## 3 Methods
### Dual-Channel Deep Counterfactual Prediction Model for OD Matrix Prediction
#### 3.3.3 Loss Function and Prediction Accuracy Evaluation Metrics
These findings not only advance the theoretical framework for OD prediction under incident conditions but also offer actionable guidance for real-time operational adjustments in urban rail networks. ### Limitation and Future Works

However, this research still has several limitations. While our model demonstrates promising results using Shanghai's urban rail transit data, we recognize the necessity of validating its applicability across different urban settings. Future research will focus on applying and testing the model in other cities, such as Beijing, Shenzhen, and London, to assess its generalizability and adaptability to various transit systems and operational conditions. Additionally, the model does not consider detailed incident characteristics, such as specific fault locations or causes, and does not account for the network-level propagation of delays. Future research could integrate detailed fault modeling and network-level delay propagation to improve the accuracy of the predictions. Although the deep counterfactual inference framework proposed in this study performs well in simulation environments, we have not yet been able to deploy and test the model in real operations of the Shanghai Metro due to the complexity of the actual operational environment and limitations in data acquisition. Therefore, direct comparison data before and after the model implementation is not available. Future research should aim to work with metro operators to conduct field tests to verify the model's effectiveness in real operations and further optimize the model for real-world applications. We fully acknowledge that our study is currently based on historical data and simulations, without examples of real-time deployment during specific disruptions. This limitation, common in academic research contexts, indeed restricts direct assessments of operational impacts, such as enabling earlier decisions for incident management strategies. Conceptualization, Q.F. ; methodology, Q.F. ; software, C.Y. ; validation, C.Y. ; formal analysis, C.Y. ; resources, J.Z. ; data curation, J.Z. ; writing--original draft preparation, Q.F. ; writing--review and editing, C.Y. ; visualization, J.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant number 62273258. ## References

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