# A Neural Operator Emulator for Coastal and Riverine Shallow Water Dynamics

arXiv: https://arxiv.org/abs/2502.14782 · HTML: https://mlsanity.com/paper/2502.14782/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Builds on (most cited first, 16 of 16)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators](https://mlsanity.com/paper/2402.12365/) (2024)
- [Variationally Mimetic Operator Networks](https://mlsanity.com/paper/2209.12871/) (2022)
- [Learning in latent spaces improves the predictive accuracy of deep neural operators](https://mlsanity.com/paper/2304.07599/) (2023)
- [A greedy non-intrusive reduced order model for shallow water equations](https://mlsanity.com/paper/2002.11329/) (2020)
- [Nonlinear integro-differential operator regression with neural networks](https://mlsanity.com/paper/1810.08552/) (2018)
- [Bathymetry Inversion using a Deep-Learning-Based Surrogate for Shallow Water Equations Solvers](https://mlsanity.com/paper/2203.02821/) (2022)
- [A Framework for Flexible Peak Storm Surge Prediction](https://mlsanity.com/paper/2204.13168/) (2022)
- [Storm Surge Modeling in the AI ERA: Using LSTM-based Machine Learning for Enhancing Forecasting Accuracy](https://mlsanity.com/paper/2403.04818/) (2024)
- [Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEs](https://mlsanity.com/paper/2107.02784/) (2021)

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

- [Operator Learning for Predicting Bulk Wave Parameters of Spectral Wave Models](https://mlsanity.com/paper/2604.06433/) (2026)
- [A Model-Agnostic Physics-Guided Adapter for Few-Shot Transfer of Coastal Flood Prediction Models to Unseen Regions](https://mlsanity.com/paper/2609.37565/) (2026)

## Abstract (arXiv)

Coastal regions and river floodplains are particularly vulnerable to the impacts of extreme weather events. Accurate real-time forecasting of hydrodynamic processes in these areas is essential for infrastructure planning and climate adaptation. Yet high-fidelity numerical models are often too computationally expensive for real-time use, and lower-cost approaches, such as traditional model order reduction algorithms or conventional neural networks, typically struggle to generalize to out-of-distribution conditions. In this study, we present the Multiple-Input Temporal Operator Network (MITONet), a novel autoregressive neural emulator that employs latent-space operator learning to efficiently approximate high-dimensional numerical solvers for complex, nonlinear problems that are governed by time-dependent, parameterized partial differential equations. We showcase MITONet's predictive capabilities by forecasting regional tide-driven dynamics in the Shinnecock Inlet in New York and riverine flow in a section of the Red River in Louisiana, both described by the two-dimensional shallow-water equations (2D SWE), while incorporating initial conditions, time-varying boundary conditions, and domain parameters such as the bottom friction coefficient. Despite the distinct flow regimes, the complex geometries and meshes, and the wide range of bottom friction coefficients studied, MITONet displays consistently high predictive skill, with anomaly correlation coefficients above 0.9, a maximum normalized root mean square error of 0.011, and computational speedups between 100x-1,250x, even for 175 days of autoregressive rollout forecast from random initial conditions and with unseen parameter values.