## 3 Results and Discussion
### Selecting the Configuration of ANNs
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**BIFidden Neuron**} & \multirow{2}{*}{**Spread**} & \multirow{2}{*}{**Dataset**} & \multicolumn{5}{c}{**Statistical Index**} \\ \cline{4-7}  & & & **AARD\%** & **MSE** & **RMSE** & **R\({}^{2}\)** \\ \hline \multirow{4}{*}{1} & \multirow{4}{*}{2.1212} & Train & 245.61 & 168,040.37 & 409.927 & \multirow{4}{*}{0.8892} \\  & & Test & 113.14 & 235,995.95 & 485.794 & 0.8892 \\  & & Total & 232.32 & 174,856.58 & 418.159 & 0.8624 \\ \hline \multirow{4}{*}{2} & \multirow{4}{*}{1.0101} & Train & 127.73 & 132,611.39 & 364.158 & 0.8856 \\  & & Test & 131.98 & 150,529.48 & 387.981 & 0.8964 \\  & & Total & 128.15 & 134,408.64 & 366.618 & 0.8862 \\ \hline \multirow{4}{*}{3} & \multirow{4}{*}{0.7071} & Train & 98.76 & 101,348.30 & 318.352 & 0.9176 \\  & & Test & 141.53 & 94,193.30 & 306.909 & 0.8996 \\  & & Total & 103.05 & 100.630.63 & 317.223 & 0.9151 \\ \hline \multirow{4}{*}{4} & \multirow{4}{*}{0.8081} & Train & 79.53 & 95,710.78 & 309.372 & 0.9196 \\  & & Test & 140.55 & 103,820.68 & 322.212 & 0.9242 \\  & & Total & 85.65 & 96,524.24 & 310.684 & 0.919 \\ \hline \multirow{4}{*}{5} & \multirow{4}{*}{0.6061} & Train & 84.45 & 73,306.36 & 270.751 & 0.9367 \\  & & Test & 69.94 & 100,134.85 & 316.441 & 0.939 \\  & & Total & 83 & 75,997.36 & 275.676 & 0.9368 \\ \hline \multirow{4}{*}{6} & \multirow{4}{*}{0.6061} & Train & 84.04 & 73,687.32 & 271.454 & 0.9413 \\  & & Test & 66.43 & 49,203.87 & 221.819 & 0.9572 \\  & & Total & 82.28 & 71,231.53 & 266.892 & 0.9404 \\ \hline \multirow{4}{*}{7} & \multirow{4}{*}{0.6061} & Train & 78.14 & 68,354.82 & 261.448 & 0.9443 \\  & & Test & 58.43 & 83,310.02 & 288.635 & 0.9363 \\  & & Total & 76.17 & 69,854.89 & 264.301 & 0.9419 \\ \hline \multirow{4}{*}{8} & \multirow{4}{*}{0.6061} & Train & 71.69 & 63,860.08 & 252.706 & 0.9466 \\  & & Test & 55.92 & 79,202.58 & 281.43 & 0.9464 \\  & & Total & 70.11 & 65,398.99 & 255.732 & 0.9461 \\ \hline \multirow{4}{*}{9} & \multirow{4}{*}{0.6061} & Train & 67.33 & 56,511.36 & 237.721 & 0.9546 \\  & & Test & 73.26 & 122,784.88 & 350.407 & 0.921 \\  & & Total & 67.92 & 63,158.85 & 251.314 & 0.9471 \\ \hline \multirow{4}{*}{10} & \multirow{4}{*}{0.7071} & Train & 63.84 & 65,435.85 & 255.804 & 0.9468 \\  & & Test & 78.67 & 88,688.61 & 297.806 & 0.9383 \\  & & Total & 65.33 & 67,768.20 & 260.323 & 0.9431 \\ \hline \multirow{4}{*}{**11**} & \multirow{4}{*}{**0.7071**} & Train & **57.93** & **57,530.63** & **239.855** & **0.9467** \\  & & Test & **70.16** & **143,614.80** & **378.965** & **0.9632** \\ \cline{1-1}  & & **Total** & **59.16** & **66,165.21** & **257.226** & **0.9469** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance of radial basis function (RBF) model with different hidden neurons. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Spread**} & \multirow{2}{*}{**Dataset**} & \multicolumn{5}{c}{**Statistical Index**} \\ \cline{3-6}  & & **AARD\%** & **MSE** & **RMSE** & **R\({}^{2}\)** \\ \hline \multirow{4}{*}{0.0056} & Train & 2.42 & 2688.514 & 51.851 & 0.9979 \\  & Test & 34.47 & 129,915.53 & 360.438 & 0.9381 \\ \cline{1-1}  & Total & 7.63 & 15,449.89 & 124.298 & 0.9881 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Accuracy of the general regression (GR) for prediction. Rationally, the AARD% values of the best models are minimum. As indicated in Table 8, the best prediction of the pressure drop belongs to the GR model, compared to other models. By considering the values obtained as the statistical error of pressure drop, the AARD% of the GR model (with the error value of 7.63) yielded the best prediction, compared with other ANN models of MLP (10.89), RBF (59.16), and CF (10.65). It should be noted that the statistical indices of R\({}^{2}\), MSE, RMSE, and AARD% served as the basis for choosing this model amongst a set of 1620 distinct models (1100 RBF models, 200 CF models, 100 GR models, 220 MLP models).