Physics-informed Graph Neural Networks for Operational Flood Modeling

TL;DR

This work tackles the need for fast, physically consistent flood predictions by developing DUALFloodGNN, a physics-informed Graph Neural Network that jointly predicts node water volumes and edge water flows on unstructured graphs. The model uses a shared message-passing architecture to enable simultaneous node/edge estimation, and enforces mass conservation at both global and local scales through dedicated loss terms, including a global balance term and a local balance term derived from edge flows. Training leverages autoregressive rollout with a multi-step loss and dynamic curriculum learning to improve robustness to accumulated prediction errors. Empirical results on a Wollombi River catchment dataset show that DUALFloodGNN outperforms standard GNN baselines and domain-specific flood models in RMSE, NSE, and CSI while maintaining efficient inference, highlighting its potential for real-time operational flood management and decision making.

Abstract

Flood models inform strategic disaster management by simulating the spatiotemporal hydrodynamics of flooding. While physics-based numerical flood models are accurate, their substantial computational cost limits their use in operational settings where rapid predictions are essential. Models designed with graph neural networks (GNNs) provide both speed and accuracy while having the ability to process unstructured spatial domains. Given its flexible input and architecture, GNNs can be leveraged alongside physics-informed techniques with ease, significantly improving interpretability. This study introduces a novel flood GNN architecture, DUALFloodGNN, which embeds physical constraints at both global and local scales through explicit loss terms. The model jointly predicts water volume at nodes and flow along edges through a shared message-passing framework. To improve performance for autoregressive inference, model training is conducted with a multi-step loss enhanced with dynamic curriculum learning. Compared with standard GNN architectures and state-of-the-art GNN flood models, DUALFloodGNN achieves substantial improvements in predicting multiple hydrologic variables while maintaining high computational efficiency. The model is open-sourced at https://github.com/acostacos/dual_flood_gnn.

Figures (4)

• Figure 1: Discretization of a target catchment. A structured mesh produces a uniform grid suitable for Convolutional Neural Networks (CNNs). A more flexible unstructured mesh can be translated into a graph for Graph Neural Networks (GNNs). The centroid of each mesh cell is represented as a node, while connections between adjacent cell centers define the edges as shown in the magnified section.
• Figure 2: The DUALFloodGNN architecture. To predict $T$ timesteps, an autoregressive rollout is performed while accumulating the loss at each timestep to compute the total rollout loss $\mathcal{L}_{rollout}$ (left). During each step, the model predicts node ($\Delta V$) and edge ($\Delta \vec{Q}$) embeddings through joint modeling which shares generated messages (bottom right). From this, the prediction loss $\mathcal{L}_{pred}$ and physics loss $\mathcal{L}_{physics}$ are calculated given the previous state ($V^t$, $\vec{Q}^t$), current state ($V^{t+1} = V^t + \Delta V$, $\vec{Q}^{t+1} = \vec{Q}^t + \Delta \vec{Q}$), and ground truth ($\overline{\Delta V}, \overline{\Delta \vec{Q}}$) (top right).
• Figure 3: Task-specific RMSE of select benchmarked GNN models for each timestep in the case study event.
• Figure 4: Maximum water depth map of flood-specific GNN models for the case study event. The maps of the ground truth, model predictions (left) and difference between the two (right) are shown.