## 3 Results and Discussion
With the three features (\(x_{1},x_{2},x_{5}\)), the resulting MLR prediction of the river flow can be expressed in the following equation:  
\[\hat{y}~{}=~{}(2120.47)x_{1}+(502.76)x_{2}-(1185.77)x_{5}+447.32 \tag{22}\]  
The MLR prediction on the test dataset produces a regression coefficient (\(R^{2}\)) of 0.73 and an RMSE of 279.3 cms, which is lower accuracy compared to the FFNNPSO and CFNNPSO prediction. This makes sense since MLR assume linear relation on the variables. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**ANN Structure**} & \multicolumn{2}{c}{**FFNNPSO**} & \multicolumn{2}{c}{**CFNNPSO**} \\ \cline{2-10} \# & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Testing**} & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Testing**} \\ \cline{2-10}  & **Number of Hidden Layer Neurons** & \(R^{2}\) & **RMSE** & \(R^{2}\) & **RMSE** & \(R^{2}\) & **RMSE** & \(R^{2}\) & **RMSE** \\ \hline
1 & [5] & 0.80 & 171.2 & 0.87 & 198.4 \({}^{\star}\) & 0.80 & 167.6 & 0.79 & 249.6 \\ \hline
2 & [10] & 0.81 & 165.4 & 0.73 & 284.3 & 0.80 & 168.7 & 0.85 & 208.4 \({}^{\star}\) \\ \hline
3 & [20] & 0.81 & 167.4 & 0.85 & 213.2 \({}^{\star}\) & 0.80 & 169.5 & 0.86 & 203.5 \({}^{\star}\) \\ \hline
4 & [5 + 5] & 0.83 & 157.3 & 0.80 & 243.7 & 0.81 & 165.6 & 0.75 & 270.6 \\ \hline
5 & [10 + 10] & 0.81 & 166.2 & 0.85 & 208.0 \({}^{\star}\) & 0.81 & 166.6 & 0.68 & 307.3 \\ \hline
6 & [20 + 20] & 0.82 & 162.4 & 0.43 & 412.8 & 0.79 & 172.2 & 0.28 & 462.1 \\ \hline
7 & [5 + 10] & 0.80 & 171.7 & 0.85 & 213.9 & 0.81 & 165.1 & 0.38 & 429.2 \\ \hline
8 & [10 + 5] & 0.83 & 158.4 & 0.74 & 279.3 & 0.81 & 163.9 & 0.73 & 284.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results on ANNs trained with 4 features (\(x_{1},x_{2},x_{4},x_{5}\)) using the Particle Swarm Optimization (PSO) algorithm. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**FFNNPSO**} & \multicolumn{2}{c}{**CFNNPSO**} \\ \cline{2-10} \# & **Number of Hidden Layer Neurons** & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Testing**} & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Testing**} \\ \cline{2-10}  & \(R^{2}\) & **RMSE** & \(R^{2}\) & **RMSE** & \(R^{2}\) & **RMSE** & \(R^{2}\) & **RMSE** \\ \hline
1 & [5] & 0.80 & 171.4 & 0.87 & 197.6 \({}^{\star}\) & 0.80 & 168.0 & 0.85 & 209.4 \\ \hline
2 & [10] & 0.80 & 170.2 & 0.76 & 268.3 & 0.77 & 181.6 & 0.88 & 191.1 \({}^{\star}\) \\ \hline
3 & [15] & 0.80 & 170.1 & 0.78 & 254.2 & 0.80 & 170.6 & 0.87 & 198.8 \({}^{\star}\) \\ \hline
4 & [20] & 0.78 & 174.2 & 0.78 & 254.7 & 0.78 & 177.9 & 0.87 & 199.5 \({}^{\star}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results on FFNN and CFNN trained using PSO with 3 features (\(x_{1},x_{2},x_{5}\)). Finally, the results of this study can be improved from the enhancement of data and improvement of the algorithm. Data-driven predictive modelling relies on the quantity and quality of the recorded data. Moreover, collection of field data is a costly practice that provides a series of snapshots of watercourse behaviour and supplements existing information. Therefore, it is essential to carry out a collaborative desk analysis to gather established existing records from different sources (consultants, environment agency or water services company) to improve current understanding and expertise deficiencies [38]. Additionally, hydrological and mathematical models play a significant role in the forecasting of river basins using field data obtained from different temporal and spatial scales [39].