## 3 Methods
### Dual-Channel Deep Counterfactual Prediction Model for OD Matrix Prediction
#### 3.3.3 Loss Function and Prediction Accuracy Evaluation Metrics
The black line is Non-incident flow, the red line is Incident flow, and the blue area is Incident period, demonstrating the real-world relevance and potential applicability of the model through descriptive analysis of passenger flow patterns under various incident conditions. It should be noted that this study employs a two-stage training approach. The first stage uses a dataset of OD flows from a continuous week of normal operations, representing factual conditions (non-incident). The second stage incorporates data on URT incidents and passenger flow disruptions collected over the past five years. This integration of incident data enables the prediction of passenger flows during operational disruptions. ### Hyperparameter Configuration and Computational Setup

The hyperparameter configuration of the proposed dual-channel deep counterfactual model is presented as Table 2. The model's architectural design includes a station embedding dimension of 64, which is sufficient to capture semantic and locational attributes without incurring excessive parameterization. The hidden layers within the network are set to a dimension of 128, ensuring adequate capacity to model complex nonlinear relationships among features. The graph attention mechanism utilizes eight attention heads, each producing an output dimension of 16, which collectively enhances the model's ability to capture diverse spatial dependencies across the transit network. Temporal dependencies are extracted through a two-layer temporal convolutional network with a kernel size of three, enabling the model to learn sequential patterns across adjacent time intervals effectively. To support the transformation of high-dimensional spatiotemporal representations into OD flow predictions, a two-layer multilayer perceptron is employed in the decoder. The first and second layers of the MLP are set to 128 and 64 dimensions respectively, enabling a gradual reduction in feature space complexity prior to output. A dropout rate of 0.3 is applied across hidden layers as a regularization strategy to mitigate overfitting, especially given the potential sparsity in counterfactual observations. The rectified linear unit is used as the activation function throughout the architecture, given its widespread success in deep learning applications due to non-saturating gradients and computational efficiency. Training procedures were conducted using the Adam optimizer with a learning rate of 0.001, a setting commonly adopted for stable and efficient convergence in temporal graph-based networks. A mini-batch size of 64 was selected to balance computational tractability with variance reduction in gradient estimates. The model was trained for up to 100 epochs, with early stopping applied if validation loss fails to improve over 10 consecutive epochs, thereby reducing the risk of overfitting. To further regularize the model, weight decay was implemented with a coefficient of 0.0001, penalizing large weights

Figure 7: Descriptive statistics of land use types around stations in different cases. and encouraging smoother solutions. Gradient clipping with a threshold of 5.0 was used to prevent exploding gradients during backpropagation, ensuring numerical stability during optimization. Training data were shuffled at the start of each epoch, and a validation split of 10 percent was reserved to monitor generalization performance. A fixed random seed of 42 was used to ensure the reproducibility of experimental results across runs and environments. ### Prediction Results

Experiments were conducted to evaluate prediction accuracy across different time scales and passenger flow conditions using MAE, MAPE, and RMSE metrics. Computational time and accuracy with marginal changes in network size are presented in Appendix A Table 1. The core observation is that prediction errors in the high passenger flow scenario are consistently larger than those in the medium and low flow scenarios.