# Physics-Informed Neural Network Surrogate Models for River Stage Prediction

arXiv: https://arxiv.org/abs/2503.16850 · HTML: https://mlsanity.com/paper/2503.16850/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 22 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Builds on (most cited first, 3 of 3)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)

## Built on by (most cited first, 2 of 2)

- [Accelerating HEC-RAS: A Recurrent Neural Operator for Rapid River Forecasting](https://mlsanity.com/paper/2507.15614/) (2025)
- [Knowledge-Graph-Augmented Chronos-2 for HEC-RAS Surrogate Forecasting](https://mlsanity.com/paper/2609.21381/) (2026)

## Abstract (arXiv)

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.