## 4 Experimental Results and Discussion
### LR-TCN Comparison Experiment  
To thoroughly evaluate the performance of LR-TCN, eight comparison models were selected to experimentally analyze and compare their estimation results across seven metrics, highlighting the performance advantages of LR-TCN. When selecting comparison models, considering the characteristics of the dataset in this paper, preference was given to models designed for time series data. The models include LSTM [15], GRU [16], SRU [44], TCN [23], Gaussian-TCN [34], GL-TCN [33], DD-TCN [32], D-TCN [45], and LR-TCN, shown in Table 3. From Table 3, it can be seen that LR-TCN performs the best on seven metrics except for SMAPE. However, compared to some other models, LR-TCN still has an advantage in terms of SMAPE, and it requires the least training time compared to other improved TCN models. Compared with TCN, the indicator RMSE has increased by 12.9%, the metric MAE has increased by 11.3%, and the metric R\({}^{2}\) has increased by 3.8%. The seven metrics of the GRU model outperform the LSTM and TCN models. Compared to the TCN, the RMSE metric is reduced by 8.9%, the MAE metric is reduced by 18.3%, and the SMAPE metric is reduced by 11.6%. The R\({}^{2}\) value of the GRU model is 0.970, ranking second among all models, just behind LR-TCN, indicating a high goodness of fit.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **RMSE** & **MSE** & **MAE** & **SMAPE** & **NAE** & **R\({}^{2}\)** & **IA** \\ \hline Original TCN[1,2,4,8,Re] & 18.787 & 352.977 & 13.067 & 23.342 & 0.042 & 0.862 & 0.959 \\ TCN[1,2,4,8,Re] & 18.773 & 352.442 & 12.887 & 22.753 & 0.041 & 0.862 & 0.962 \\ TCN[1,2,4,8,Lr] & 17.686 & 312.809 & 11.401 & 20.356 & 0.036 & 0.878 & 0.966 \\ TCN[Re] & 17.929 & 321.462 & 11.917 & 21.541 & 0.038 & 0.874 & 0.966 \\ TCN[Lr] & 17.298 & 299.246 & 11.221 & 20.059 & 0.036 & 0.883 & 0.967 \\ CNN-TCN[1,2,4,8,Re] & 16.433 & 270.064 & 10.680 & 19.542 & 0.034 & 0.894 & 0.970 \\ CNN-TCN[1,2,4,8,Lr] & 16.529 & 273.223 & 10.695 & 19.596 & 0.034 & 0.893 & 0.970 \\ CNN-TCN[Re] & 16.504 & 272.414 & 10.762 & 20.174 & 0.034 & 0.893 & 0.971 \\ CNN-TCN[Lr] & 16.306 & 265.900 & 10.593 & 20.440 & 0.034 & 0.896 & 0.972 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Ablation experiments for regression estimation of PM\({}_{2.5}\) concentration in monitoring station 1001.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **RMSE** & **MSE** & **MAE** & **SMAPE** & **NAE** & **R\({}^{2}\)** & **IA** & **Time** \\ \hline LSTM & 18.719 & 350.411 & 11.941 & 26.959 & 0.036 & 0.863 & 0.963 & 21.46 s \\ GRU & 17.090 & 292.075 & 10.678 & 20.628 & 0.034 & 0.886 & 0.970 & 24.10 s \\ SRU & 17.223 & 296.632 & 10.543 & 20.720 & 0.033 & 0.884 & 0.969 & 23.29 s \\ TCN & 18.787 & 352.977 & 13.067 & 23.342 & 0.042 & 0.862 & 0.959 & 64.66 s \\ Gaussian-TCN & 17.592 & 309.499 & 11.427 & 20.874 & 0.036 & 0.879 & 0.969 & 80.38 s \\ GL-TCN & 17.349 & 300.988 & 11.361 & 21.106 & 0.036 & 0.882 & 0.968 & 67.69 s \\ DD-TCN & 17.621 & 310.518 & 11.222 & 19.906 & 0.036 & 0.879 & 0.969 & 108.34 s \\ D-TCN & 17.675 & 312.411 & 11.211 & 19.921 & 0.036 & 0.878 & 0.968 & 80.01 s \\ LR-TCN & 16.306 & 265.900 & 10.593 & 20.440 & 0.034 & 0.896 & 0.972 & 55.62 s \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison experiments of regression estimation monolithic models for PM\({}_{2.5}\) concentration in monitoring station 1001.