that the R\({}^{2}\) values were 0.907, 0.948 for the training and testing datasets, respectively, for the ANN model. Concerning the ANN-TLBO model, these values were 0.975, 0.981 for the training and testing datasets, respectively. These results showed a very good prediction performance of the two proposed models. However, using an optimization, the ANN-TLBO was found to be the superior predictor compared with the single ANN.  
Figure 6: Optimization of weight parameters of ANN models using the TLBO algorithm: (**a**) R\({}^{2}\), (**b**) RMSE, and (**c**) MAE.  
The summary of the prediction performance of ANN and ANN-TLBO is presented in Table 6. The values of R\({}^{2}\), RMSE, and MAE were calculated based on the formulations given in the previous section, whereas ErrorMean was the mean values of errors and ErrorStD was the standard deviation of errors. The \"Slope\" represented the slope between the ideal regression line (discontinuous lines in Figure 7) and the linear fit, given by the models (continuous lines in Figure 7). The two additional error criteria also confirmed that ANN-TLBO is superior to ANN in predicting the dynamic modulus \(|\)E*\(|\). For illustration purposes, the values of the dynamic modulus \(|\)E*\(|\) in function of sample index using individual ANN and ANN-TLBO models are plotted in Figure 8 for the training and testing datasets. It is clearly seen that the predicted values were in excellent agreement with the experimental dynamic modulus \(|\)E*\(|\) values.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Model** & **Data** & **RMSE** & **MAE** & **ErrorMean** & **ErrorStD** & **R\({}^{2}\)** & **Slope** \\ \hline Unit & & MPa & MPa & MPa & MPa & - & - \\ ANN & Training & 379.035 & 291.815 & \(-\)126.527 & 360.414 & 0.907 & 0.914 \\  & Testing & 292.828 & 236.917 & \(-\)31.099 & 295.080 & 0.948 & 0.932 \\ ANN-TLBO & Training & 189.666 & 153.851 & 18.639 & 190.396 & 0.975 & 0.958 \\  & Testing & 183.308 & 141.540 & 21.294 & 184.511 & 0.981 & 0.936 \\ \% Gain & Training & +50.0 & +47.3 & +114.7 & +47.2 & +7.5 & +4.8 \\  & Testing & +37.4 & +40.3 & +168.5 & +37.5 & +3.5 & +0.4 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Summary of prediction capability of the ANN-TLBO model.  
Figure 7: Regression graphs using individual ANN model: (**a**) training and (**b**) testing parts; ANN-TLBO model: (**c**) training and (**d**) testing parts.  
Figure 8: Dynamic modulus in function of sample index, using individual ANN model for (**a**) training part and (**b**) testing part, using ANN-TLBO model for (**c**) training part and (**d**) testing part.  
Overall, the prediction capability of ANN-TLBO was quantified based on various performance indicators. The proposed hybrid model showed high prediction capability and outperformed individual ANN, clearly demonstrating the efficiency of using TLBO as an optimization tool.