## 4 Results and Discussion
Figure 5 shows the correlation and residual curve between the experimental values and the predicted values of each model in the testing set. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sets** & \(AARD\) & \(RMSEP\) & \(R^{2}\) \\ \hline Training & 0.3436 & 0.0335 & 0.9771 \\ Validation & 0.3101 & 0.0211 & 0.9886 \\ Testing & 0.5364 & 0.0632 & 0.9438 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistics of the model prediction performance. \(AARD\): Absolute average relative deviation. \(RMSEP\): Root mean square error of prediction. \(R^{2}\): Squared correlation coefficient. Figure 3: Comparison between the predicted and experimental values in the testing set. As shown in Figure 5a, the vertical distance between the prediction data points and the experimental data indicates that the prediction data of CAPSO BP ANN model are close to the experimental values. The prediction performance of the method proposed in this study is better than that of other methods. It can be seen from the residual curve that the error of the model proposed in this study is close to 0 (Figure 5b). Apart from some prediction points that have large errors, the prediction errors are generally smaller than those of other comparison models. Table 5 shows the evaluation results of each model. Figure 4: Contributions of the five molecular descriptors. Figure 5: Comparison of the testing results of each model. In order to verify the performance of each comparison model, the confidence interval (_C.I._) of RMSE in the testing set was calculated [49; 50; 51; 52; 53; 54; 55] (Table 6). Table 5 shows that the accuracy and relevance of the CAPSO BP ANN model have obvious advantages, including the lowest _RMSE_ and the highest \(R^{2}\). The performances of PM3/COSMO and SVM are equivalent to that of the PSO BP ANN model. From Table 6, it can be observed that the CAPSO BP ANN model has the narrowest _C.I._, 90%, 95%, or 99%. From the tables, we can see that the CAPSO BP ANN model with the lowest _RMSE_ and the narrowest _C.I._ is superior to other models. To verify the stability and robustness of the models, an applicability domain study was proposed, as shown in Figure 6. The critical leverage is 0.213. The CAPSO BP ANN model has eight outliers (four outliers from the training set, two outliers from validation set, and two outliers from the testing set) and six influential values. The PSO BP ANN model has 11 outliers, including six outliers from training sets, three outliers from the verification set, and one outlier from the testing set. The SVM model has nine outliers and seven influential values, while the BP ANN model has 10 outliers and six influential values. All of the other values are within the applicability domain. Although all models show good performance, the CAPSO BP ANN proved its superiority, and the highest number of its respective observations was found to be within the warning limits of the defined applicability domain. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Models** & _C.I. (90\%)_ & _C.I. (95\%)_ & _C.I. (99\%)_ \\ \hline PM3/COSMO & (0.04721, 0.24059) & (0.02904, 0.25876) & (0.00067, 0.29450) \\ SVM & (0.03368, 0.17393) & (0.02050, 0.18710) & (0.00054, 0.21303) \\ BP ANN & (0.39482, 0.67598) & (0.36841, 0.70240) & (0.31644, 0.75437) \\ PSO BP ANN & (0.03327, 0.17253) & (0.02019, 0.18561) & (0.00056, 0.21135) \\ CAPSO BP ANN & (0.05066, 0.07574) & (0.04830, 0.07810) & (0.04367, 0.08273) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Confidence intervals of _RMSE_ for each model. _C.I._: Confidence interval. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Models** & _AARD_ & _RMSE_ & \(\mathbf{R^{2}}\) \\ \hline PM3/COSMO & 0.8724 & 0.1439 & 0.8346 \\ SVM & 0.7333 & 0.1038 & 0.8863 \\ BP ANN & 1.2134 & 0.5354 & 0.6958 \\ PSO BP ANN & 0.7229 & 0.1029 & 0.8872 \\ CAPSO BP ANN & 0.5364 & 0.0632 & 0.9438 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical results of each model. _AARD_: Absolute average relative deviation. _RMSEP_: Root mean square error of prediction.