Physics-guided networks for probabilistic hydrodynamic forecasting in canal systems.

Area of Science:

• Hydrology
• Water Resource Management
• Machine Learning

Background:

• Accurate water supply prediction is vital for large-scale canal systems and inter-basin water transfers.
• Evolving, multi-peaked uncertainty in lateral offtake discharges poses challenges for real-time operational decisions.
• Existing methods struggle to quantify and interpret dynamic uncertainty under small-sample conditions.

Purpose of the Study:

• To develop a physically consistent model for characterizing and interpreting evolving uncertainty in water supply dynamics.
• To improve the reliability and accuracy of predictions in large-scale canal systems.
• To provide a scalable and interpretable tool for operational management.

Main Methods:

• A physics-guided mixture density network (PgMDN) was developed, incorporating physical knowledge (local mass balance, prediction-uncertainty consistency) into the loss function.
• Long short-term memory (LSTM) layers were used to capture temporal dependencies and multi-factor influences.
• Shapley additive explanation (SHAP) analysis was employed to identify key drivers of predictive uncertainty.

Main Results:

• The PgMDN significantly outperformed standard mixture density networks, reducing mean absolute error and root mean square error by over 25%.
• Model reliability, measured by the R-index, improved substantially from 0.45 to 0.82.
• Water level fluctuations and boundary inflow were identified as primary contributors to predictive uncertainty.

Conclusions:

• The PgMDN offers a scalable and interpretable solution for real-time modeling of environmental infrastructure.
• The model effectively characterizes and interprets evolving uncertainty in water supply dynamics.
• This approach enhances decision-making for operational management in large-scale water diversion systems.