## 5 Results and Discussion
### Effect of Smaller Training Dataset Size
The fact that the relative error reduction achieved using the four assisted scenarios is fairly high (\(>\)30%) for reduced-3 training dataset size, indicates that the assisted approach helped the ANN to properly capture the input/output relations, though no intermediate values (for some of the inputs) are available in the training dataset. This observation further confirms the importance of using the proposed assisted approach for small size datasets. In order to further examine the effect of the assisted approach for smaller dataset sizes, Figure 6 shows exemplary results for one of the 80 testing datasets combinations (the same testing dataset shown previously in Figure 4). The upper part of the figure shows the experimental residual strength value and the ANN predictions (for traditional, assisted 3 and 4 scenarios); while the lower part shows  
Figure 5: The effect of the assisted approach on the ANN prediction accuracy using the different learning algorithms. The MAE\({}_{\text{P}}\) values for the traditional and assisted approaches residual strength predictions (**top**), together with the error reduction of the assisted approach relative to the traditional approach (**bottom**). Averaged results for the 80 random combinations of the testing dataset. \begin{table}
\begin{tabular}{c c c c|c c c|c c c} \hline \hline  & \multicolumn{3}{c|}{**Reduced 1 (48)**} & \multicolumn{3}{c|}{**Reduced 2 (35)**} & \multicolumn{3}{c}{**Reduced 3 (22)**} \\ \cline{2-10}
**Scenario** & \(\mathbf{MAE_{P}}\) & \(\mathbf{RSME_{P}}\) & \(\mathbf{R^{2}}\) & \(\mathbf{MAE_{P}}\) & \(\mathbf{RSME_{P}}\) & \(\mathbf{R^{2}}\) & \(\mathbf{MAE_{P}}\) & \(\mathbf{RSME_{P}}\) & \(\mathbf{R^{2}}\) \\  & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] \\ \hline
**Traditional** & 4.68 & 6.52 & 88.73 & 5.55 & 7.52 & 85.77 & 6.86 & 9.54 & 80.97 \\ \hline
**Assisted 1** & 4.67 & 6.61 & 89.59 & 5.1 & 7.01 & 87.65 & 4.51 & 5.93 & 90.24 \\ \hline
**Assisted 2** & 4.16 & 5.82 & 91.46 & 4.65 & 6.32 & 90.2 & 4.52 & 5.92 & 90.97 \\ \hline
**Assisted 3** & 3.55 & 4.88 & 93.91 & 3.84 & 5.33 & 92.85 & 4.63 & 6.21 & 91.64 \\ \hline
**Assisted 4** & 3.46 & 4.54 & 95.21 & 3.46 & 4.52 & 95.16 & 4.26 & 5.83 & 92.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance metrics for the reduced size training datasets using the traditional and assisted ANN modeling approaches (averages for the 80 random combinations of the testing dataset). the magnitude of error in ANN predictions. The figure shows that for most of the samples shown in the figure (15 out of 19) the ANN residual strength predictions obtained using the two assisted scenarios are superior to the predictions obtained using the traditional approach. It should be clear here that the purpose of Figure 6 is to observe the overall predictions accuracy for the individual samples. The fact that the traditional approach predictions for some of the samples (U-25 for instance) are more accurate, does not affect the overall conclusions which are based on the averages for large numbers of data points. Finally, in order to visualize the overall accuracy improvement for the ANN residual strength predictions when using the assisted approach, the correlation between the experimental results and ANN predictions for the different training dataset sizes are shown in Figure 7. The data shown in this figure are for one of the 80 datasets combinations, and the figure shows the correlation for all data points (training, validation and testing). In all of the subfigures, the points are distributed uniformly above and below the 45-degrees line; this indicates that there is no over-or-under prediction tendency in the ANN predictions, and the prediction errors are fairly random (no systematic error is observed). In this type of figures, the closer the points to the 45-degrees line, the more accurate the predictions are.