## 3 Results and Discussion
### Comparison of CNN with Other Neural Networks  
As mentioned before, the CNN method is made up of two steps for predicting pressure drop parameters. The first is by applying it in committee neural network methodology to determine pressure drop parameters, and the second one is implementing it in a genetic algorithm to find the share (weight) of each algorithm in building CNN.  
By joining the outputs of the three models MLP, GR, and CF, the microchannel pressure drop was predicted in more precision. It should be noted that, due to the high error of the RBF method, the predicted data from this model has not been used in the CNN model. To describe the coefficient of every single model, GA is merged as follows:  
\[Y_{CNN}=(aY_{MLP}+bY_{GR}+cY_{CF}+d) \tag{8}\]  
where calculated values of \(a\), \(b\), \(c\) and \(d\) are 0.0534, 0.9281, 0.01725, and \(-\)0.1574, respectively. Figure 4 illustrates the actual outputs versus the values of predicted outputs by CNN for the entire dataset of pressure drop. It is evident that the CNN model is remarkably capable of forecasting results for the whole dataset, as the concentration of symbols around the solid 45\({}^{\circ}\) line confirms this.  
The absolute error histogram for the entire data by the CNN network is presented in Figure 5, which is an approximately normal distribution. As shown, it can be seen that the absolute error distribution histogram is stable, and most of the prediction errors belong to the \(-\)200 to 200 absolute error intervals.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Dataset**} & \multicolumn{4}{c}{**Statistical Index**} \\ \cline{3-6}  & & **AARD\%** & **MSE** & **RMSE** & **R\({}^{2}\)** \\ \hline \multirow{3}{*}{MLP} & 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 \multirow{3}{*}{CF} & Train & 9.78 & 2434.457 & 49.34 & 0.998 \\  & Test & 18.48 & 7820.685 & 88.435 & 0.9926 \\  & Total & 10.65 & 2974.717 & 54.541 & 0.9976 \\ \hline \multirow{3}{*}{GR} & Train & 2.42 & 2688.514 & 51.851 & 0.9979 \\  & Test & 34.47 & 129,915.53 & 360.438 & 0.9381 \\  & Total & 7.63 & 15,449.89 & 124.298 & 0.9881 \\ \hline \multirow{3}{*}{RBF} & 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 8: Comparison of the statistical values for various artificial neural network (ANN) models.  
The comparison between the suggested CNN model and the three other models of MLP, CF, and GR are presented in Figure 6, based on the statistical indices of AARD%. This figure indicates the performance superiority of the CNN model, compared with the other models. In other words, it depicts the capability of CNN to increase the accuracy of the prediction.  
Figure 4: Performance of the committee neural network (CNN) for prediction.  
Figure 5: Histogram of CNN for all data.  
Finally, the predicted values from the CNN model representing microchannel pressure drop prediction were evaluated for different experimental datasets. The AARD% values in Figure 7 were obtained to compare the predicted values and experimental datasets. As can be seen, the CNN model can predict all experimental data with great accuracy. However, the predictive precision of the CNN model can slightly depend on the distribution pattern of the data, as expected. This is consistent with the recent data of [41].  
Figure 6: Evaluation between predicted values of three artificial neural network models and committee neural network.  
Figure 7: Evaluation of predicted values with regards to various experimental datasets in the literature.