## 3 Results and Discussions
### Jet-Cleaning Model Prediction  
Figure 9 summarizes the \(R^{2}\) and \(MAE\) values for predictions generated using the nine artificial intelligence algorithms. As shown, algorithms achieving \(R^{2}>0.90\) include support vector machines (SVM), extreme gradient boosting (XGBoost), Gaussian kernel regression (GKR), and artificial neural networks (ANN). In contrast, decision trees (DT) exhibited the lowest \(R^{2}\) value of 0.73. Consequently, the ANN demonstrated optimal regression performance with the minimal \(MAE\) and was therefore selected in this study to predict jet-cleaning performance.  
The iteration process of the artificial neural network ANN model after training is shown in Figure 10. In Figure 10, the vertical coordinate is the mean square error \(MSE\), the horizontal coordinate is the number of iterations of the artificial neural network, the blue, green, and red curves represent the whole process of training, validation, and testing, respectively, and the green circle represents the point that satisfies the set condition after 21 iterations. As shown in Figure 11, the coefficient of determination \(R^{2}\) of the training set, validation set, test set, and all sets are 0.99972, 0.99691, 0.99832, and 0.9991, respectively, which are above 0.995, proving that the artificial neural network model can predict with high accuracy. This is consistent with [PERSON] et al. [51], who demonstrated that neural  
Figure 9: The \(R^{2}\) and \(MAE\) values for predictions generated using the nine artificial intelligence algorithms.  
networks can predict with high accuracy. Therefore, the artificial neural network model can replace the CFD numerical model, which is complicated and time-consuming in the calculation process, so as to predict the cleaning performance of aerated jets with different combinations of nozzles' parameters relatively quickly and accurately.  
Figure 11: The coefficient of determination (\(R^{2}\)) values for the training set, validation set, test set, and all sets.  
Figure 10: The variation of the mean squared error (_MSE_) across 21 training epochs.  
To verify the prediction ability of the artificial neural network ANN agent model on the performance indicators of aerated jet cleaning (peak wall shear stress, action area, and cleaning water consumption), this study selects a variety of parameter combinations of the aerated jet cleaning model to carry out the comparison between the artificial neural network ANN prediction and the CFD numerical simulation to validate the prediction. By systematically comparing the calculation results of the two methods, it is found that the evaluation index values of aerated jet cleaning obtained using the artificial neural network ANN agent model and CFD numerical simulation are in good agreement. Their relative errors are always lower than 3%, as shown in Figure 12, which proves that the model has a high degree of accuracy, validity, and generalization ability. The study confirms that the artificial neural network (ANN) agent model can not only accurately characterize the mapping relationship between the geometric parameters of the injector and the cleaning effect, but also has a significant computational efficiency advantage over traditional CFD numerical simulations. Based on this, the artificial neural network ANN agent model can be combined with genetic algorithms to provide a reliable basis for adaptation assessment for the optimization of the subsequent aerated jet cleaning model.