# Rapid Flood Inundation Forecast Using Fourier Neural Operator

arXiv: https://arxiv.org/abs/2307.16090 · HTML: https://mlsanity.com/paper/2307.16090/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 45 references that are in the map.
- First posted on arXiv 29 Jul 2023.

## Builds on (most cited first, 7 of 7)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [MetNet: A Neural Weather Model for Precipitation Forecasting](https://mlsanity.com/paper/2003.12140/) (2020)
- [Data-driven Flood Emulation: Speeding up Urban Flood Predictions by Deep Convolutional Neural Networks](https://mlsanity.com/paper/2004.08340/) (2020)

## Built on by (most cited first, 9 of 9)

- [ClimateLLM: Efficient Weather Forecasting via Frequency-Aware Large Language Models](https://mlsanity.com/paper/2502.11059/) (2025)
- [Time Series Predictions in Unmonitored Sites: A Survey of Machine Learning Techniques in Water Resources](https://mlsanity.com/paper/2308.09766/) (2023)
- [RiverMamba: A State Space Model for Global River Discharge and Flood Forecasting](https://mlsanity.com/paper/2505.22535/) (2025)
- [DUALFloodGNN: Physics-informed Graph Neural Network for Operational Flood Modeling](https://mlsanity.com/paper/2512.23964/) (2025)
- [EvaNet: Elevation-Guided Flood Extent Mapping on Earth Imagery (Extended Version)](https://mlsanity.com/paper/2404.17917/) (2024)
- [Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations](https://mlsanity.com/paper/2605.13761/) (2026)
- [Learned Response-Field Inertia Operator for HEC-RAS 2D Water-Surface Elevation Prediction](https://mlsanity.com/paper/2606.06385/) (2026)
- [Analysis of Fourier Neural Operators via Effective Field Theory](https://mlsanity.com/paper/2507.21833/) (2025)
- [Advanced Flood Prediction with Physics-Guided Deep Learning: Combining UNet, FNO, and SAR/Optical Imagery](https://mlsanity.com/paper/2606.06524/) (2026)

## Abstract (arXiv)

Flood inundation forecast provides critical information for emergency planning before and during flood events. Real time flood inundation forecast tools are still lacking. High-resolution hydrodynamic modeling has become more accessible in recent years, however, predicting flood extents at the street and building levels in real-time is still computationally demanding. Here we present a hybrid process-based and data-driven machine learning (ML) approach for flood extent and inundation depth prediction. We used the Fourier neural operator (FNO), a highly efficient ML method, for surrogate modeling. The FNO model is demonstrated over an urban area in Houston (Texas, U.S.) by training using simulated water depths (in 15-min intervals) from six historical storm events and then tested over two holdout events. Results show FNO outperforms the baseline U-Net model. It maintains high predictability at all lead times tested (up to 3 hrs) and performs well when applying to new sites, suggesting strong generalization skill.