## 4 Experiments
### Performance Evaluation  
#### 4.4.1 Comparison with Baseline Methods  
The proposed STGNN model is compared with various baseline methods for predicting 10, 20, 30, and 60 steps on a simulated metro flow dataset. The results in Table 2 substantiate the superior efficacy of the proposed STGNN model across all evaluated metrics. \begin{table}
\begin{tabular}{c c c c} \hline
**Datasets** & **Nodes** & **Time Span** & **Daily Range** \\ \hline Ours & 13 & 1 January–21 January & 6:00–23:00 \\ \hline Hangzhou & 81 & 1 January 2019–26 January 2019 & 6:00–23:30 \\ \hline \end{tabular}
\end{table} 
Table 1: Dataset description. Among the non-graph methods, LSTM exhibits the least favorable performance, primarily attributed to its inability to effectively capture the recurrent and daily patterns inherent in urban commuter behavior, as well as the broader fluctuations within metro flow dynamics. Autotormer, while slightly outperforming LSTM, struggles to capture the subtle long-term patterns in metro flow variations, indicating limitations in its autocorrelation mechanism. Conversely, the Reformer leveraging attention mechanism, demonstrates superior performance over other non-graph methods in shorter prediction intervals (i.e., 10 and 20 steps). Notably, TimesNet, which scrutinizes complex temporal metro flow patterns from a two-dimensional space, excels over non-graph methods in longer prediction horizons (i.e., 30 and 60 steps). Turning to the graph-based methods, GCN fares relatively poorly owing to its exclusive focus on static spatial features, overlooking the temporal evolution of metro flow distribution. In contrast, T-GCN incorporates temporal dynamics and employs gated recurrent units (GRUs) to capture temporal dependencies, thereby exhibiting notable enhancements in short-term prediction accuracy. STG-NCDE, integrating spatiotemporal controlled differential equations, demonstrates commendable performance in analyzing traffic flow data, albeit its effectiveness wanes in capturing prolonged temporal dependencies within the metro flow. ASTGCN and ASTGNN excel in capturing spatial-temporal dependencies, with ASTGNN surpassing all methods in short-term predictions (10 and 20 steps). Notably, STGNN outperforms ASTGNN in 30 and 60 steps, underscoring its capability to enhance long-term prediction accuracy. Specifically, STGNN exhibits improvements over ASTGNN by 15.4% and 5.4% in terms of RMSE and by 0.6% and 0.3% in MAE for intervals of 30 and 60 steps, respectively. Tables 3 and 4 illustrate the average prediction performance over 10, 20, 30, and 60 steps ahead on the Hangzhou metro flow dataset. The findings consistently affirm the superior performance of the STGNN model across all evaluated metrics. Notably, among the non-graph methods, Reformer outperforms TimesNet, suggesting that the efficacy of analyzing complex spatial-temporal patterns within metro flow data in a two-dimensional space diminishes with an expanded node count. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{2}{c}{**Prediction Step = 10**} & \multicolumn{2}{c}{**Prediction Step = 20**} & \multicolumn{2}{c}{**Prediction Step = 30**} & \multicolumn{2}{c}{**Prediction Step = 60**} \\  & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** & **RMSE** & **MAE** \\ \hline LSTM & 6.40 & 3.68 & 6.65 & 3.81 & 7.43 & 4.10 & 9.62 & 5.39 \\ Reformer & 6.80 & 3.25 & 7.38 & 3.43 & 8.68 & 3.98 & 9.27 & 4.56 \\ Autoformer & 6.45 & 2.85 & 6.64 & 2.98 & 7.55 & 3.58 & 9.60 & 4.77 \\ TimesNet & 5.41 & 2.38 & 6.02 & 2.61 & 6.46 & 2.98 & 7.41 & 3.39 \\ \hline GCN & 9.33 & 5.04 & 10.11 & 6.02 & 10.59 & 6.18 & 11.17 & 7.55 \\ T-GCN & 5.85 & 2.76 & 6.54 & 3.14 & 7.30 & 3.35 & 8.72 & 4.22 \\ STG-NCDE & 7.39 & 3.94 & 8.30 & 3.89 & 9.93 & 4.66 & 10.81 & 5.89 \\ ASTGCN & 5.14 & 2.19 & 5.81 & 2.61 & 6.92 & 2.69 & 7.71 & 3.42 \\ ASTGNN & 4.89 & 2.01 & 5.55 & 2.46 & 6.71 & 2.47 & 7.58 & 3.29 \\ \hline STGNN (ours) & 4.58 & 1.91 & 5.07 & 2.23 & 5.67 & 2.39 & 7.17 & 3.08 \\ \hline \hline \end{tabular}
\end{table}