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.

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The challenge is that the math behind it is somewhat complicated, and that it has to be run, over and over, across vast quantities of data to suss out the statistical weights and biases of a particular system. The work will get done; it might just take a long time. Data scientists and machine learning researchers have long used graphics processing units (GPUs) because of their highly parallelized architecture and relatively abundant on-chip memory available. But as industry and research groups alike seek more efficiency and need to accommodate ever-larger quantities of information, more specialized computing hardware is required for the task. Headquartered in Bristol, U.K., Graphcore is in the business of producing silicon purpose-built for munching through machine-learning math at high rates of speed and using less electricity than GPUs. Benchmarks for Graphcore's Intelligence Processing Unit (IPU) state that it offers notably less latency and higher computational throughput, and uses less power than GPUs.