Mu et al. (2026) A probabilistic prediction model based on uncertainty quantification and interpretable deep learning: Application to runoff prediction in the Yellow River mainstream

Identification

• Journal: Journal of Hydrology
• Year: 2026
• Date: 2026-07-13
• Authors: Liang Mu, J G Chen, Zhiguo Yu, Hongyun Zhao, Zhibo Yang
• DOI: 10.1016/j.jhydrol.2026.136013

Research Groups

School of Intelligent Engineering, Shandong Management University School of Traffic and Transportation, Beijing Jiaotong University School of Mechanical and Electrical Engineering, Qingdao University The Nuclear and Radiation Safety Center, Ministry of Ecology and Environment

Short Summary

This study develops a probabilistic runoff prediction method that integrates uncertainty quantification with interpretable deep learning for both point and probabilistic runoff forecasting in the Yellow River mainstream. The proposed model improves predictive accuracy and uncertainty quantification compared to benchmark models.

Objective

• Investigate the feasibility of using probabilistic runoff prediction methods that integrate uncertainty quantification with interpretable deep learning for runoff forecasting in the Yellow River mainstream.

Study Configuration

• Spatial Scale: Mainstream of the Yellow River, China.
• Temporal Scale: Daily observations from hydrological stations along the river.

Methodology and Data

• Models used: Spatio-temporal graph convolutional network (STGCN) with predictive variance and Gaussian negative log-likelihood function for uncertainty quantification.
• Data sources: Daily observations from hydrological stations along the Yellow River mainstream.

Main Results

• The proposed model improves RMSE, MAE, and MAPE for point prediction by at least 11.46%, 13.21%, and 15.45%, respectively.
• The proposed model improves CRPS and PICP for probabilistic prediction by at least 10.42% and 7.32%, respectively.

Contributions

• This study provides a reliable runoff prediction method that can quantify uncertainty, addressing the limitations of conventional deterministic forecasting models.
• The proposed model demonstrates improved predictive accuracy and uncertainty quantification compared to benchmark models.

Funding

• This research was funded by the National Natural Science Foundation of China (Grant No. 51979003) and the Ministry of Ecology and Environment of China (Grant No. 2019ZX07101).

Citation

@article{Mu2026probabilistic,
  author = {Mu, Liang and Chen, J G and Yu, Zhiguo and Zhao, Hongyun and Yang, Zhibo},
  title = {A probabilistic prediction model based on uncertainty quantification and interpretable deep learning: Application to runoff prediction in the Yellow River mainstream},
  journal = {Journal of Hydrology},
  year = {2026},
  doi = {10.1016/j.jhydrol.2026.136013},
  url = {https://doi.org/10.1016/j.jhydrol.2026.136013}
}