## 4 Results and Discussion  
A three-layer (5-7-1) CAPSO BP ANN prediction model was established to predict the pKa values of the compounds. MSE values were adopted as performance metrics for the model. To ensure the  
Figure 1: Optimization comparison diagram of the number of hidden layer neurons. MSE: Mean square error. generalization ability, the model was run 10 times. The optimized CAPSO BP ANN parameters used in this paper are summarized in Table 3.  
First, 188 sets of data from the training set and 40 sets of data from the validation set were respectively used for model training and validation. Figure 2 shows the comparison between the experimental value and the predicted value in the training set and validation set, respectively. The circle and square respectively represent the predicted values of the model in the training set and the validation set. The vertical distances between the predicted data points and lines represent the absolute error of predicted values and experimental values. In the training set, the predicted value of the model training is distributed around the actual value, indicating the high coincidence degree. From the vertical distance between the prediction data points and the line, we can see that the prediction error of the model is small and that the prediction accuracy is high. In the validation set, the prediction results are significantly better than those in the training set, indicating that the training effect of the model is good. Figure 3 shows the correlation between the actual value and the predicted value of the model in the testing set. In the testing set, the predicted value of the model is also consistent with the actual value. Table 4 shows the results of the model in the training set, validation set, and testing set. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Training data proportion & 70\% \\ Validation data proportion & 15\% \\ Testing data proportion & 15\% \\ Training algorithm & CAPSO \\ Number of input neurons & 5 \\ Number of hidden neurons & 7 \\ Number of output neuron & 1 \\ Number of particles in CAPSO & 50 \\ Maximum iteration times & 1000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimized model parameters. Figure 2: Comparison between the predicted and experimental values in the training and validation sets. The prediction results of the model in each subset are good and the prediction error is small, indicating the better comprehensive performance. The prediction performance of the model is better in terms of prediction accuracy and correlation. The above results prove that the prediction performance of the model is excellent. In this paper, the partial derivative (PaD) method [13; 54] was adopted to assess the sensitivity of the output against slight changes of the five molecular descriptors in the inputs. Figure 4 shows the contributions of the five input variables (five molecular descriptors). Quantitatively, the Randic index (order 3) (MD2) contributes the most; the relative number of N atoms (MD1) and maximum net atomic charge (MD5) contribute roughly the same proportion (about 20%). The contributions of RNCG relative negative charged (QMNEG/QTMINUS) (Quantum-Chemical PC) (MD3) and RNCS relative negative charged SA (SAMNEG * RNCG) (Zefirov's PC) (MD4) are relatively small, but they all belong to the electrostatic descriptors. Among the four types of descriptors, electrostatic descriptors contribute the most, followed by topological descriptors and constitutional descriptors, and the quantum descriptors contribute the least (Figure 4). Moreover, three artificial intelligence models, BP ANN, SVM, and PSO BP ANN, were selected as the comparison models. In addition, [PERSON] et al. [50] used PM6, PM7, PM3, AM1, and DFTB3 methods to predict the pKa values of some amine groups and indicated that PM3/COSMO was the best pKa prediction method. Therefore, in order to verify the performance of the model, the PM3/COSMO model [50] was selected as the comparison model in the study.