Towards Physics-consistent Foundation Models for Flood Forecasting

Effective flood forecasting is critical for informed decision-making and timely emergency response. Traditional physical models, which rely on fixed-resolution spatial grids and input parameters, often incur substantial computational costs, limiting their capacity to accurately predict flood peaks and provide prompt hazard warnings.  This paper introduces methods to ensure physical consistency in machine learning models, aiming to develop a fast, stable, accurate, cross-regional, and downscaled neural flood forecasting foundation model. Specifically, we present a Physics-embedded Neural Network, which integrates the momentum and mass conservations of flood dynamics into a neural network. Additionally, we combine this Physics-embedded Neural Network with a diffusion-based generative model, enhancing physical process consistency for long-term, large-scale flood forecasting. We also briefly introduce other models that integrate physics and machine learning, such as the FloodCast model by incorporating hydrodynamic equations into its loss function to maintain physical consistency, and the UrbanFloodCast model by learning physical consistency from urban flood dynamic data. The performance of these models will be analyzed using our proposed FloodCastBench dataset, a comprehensive collection of low-fidelity and high-fidelity flood forecasting dataset and benchmark. Results from the dataset demonstrate that incorporating physical consistency significantly enhances flood forecasting accuracy, demystifies the black-box nature of machine learning frameworks, and increases confidence in addressing dynamical systems. Finally, we propose a Spatiotemporal Foundation Model capable of forecasting floods across a variety of scales and regions.