# Urban PM2.5 Concentration Prediction via Attention-Based CNN-LSTM
## 4 Results and Discussion
### Model Comparison  
To verify the feasibility and efficacy of the proposed model in this paper, we compared our proposed AC-LSTM model with six state-of-the-art models, including support vector regression (SVR) [6], random forest regression (RFR) [9], multilayer perceptron (MLP) [25], simple RNN [9; 26], LSTM [27], and CNN-LSTM [28]. After training all the models with the same training and testing datasets, the PM\({}_{2.5}\) concentrations of all stations at different time scales were predicted for performance evaluation. We selected appropriate time lag and hyperparameters for different scale prediction tasks in our AC-LSTM model in the same way. Furthermore, each experiment was repeated five times, and the averaged results were used for comparison, as shown in Tables 6 and 7. The prediction results from our approach and six others in terms of MAE and RMSE are compared in Tables 6 and 7, where several interesting observations can be highlighted. Firstly, the performance of all models gradually deteriorated as the time to predict became longer. For this purpose, the detailed comparison results of each model for different scale prediction tasks are shown in Figures 11-14 in Appendix A. From Figures 11-14, it is more obvious that the prediction accuracy of the three models (SVR, RFR, and MLP) worsened as the time to predict became longer. The lack of sufficient and directly relevant input data makes it difficult to predict PM\({}_{2.5}\) concentrations for longer future periods. Figure 8: The loss convergence of deep learning methods in one-hour PM\({}_{2.5}\) prediction: (**a**) loss convergence of LSTM, convolution neural network (CNN)–LSTM, and AC-LSTM models; (**b**) loss convergence of simple recurrent neural network (RNN) model. Secondly, the performance of the four deep learning methods, i.e., simple RNN, LSTM, CNN-LSTM, and AC-LSTM, was much better than that of the three traditional shallow learning methods, SVR, RFR, and MLP, particularly in predicting over an hour. As can be seen from Tables 4 and 5, the MAE and RMSE of the four deep learning methods were relatively low. The predicted values of the four models on the multiscale prediction task were closer to the observed values in Figures A1-A4. Thirdly, as can be seen from Figure A1 and the tables, the prediction accuracy of the three non-deep learning models on the one-hour prediction task was comparable to that of the four deep learning models. However, according to the goodness-of-fit plots for all models in Figure A5 the predicted value distributions of the three models were relatively dispersed, and their \(R^{2}\) values were lower than those of the four deep learning models. The predicted value distributions of the four deep learning models were close to a 45-degree line (\(y=x\)). This, on one hand, shows the limitation of conventional approaches; on the other hand, it fully demonstrates the superior performance of the deep learning models in modeling long-term dependency for effective prediction of the PM\({}_{2.5}\) concentration in the future. The reason for this is that these three traditional shallow models cannot process time-series data and fail to learn the temporal correlation of air pollutants. By contrast, simple RNN is able to predict PM\({}_{2.5}\) concentrations over the next 24 h. Compared to simple RNN, the three models of LSTM, CNN-LSTM, and AC-LSTM bring further improved result from overcoming the defects of the conventional RNN. Furthermore, according to the tables, the MAE and RMSE of AC-LSTM models were the lowest compared to other benchmarking models, except for the MAE for the 13-24 h prediction task. The predicted values of AC-LSTM models on the multiscale prediction task were closer to the observed values in Figures A1-A4. Moreover, the \(R^{2}\) of the AC-LSTM model in the one-hour PM\({}_{2.5}\) prediction task in Figure A5 was highest. After adding the attention mechanism, AC-LSTM could outperform the LSTM and CNN-LSTM in multiscale prediction tasks.