Physics-Informed Neural Network Surrogate Models for River Stage Prediction

TL;DR

This paper demonstrates that Physics-Informed Neural Networks can act as fast, physically consistent surrogates for river stage prediction by learning from HEC-RAS data on a single Mississippi River. By embedding the Saint-Venant equations into the training loss and employing Fourier feature encoding, the PINN achieves accurate predictions with substantially reduced inference time compared to HEC-RAS, enabling real-time forecasting. The study provides a comprehensive benchmark against a CPU-based solver, showing roughly a 100x speedup while maintaining low relative errors on most river stations, and it includes an ablation analysis to highlight the benefits of Fourier features and physics regularization. The authors discuss extending the framework to a generalized multi-river model via geometry-encoding and ensemble strategies, with future work addressing 2D/3D extensions, real-world validation, and adaptive loss weighting for stability.

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.

Figures (4)

• Figure 1: System overview of the single-river PINN surrogate model.
• Figure 2: Structure of the single-river surrogate model.
• Figure 3: Histogram of relative error scores across river stations for the single-river model.
• Figure 4: Ablation study results demonstrating the impact of Fourier features and physics-informed regularization.