## 3 Methods
### Dual-Channel Deep Counterfactual Prediction Model for OD Matrix Prediction
#### 3.3.3 Loss Function and Prediction Accuracy Evaluation Metrics
This is primarily due to the higher fluctuation and wider variation in passenger flows under high flow conditions, which makes accurate predictions more challenging. Larger time scales tend to result in higher prediction errors compared to smaller time scales. However, the increase in MAE and RMSE is proportional to the time scale, suggesting that the error mainly reflects the impact of time granularity on the model's performance. In contrast, the MAPE metric does not increase proportionally. The reason for this discrepancy is that as the base value for comparison grows with the time scale, the relative prediction error becomes less significant. For instance, as illustrated in Table 3, the MAE for the high passenger flow case increases from 0.773 at the 10 min scale to 4.655 at the 60 min scale. At the same time, the MAPE increases from 6.437% at the 10 min scale to 13.849% at the 60 min scale, which demonstrates that the relative error increases less dramatically. Similarly, the RMSE increases from 4.518 at the 10 min scale to 25.642 at the 60 min scale, confirming the trend that larger time scales tend to amplify prediction errors, particularly in high flow scenarios. Statistical significance tests were also conducted to assess the concentration of prediction errors for MAE, MAPE, and RMSE by calculating the percentage of samples within \(\pm 3\sigma\) of each error distribution. Across all passenger flow cases and time scales, the coverage ratios consistently exceed 90%, indicating robust performance. The low passenger flow \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter Name** & **Description** & **Value** \\ \hline Embedding Dimension & Dimension of station semantic embeddings & 64 \\ Hidden Layer Dimension & Dimension of hidden layers in neural networks & 128 \\ Number of GAT Heads & Number of attention heads in the Graph Attention Network (GAT) & 8 \\ GAT Output Dimension per Head & Output dimension of each GAT head & 16 \\ TCN Kernel Size & Kernel size of the temporal convolution layers & 3 \\ Number of TCN Layers & Number of layers in the temporal convolution network & 2 \\ First MLP Layer Dimension & Dimension of the first layer in the final MLP decoder & 128 \\ Second MLP Layer Dimension & Dimension of the second layer in the final MLP decoder & 64 \\ Dropout Rate & Dropout rate applied to avoid overfitting & 0.3 \\ Activation Function & Activation function used in all hidden layers & ReLU \\ Learning Rate & Initial learning rate for the optimizer & 0.001 \\ Optimizer Type & Optimization algorithm used for training & Adam \\ Batch Size & Number of samples per batch & 64 \\ Number of Training Epochs & Number of training epochs & 100 \\ Weight Decay Coefficient & Weight decay (L2 regularization coefficient) & 0.0001 \\ Early Stopping Patience & Number of epochs to wait before early stopping & 10 \\ Gradient Clipping Threshold & Gradient clipping threshold to prevent explosion & 5 \\ Shuffle Training Data & Whether to shuffle training data each epoch & True \\ Validation Split Ratio & Proportion of training data used for validation & 0.1 \\ Random Seed & Random seed for reproducibility & 42 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hyperparameter configuration of the dual-channel deep counterfactual model. case exhibits the highest significance levels, followed by the medium and high flow cases, suggesting that reduced flow variability yields more concentrated predictions. Shorter time intervals (10 min and 20 min) demonstrate higher coverage proportions than longer intervals (30 min and 60 min), reflecting the greater absolute variation inherent in larger time scales. A comparison of the proposed dual-channel deep counterfactual (DC-DCF) model with several baseline models was also performed under the 10 min time scale. These baseline models included LSTM+GCN, LSTM+GAT, and TCN, along with a Transformer model that encodes incident features but lacks the dual-channel counterfactual component.