## 3 Results and Discussions
### Result of AI-Based Model  
Many studies have popularly used the sensitivity analysis of datasets to treat the inappropriate potential input variable in the modeling task, because utilizing the irrelevant variable in the AI-based model reduces the accuracy of the prediction model and increases the computational demand [58]. Therefore, the Pearson correlation matrix was used in this study to determine the most sensitive variables from the experimental datasets, as depicted in Figure 13. The parameter relevance decreases as it become closer to zero and increases to unity (\(-1\) or \(+1\)). The unity values translate the perfect variable. The \(+\)ve and \(-\)ve values demonstrate a direct and inverse relationship between the independent and dependent parameters. As shown in Figure 14, most input parameters showed a low correlation value with the target parameter. Moreover, an inverse relationship existed between flowability and target parameter, and compressive strength appeared to be the most sensitive parameter for predicting the flexural of the PU-cement mortar with a PC value of 4. The low correlation value between all input and target parameters is attributed to the abnormal distribution of the datasets. The descriptive statistical feature of the input and output parameters are summarized in Table 10. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Parameters** & **Description** & **Symbol** & **Unit** & **Max** & **Min** & **Mean** & **STD** & **Skew.** & **Kurt.** \\ \hline Input 1 & Curing age & \(C\) & \(d\) & 7.00 & 28 & 17.04 & 10.56 & \(-\)2.05 & 0.089 \\ Input 2 & PU binder content & \(PU\) & \% & 0.00 & 25.0 & 13.69 & 10.31 & \(-\)1.48 & \(-\)0.30 \\ Input 3 & Compressive strength & \(f_{\mathrm{c}}\) & MPa & 21.80 & 71.6 & 40.61 & 12.70 & \(-\)0.65 & 0.636 \\ Input 4 & Flow ability & \(F\) & mm & 90.00 & 230 & 178.6 & 61.68 & \(-\)1.41 & \(-\)0.74 \\ Output & Flexural strength & \(f_{\mathrm{f}}\) & MPa & 8.400 & 15.9 & 12.13 & 1.833 & \(-\)0.98 & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The statistical description of the dataset. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variables** & **Symbol** & **Goal** & **Lower Limit** & **Upper Limit** \\ \hline PU binder (\%) & PU & In range & 0 & 25 \\ Nano silica (\%) & NS & In range & 0 & 3 \\ Flexural strength (MPa) & \(f_{\mathrm{t}}\) & Maximize & 11.34 & 15.13 \\ Compressive strength (MPa) & \(f_{\mathrm{c}}\) & Maximize & 33.5 & 53.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Evaluation criteria for optimization process. Figure 12: Optimized mechanical properties of PU–cement mortar. The variation and distribution in the strength of the most sensitive parameter and target parameter in the modeling task are depicted in Figure 14. As noted in Figure 14,b, the flexural and compressive strength nearly follow normal distribution. Most of the datasets are within the superimposed curve, and the mean values are concentrated at the center of the curve, particularly for flexural strength data shown in Figure 14, which reflect  
Figure 14: Variation in and frequency distribution of (**a**) compressive strength and (**b**) flexural strength. Figure 13: Pearson correlation matrix. the lesser variation in the flexural strength dataset. The training data and testing data was separated with vertical dotted line, shown on the left side of Figure 14a,b. Figure 15 presented an agreement plot between the measured and predicted flexural strength from ANN and GPR. It can be observed that predicted values using the GPR model lie closer to the line with minimum deviation than the ANN model. The GPR model achieved a higher coefficient of determination R\({}^{2}\) values = 0.928 and 0.896 in the training and testing phase than the ANN model, with 0.761 and 0.749. Similarly, the GPR model has the lowest MSE, RMSE, and MAE values in both train and testing phases than the ANN model (see Table 11), indicating that the GPR model outperformed ANN in predicting flexural strength in both the training and testing phases.