## 3 Results and Discussion
### Selecting the Configuration of ANNs
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Hidden** \\ **Neuron** \\ \end{tabular} } & \multirow{2}{*}{**Dataset**} & \multicolumn{4}{c}{**Statistical Index**} \\ \cline{3-6}  & & **AARD\%** & **MSE** & **RMSE** & **R2** \\ \hline \multirow{3}{*}{1} & Train & 101.57 & 113,482.04 & 336.871 & 0.9004 \\  & Test & 129.45 & 140,778.92 & 375.205 & 0.9111 \\  & Total & 104.36 & 116,220.03 & 340.911 & 0.9017 \\ \hline \multirow{3}{*}{2} & Train & 53.22 & 55,622.25 & 235.844 & 0.9502 \\  & Test & 68.21 & 279,407.52 & 528.59 & 0.8965 \\  & Total & 54.73 & 78,068.80 & 279.408 & 0.9362 \\ \hline \multirow{3}{*}{3} & Train & 37.34 & 57,662.92 & 240.131 & 0.9519 \\  & Test & 53.07 & 70,940.72 & 266.347 & 0.9407 \\  & Total & 38.92 & 58,994.74 & 242.888 & 0.9507 \\ \hline \multirow{3}{*}{4} & Train & 34.92 & 52,085.74 & 228.223 & 0.96 \\  & Test & 28.75 & 28,003.70 & 167.343 & 0.9048 \\  & Total & 34.3 & 49,670.22 & 222.868 & 0.9588 \\ \hline \multirow{3}{*}{5} & Train & 27.89 & 49,789.84 & 223.136 & 0.957 \\  & Test & 25.89 & 60,526.28 & 246.021 & 0.9626 \\  & Total & 27.69 & 50,866.74 & 225.537 & 0.9576 \\ \hline \multirow{3}{*}{6} & Train & 25 & 44,457.30 & 210.849 & 0.9624 \\  & Test & 32.34 & 66,664.92 & 258.195 & 0.9532 \\  & Total & 25.73 & 46,684.82 & 216.067 & 0.9612 \\ \hline \multirow{3}{*}{7} & Train & 17.86 & 7611.552 & 87.244 & 0.9941 \\  & Test & 39.8 & 23,686.50 & 153.904 & 0.9832 \\ \cline{1-1}  & Total & 20.06 & 9223.933 & 96.041 & 0.9929 \\ \hline \multirow{3}{*}{8} & Train & 16.82 & 5794.544 & 76.122 & 0.995 \\ \cline{1-1}  & Test & 23.06 & 16,642.14 & 129.004 & 0.9919 \\ \cline{1-1}  & Total & 17.45 & 6882.601 & 82.961 & 0.9946 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Determining the greatest hidden neurons for multilayer perceptron (MLP). Considering the minimum MSE value and the maximum R-squared value, eleven hidden neurons in MLP networks are optimum. The efficiencies of different types of ANNs were compared to find a suitable model for pressure drop prediction. Hence, a comparison was performed between the optimum MLP network structure and other ANN models, such as CF, RBF, and GR. The exactness of sensitivity for finding the optimum hidden neurons number is listed in Tables 5-7. It should be noted that the determination of the number of hidden neurons is similar in all kinds of ANNs and has regulations similar to MLP. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Hidden** \\ **Neuron** \\ \end{tabular} } & \multirow{2}{*}{**Dataset**} & \multicolumn{4}{c}{**Statistical Index**} \\ \cline{3-6}  & & **AARD\%** & **MSE** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline \multirow{4}{*}{9} & Train & 12.7 & 3905.889 & 62.497 & 0.997 \\  & Test & 27.03 & 7658.826 & 87.515 & 0.9892 \\  & Total & 14.13 & 4282.324 & 65.439 & 0.9965 \\ \hline \multirow{4}{*}{10} & Train & 12.1 & 3631.65 & 60.263 & 0.9972 \\  & Test & 16.12 & 8260.039 & 90.885 & 0.9893 \\  & Total & 12.5 & 4095.895 & 63.999 & 0.9966 \\ \hline \multirow{4}{*}{**11**} & Train & **10.33** & **5773.065** & **75.981** & **0.9956** \\  & **Test** & **15.91** & **3095.685** & **55.639** & **0.9974** \\  & **Total** & **10.89** & **5504.513** & **74.192** & **0.9957** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._