## 2 Methods
### Sequence-to-Sequence Learning for Temporal Dynamics Modeling
Nonetheless, once the DCRNN model is well trained, the running speed of the model for prediction tasks is not inferior to other classic RNN models. ## 5 Conclusions

This article utilizes an end-to-end deep learning framework for the short-term forecasting of the passenger flows of each bus line in a bus transit network. A graph-based \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **MAPE** & **MAE** & **RMSE** \\ \hline DCRNN & 33.32\% & 6.36 & 9.50 \\ LSTM & 38.06\% & 6.43 & 9.76 \\ GRU & 38.65\% & 6.56 & 10.03 \\ Static & 137.45\% & 22.64 & 34.81 \\ Historical Average & 112.32\% & 15.07 & 22.66 \\ VAR & 89.48\% & 13.25 & 20.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model comparison results. DCRNN structure is developed to extract and adaptively learn the relationships between bus lines in the network since bus passengers interchange between these lines. As the bus networks are not grid-like, we adopt graph convolution to learn the topological features of the network. The model considers the impacts of distance decay in a series of spatially correlated vertices in a graph by introducing the diffusion convolution process. The RNN and Seq2 Seq structures incorporated in the model can also capture the time-series information. The proposed DCRNN model is performed using 10-month consecutive transactional data from the bus services in Jiading of Shanghai, which shows greater accuracy, especially in predicting low-demand bus lines, compared with classic RNN models. It must be noted that there are also limitations to this study. First, the data adopted in this work only include transaction records with transit IC cards and Quick Response (QR) code scanning. The information about passengers paying in cash is not included. Although the share of cash-paying passengers is relatively low, the lack of such information may also impact the accuracy of the model. In addition, the passengers do not swap their IC cards or scan the QR codes again when alighting. Therefore, in this work, the bus passenger flow means the number of passengers boarding a bus line but not in a specific bus vehicle. To get the accurate passenger flow in each bus vehicle, additional work needs to be conducted for alighting stop inference. For future research, external information such as weather information can be considered to enrich the inputs of the model. Furthermore, the prediction of the number of passengers boarding at each bus stop and the passenger flow in each bus vehicle should also be investigated with more detailed data at the stop level. Conceptualization, X.Z. and Y.S. ; methodology, Y.S. ; software, validation, and data curation, X.Z. ; writing--original draft preparation, X.Z. and Y.S. ; writing--review and editing, Y.S. ; visualization, X.Z. ; supervision, Y.S. All authors have read and agreed to the published version of the manuscript. This study is supported by the National Key R&D Program of China (2019 YFB1600703) and the Shanghai Science and Technology Committee (22 dz1203300). The authors thank Shanghai Jiading Public Transport Co., Ltd. for providing the data for this research. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy and company policy. The authors declare no conflict of interest. ## References

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