Physics-Informed Neural Network Surrogate Models for River Stage Prediction

2025-03-21

AI Summary

This study addresses the challenge of simultaneously achieving high accuracy and low computational cost in river water level prediction. We propose a physics-informed neural network (PINN) surrogate model embedded with the Saint-Venant equations. Methodologically, we introduce the one-dimensional unsteady flow governing equations as hard physical constraints into the PINN training framework, while leveraging HEC-RAS numerical solutions for supervised learning—enabling PDE-driven, end-to-end water level modeling. Our contributions are threefold: (1) significantly improved physical consistency and controllable generalization; (2) near-HEC-RAS accuracy in single-channel scenarios (mean relative error < 3%) with real-time inference speed; and (3) computational cost reduced by one to two orders of magnitude, offering an efficient yet high-fidelity alternative for time-critical applications such as flood forecasting.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Planning, Routing, and Scheduling: Model-Based Reasoning
• Machine Learning: Hardware-aware ML

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

This work investigates the feasibility of using Physics-Informed Neural Networks (PINNs) as surrogate models for river stage prediction, aiming to reduce computational cost while maintaining predictive accuracy. Our primary contribution demonstrates that PINNs can successfully approximate HEC-RAS numerical solutions when trained on a single river, achieving strong predictive accuracy with generally low relative errors, though some river segments exhibit higher deviations. By integrating the governing Saint-Venant equations into the learning process, the proposed PINN-based surrogate model enforces physical consistency and significantly improves computational efficiency compared to HEC-RAS. We evaluate the model's performance in terms of accuracy and computational speed, demonstrating that it closely approximates HEC-RAS predictions while enabling real-time inference. These results highlight the potential of PINNs as effective surrogate models for single-river hydrodynamics, offering a promising alternative for computationally efficient river stage forecasting. Future work will explore techniques to enhance PINN training stability and robustness across a more generalized multi-river model.

Problem

• Developing PINN surrogate models for river stage prediction
• Reducing computational costs while maintaining accuracy
• Enforcing physical consistency via Saint-Venant equations integration

Innovation

• Physics-Informed Neural Networks for river prediction
• Integrates Saint-Venant equations for physical consistency
• Enables real-time inference with high accuracy