## 5 Experimental Programme
### Estimative Performance of ANN, DNN, and ResNet Approaches
For the same RMSE, higher iteration numbers of 6000 and 148,000 were required for DNN and ANN models, respectively. After convergence, sufficiently low values of RMSE were observed in the ResNet and DNN models, indicating better performances over the ANN model. For instance, at the same iteration value of 152,000, the ANN model converged at an RMSE of 4.7 MPa while ResNet and DNN models achieved lower values of RMSE (2.1 MPa and 2.7 MPa, respectively). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{**Metric**} & \multicolumn{3}{c}{**Training**} & \multicolumn{3}{c}{**Validation**} \\ \cline{3-8}  & & **R\({}^{2}\)** & **RMSE** & **MAPE** & **R\({}^{2}\)** & **RMSE** & **MAPE** \\ \hline \multirow{3}{*}{ANN} & Architecture 1 & **0.921** & **3.153** & **9.291** & **0.889** & **4.711** & **14.06** \\  & Architecture 2 & 0.827 & 4.802 & 12.712 & 0.798 & 5.059 & 11.818 \\ \cline{1-1}  & Architecture 3 & **0.923** & **3.273** & **11.54** & **0.898** & **2.521** & **9.496** \\ \cline{1-1}  & Architecture 4 & 0.821 & 5.004 & 14.03 & 0.84 & 3.161 & 13.486 \\ \cline{1-1}  & Architecture 5 & 0.921 & 3.244 & 9.105 & 0.915 & 3.288 & 8.581 \\ \cline{1-1}  & Architecture 6 & **0.896** & **3.815** & **9.797** & **0.937** & **1.987** & **6.600** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison of six architectures for FAGP compressive strength prediction in terms of R-squared (R\({}^{2}\)), root mean square error (RMSE) and mean absolute percentage error (MAPE). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{\(p\)**-Value**} & **ResNet vs. ANN** & **ResNet vs. DNN** \\ \hline R\({}^{2}\) & 0.00193 & 0.00053 \\ \hline RMSE & 0.00616 & 0.00395 \\ \hline MAPE & 0.04952 & 0.00499 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Paired \(t\)-test for statistical significance between ResNet and ANN-based models (architecture 6 and 1) and between ResNet and DNN-based models (architecture 6 and architecture 3). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{\(p\)-Value**} & **ResNet vs. ANN** & **ResNet vs. DNN** \\ \hline R\({}^{2}\) & 0.00193 & 0.00053 \\ \hline RMSE & 0.00616 & 0.00395 \\ \hline MAPE & 0.04952 & 0.00499 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Accuracy measurements on validation sets for the proposed machine learning approaches (architectures 1, 3, and 6) under K-fold cross validation scheme. Figure 6: Relationship between compressive strength values obtained from experiments (actual value) and machine learning approaches (predicted value): (**a**) training ANN; (**b**) validation ANN; (**c**) training DNN; (**d**) validation DNN; (**e**) training ResNet; (**f**) validation ResNet. Figure 8: Relationship between validation RMSE and iterations. Figure 7: Correlation coefficients R of three proposed approaches: (**a**) training ANN; (**b**) validation ANN; (**c**) training DNN; (**d**) validation DNN; (**e**) training ResNet; (**f**) validation ResNet. Figure 9 presents the distribution of error rates at 5% increments for predicted results obtained from architectures 1, 3, and 6. It is noted that the majority of datasets (61%) from the ResNet model exhibited error levels less than 5%. Corresponding frequencies of errors less than 5% for the ANN and DNN models were significantly lower (approximately 21 and 35%, respectively). In terms of errors less than 20%, frequencies for the ANN, DNN, and ResNet models were 79, 89, and 89%, respectively. In terms of ranking, therefore, the ResNet model provided the best estimative performance, followed by the DNN and ANN models.