## 2 Methods
### Sequence-to-Sequence Learning for Temporal Dynamics Modeling
The number of hidden units in each layer: the RNN units determine the model's capacity and representational power, where a greater number of units result in a more complex model but also increase the risk of overfitting. 2. The number of layers in the model: The RNN layers also affect the complexity and learning capability of the model. Deeper layers make the modeling structure more sophisticated, but can also lead to potential issues such as gradient vanishing and/or exploding. 3. The diffusion steps of the graph convolutional filter: The diffusion steps affect the model's ability to capture spatial information. A larger number of steps enable the model to better capture the relationships between the vertices in a network that are distant from each other. However, it may also lead to the overfitting of the model and make it more demanding in computation. 4. The dropout parameter of the model: the dropout parameter helps the model mitigate the overfitting issue by randomly dropping a certain proportion of neurons during the training process. Figure 6: Comparison of the effect of each set of experiments on the model accuracy: (**a**) The impact of the number of hidden units; (**b**) The impact of the number of layers; (**c**) The impact of the diffusion steps; (**d**) The impact of dropout parameter. The detailed results with four different hyperparameters on the model are listed in Table 1. In case 1, with the increasing number of hidden units per layer in the neural network, the accuracy of the model gradually improves. However, after reaching a certain point, with 256 hidden units, the model accuracy suddenly decreases. Similarly, in case 2, the model accuracy presents a similar pattern. There is not much difference in accuracy between a one-layer and a two-layer network. However, when the number of layers increases to three, the MAPE increases from 33.3% to 35.5%, and the other performance metrics also show significant degradation. In case 1 and case 2, we can find that the increase in the number of units and layers does not necessarily lead to a monotonic improvement of network performance. The increased depth of the network may bring the gradient to vanish or explode, resulting in unstable updates of the gradient during the training process. Second, with more units and layers, the number of trainable parameters largely increases, potentially leading to overfitting if the volume of training data is limited. It thus reduces the generalization ability of the models. In addition, a more complex network structure prolongs the training time with greater computational costs. In case 3, we test the impacts of different diffusion steps. The diffusion step can be interpreted as proximity to the size of the receptive field. With larger receptive fields, the model captures broader spatial dependencies. However, the complexity of the model also increases. With diffusion steps increasing from one to three, the predicted MAPE decreases from 34% to 33%, but then sharply rises to 47%. It indicates that with greater diffusion steps, the weights of the graph become more evenly distributed. Therefore, the neural network learns less effective knowledge. This also suggests that the number of passengers in a bus line is more similar to the numbers in the closely related bus lines. The distant lines may have little impact, which also confirms the effectiveness of the incorporation of diffusion convolution. With more diffusion steps, the total number of trainable parameters significantly increases, resulting in a longer training time. In case 4, it shows that different settings of dropout parameters do not lead to a significant improvement in performance. In summary, to ensure the accuracy of the model with a greater sensitivity on smaller prediction values, we choose the group of hyperparameters with the smallest MAPE. The chosen set of hyperparameters is: {number of hidden units in each layer = 128, number of layers = 2, diffusion steps = 2, dropout = 0}.