## 2 Methods
### Bb-Ann
According to the predicted values, Tables 7 and 8 show the values of different statistical indices of the models for both training and testing phases. Additionally, Figure 6 shows the scatter plot of the actual and the predicted PPV involving four soft computing techniques and empirical methods only for the testing phase. From these results, it is evident that all the models performed efficiently in predicting PPV in terms of statistical indices. Regarding the prediction accuracy, the \(R^{2}\) was found to be higher in the case of BBO-ANN (\(R^{2}=0.988\)) compared to the other seven models: DIRECT-ANN (\(R^{2}=0.981\)), PSO-ANN (\(R^{2}=0.972\)), MPMR (\(R^{2}=0.971\)), ELM (\(R^{2}=0.965\)), USBM (\(R^{2}=0.747\)), Indian standard (\(R^{2}=0.799\)), and Ambraseys-Hendron (\(R^{2}=0.724\)). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model No.**} & \multirow{2}{*}{**Number of Habitats**} & \multicolumn{2}{c}{**Network Result**} \\ \cline{3-4}  & & \multicolumn{2}{c}{\(R^{2}\)} \\ \cline{3-4}  & & **Train** & **Test** \\ \hline
1 & 30 & 0.889 & 0.834 \\
2 & 50 & 0.972 & 0.984 \\
3 & 100 & 0.96 & 0.968 \\
4 & 150 & 0.974 & 0.976 \\
5 & 200 & 0.97 & 0.974 \\
6 & 250 & 0.976 & 0.98 \\
7 & 300 & 0.976 & 0.982 \\
8 & 350 & 0.976 & 0.984 \\
9 & 400 & 0.976 & 0.978 \\
10 & 450 & 0.974 & 0.974 \\
11 & 500 & 0.974 & 0.978 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Testing the different values of number of habitats with their \(R^{2}\). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Number of**} & \multicolumn{3}{c}{**BBO-ANN**} & \multicolumn{3}{c}{**MPMR**} & \multicolumn{3}{c}{**ELM**} & \multicolumn{3}{c}{**PSO-ANN**} & \multicolumn{3}{c}{**DIRECT-ANN**} & \multicolumn{3}{c}{**USBM**} & \multicolumn{3}{c}{**Indian Standard**} & \multicolumn{3}{c}{**Ambrases-Hendron**} \\ \cline{2-13} \multicolumn{1}{c}{**Data Values**} & **P** & **k** & \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Statistical**} & \multicolumn{8}{c}{**Models**} \\ \cline{2-10}  & **BBO-** & **PSO-** & **MPMR** & **ELM** & **DIRECT-** & **USBM** & **Indian** & **Ambraseys** \\  & **ANN** & **ANN** & **MPMR** & **ELM** & **ANN** & **UsBM** & **Standard** & **–Hendron** \\ \hline MAE & 0.024 & 0.034 & 0.036 & 0.035 & 0.036 & 0.112 & 0.103 & 0.115 \\ RMSE & 0.029 & 0.042 & 0.043 & 0.044 & 0.051 & 0.135 & 0.125 & 0.138 \\ RSR & 0.129 & 0.181 & 0.185 & 0.191 & 0.218 & 0.579 & 0.539 & 0.594 \\ \(d\) & 0.996 & 0.991 & 0.991 & 0.990 & 0.988 & 0.865 & 0.891 & 0.856 \\ R\({}^{2}\) & 0.983 & 0.967 & 0.965 & 0.963 & 0.953 & 0.684 & 0.724 & 0.668 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Statistical indices obtained from the applied predictive models using training phase. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Statistical**} & \multicolumn{8}{c}{**Models**} \\ \cline{2-10}  & **BBO-** & **PSO-** & **MPMR** & **ELM** & **DIRECT-** & **USBM** & **Indian** & **Ambraseys** \\  & **ANN** & **ANN** & **MPMR** & **ELM** & **ANN** & **UsBM** & **Standard** & **–Hendron** \\ \hline MAE & 0.022 & 0.034 & 0.034 & 0.037 & 0.024 & 0.100 & 0.087 & 0.105 \\ RMSE & 0.026 & 0.041 & 0.040 & 0.045 & 0.036 & 0.117 & 0.105 & 0.123 \\ RSR & 0.109 & 0.174 & 0.169 & 0.188 & 0.151 & 0.494 & 0.444 & 0.517 \\ \(d\) & 0.997 & 0.991 & 0.992 & 0.991 & 0.994 & 0.924 & 0.943 & 0.914 \\ \(R^{2}\) & 0.988 & 0.972 & 0.971 & 0.965 & 0.981 & 0.747 & 0.799 & 0.724 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Statistical indices obtained from the applied predictive models using the testing phase. Figure 6: Scatter plot displaying the actual PPV values the predicted PPV values on the testing dataset using the (**a**) BBO-ANN, (**b**) MPMR, (**c**) ELM, (**d**) PSO-ANN, (**e**) DIRECT-ANN, (**f**) USBM, (**g**) Indian Standard, and (**h**) Ambraseys–Hendron methods.