## 4 Results and Discussion
### Experimental Results  
#### 4.2.1 Performance Comparisons  
We compared FedDeep with five state-of-the-art baselines, including HA [20], SVR [21], LSTM [23], CNN-LSTM [24], and GAT-LSTM [25] for \(PM_{2.5}\) forecasting of the next 12 h for the 133 sites distributed in the 13 prefecture-level cities of Jiangsu province. The comparison results are displayed in Table 3. TT in this table stands for the total training time. GPUM indicates the utilization of GPU memory during the training process. '-' indicates that the model does not adopt GPU for running. FedDeep (w/o) indicates that only one central cloud was used to train and infer urban \(PM_{2.5}\). \begin{table}
\begin{tabular}{c c c} \hline \hline  & The number of heads in MHSA & \(N_{h}=4\) \\ \cline{2-3}  & The dimensions of each head & \(N_{d}=8\) \\ \cline{2-3}  & The MHSA layers & \(L_{MHSA}=3\) \\ \cline{2-3}  & LSTM layers in the spatio-temporal learning layer & \(L_{LSTM(ST)}=1\) \\ \cline{2-3}  & LSTM layers in the decoder of seq2 seq & \(L_{LSTM(dec)}=1\) \\ \hline  & The number of heads in MHSA & \(N_{h}=4\) \\ \cline{2-3}  & The dimensions of each head & \(N_{d}=8\) \\ \cline{2-3}  & The MHSA layers & \(L_{MHSA}=3\) \\ \cline{2-3}  & LSTM layers in the spatio-temporal learning layer & \(L_{LSTM(ST)}=1\) \\ \cline{2-3}  & LSTM layers in the decoder of seq2 seq & \(L_{LSTM(dec)}=1\) \\ \hline \(d_{model}\) & 32 \\ \hline Historical timesteps & \(P=12\) \\ \hline Prediction timesteps & \(Q=12\) \\ \hline The Central Cloud & 1 A100 card \\ \hline ECS & 13 Nvidia 3090 Ti GPU cards \\ \hline Batchsize & 32 \\ \hline Learning rate & 0.0001 \\ \hline Epochs & 64 \\ \hline Optimizer & Stochastic Gradient Descent \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Implementation details of FedDeep. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **MAE** & **RMSE** & **R2** & **TT** & **GPU** \\ \hline HA & 23.19 & 36.57 & 0.869 & 24.87 min & - \\ SVR & 22.75 & 32.36 & 0.878 & 25.76 min & - \\ LSTM & 17.66 & 26.34 & 0.904 & 43.55 min & 1.53 GB \\ CNN-LSTM & 15.64 & 24.90 & 0.913 & 54.19 min & 2.45 GB \\ GAT-LSTM & 13.13 & 21.82 & 0.945 & 67.20 min & 3.27 GB \\ FedDeep (w/o) & 12.43 & 19.32 & 0.973 & 65.28 min & 3.12 GB \\ FedDeep & 12.38 & 19.19 & 0.972 & 28.32 min & 0.87 GB \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The performance comparison of the 12 h \(PM_{2.5}\) forecasting task at 133 air quality monitoring sites of 13 prefecture-level cities in Jiangsu province. _(1) Prediction Accuracy Analysis_. We measured the forecasting accuracy of the models with three evaluation metrics (e.g., MAE, RMSE, and \(R^{2}\)), and found that FedDeep outperformed the other baslines, thus demonstrating the effectiveness of our proposed model. In detail, the non-deep learning models HA and SVR had the lowest prediction accuracy. This was mainly because the simple structures of these models are unsuitable for meeting the requirements of processing multi-site \(PM_{2.5}\) data from multiple urban regions. Compared with HA and SVR, LSTM presented a higher prediction accuracy. Nonetheless, LSTM only attended to temporal dependencies in \(PM_{2.5}\), and its accuracy was lower than the models that simultaneously captured spatio-temporal correlations (CNN-LSTM, GAT-LSTM, and FedDeep). Among the three spatio-temporal networks, CNN-LSTM was inferior to the others. One potential reason exists: the distributions of monitoring sites were irregular and treated as a graph in each urban region. When CNN is adopted to capture spatial dependencies, this requires converting the site data into a standard form, such as a 2D-matrix, which brings about a loss of crucial spatial information. In contrast, GAT-LSTM and FedDeep directly processed the graph structure, thus preserving more spatial information. Compared to GAT-LSTM, FedDeep provided a higher prediction accuracy. This result demonstrates that our proposed model could effectively mine spatio-temporal correlations in urban multi-site \(PM_{2.5}\) data by taking advantage of its sensible structural design.