Yang et al. (2026) Fusing dynamic physical constraints with PINN-xLSTM to enhance accuracy and physical consistency in runoff prediction under extreme hydrological events

Identification

• Journal: Journal of Hydrology
• Year: 2026
• Date: 2026-03-20
• Authors: Yafeng Yang, Wenbao Zhang, Fawen Li, Hao Wang, Haoran Zhang
• DOI: 10.1016/j.jhydrol.2026.135310

Research Groups

• College of Science, North China University of Science and Technology, Tangshan, China
• State Key Laboratory of Hydraulic Engineering Intelligent Construction and Operation, Tianjin University, Tianjin, China
• College of Water Science, Beijing Normal University, Beijing, China

Short Summary

This study introduces a novel PINN-xLSTM model with a dynamic physical constraint weighting mechanism to enhance runoff prediction accuracy and physical consistency, particularly during extreme hydrological events. The model demonstrates superior performance in accuracy, flood peak characterization, and adherence to hydrological principles compared to existing models.

Objective

• To develop a runoff forecasting method that integrates time series modeling with adaptive, dynamic physical constraints to improve prediction accuracy and physical consistency, especially under extreme hydrological events.

Study Configuration

• Spatial Scale: Yellow River basin, specifically evaluated at Tangnaihai hydrological station and validated at Toudaoguai and Luokou stations.
• Temporal Scale: Continuous runoff forecasting, with a focus on adapting to normal, flood, and drought periods.

Methodology and Data

• Models used: Hybrid model combining a Physical Information Neural Network (PINN) and an extended Long Short-Term Memory (xLSTM) network, incorporating a dynamic physical constraint weighting mechanism.
• Data sources: Hydrological observations (runoff data) from hydrological stations.

Main Results

• The proposed PINN-xLSTM model with dynamic physical constraints significantly outperforms comparison models in runoff prediction.
• Achieved high prediction accuracy with a coefficient of determination (R²) of 0.985 and a Root Mean Square Error (RMSE) of 53.18 cubic meters per second (m³/s).
• Demonstrated strong physical consistency with a physical constraint violation rate of 0.008.
• Improved characterization of flood peaks and better representation of runoff abruptness and persistence during extreme events.

Contributions

• Introduction of a dynamic physical constraint weighting mechanism that adaptively adjusts constraint importance based on hydrological scenarios (normal, flood, drought).
• Development of a hybrid PINN-xLSTM model that synergistically combines time-dependent modeling with enhanced physical consistency.
• Improved representation of abruptness and persistence of runoff during extreme events by amplifying runoff generation limits during floods and emphasizing groundwater attenuation during droughts.
• Provides a reliable, accurate, and interpretable approach for runoff prediction under extreme hydrological conditions.

Funding

• Not specified in the provided text.

Citation

@article{Yang2026Fusing,
  author = {Yang, Yafeng and Zhang, Wenbao and Li, Fawen and Wang, Hao and Zhang, Haoran},
  title = {Fusing dynamic physical constraints with PINN-xLSTM to enhance accuracy and physical consistency in runoff prediction under extreme hydrological events},
  journal = {Journal of Hydrology},
  year = {2026},
  doi = {10.1016/j.jhydrol.2026.135310},
  url = {https://doi.org/10.1016/j.jhydrol.2026.135310}
}