Toward an Operational GNN-Based Multimesh Surrogate for Fast Flood Forecasting

Abstract

Operational flood forecasting still relies on high-fidelity two-dimensional hydraulic solvers, but their runtime can be prohibitive for rapid decision support on large urban floodplains. In parallel, AI-based surrogate models have shown strong potential in several areas of computational physics for accelerating otherwise expensive high-fidelity simulations. We address this issue on the lower Têt River (France), starting from a production-grade Telemac2D model defined on a high-resolution unstructured finite-element mesh with more than $4\times 10^5$ nodes. From this setup, we build a learning-ready database of synthetic but operationally grounded flood events covering several representative hydrograph families and peak discharges. On top of this database, we develop a graph-neural surrogate based on projected meshes and multimesh connectivity. The projected-mesh strategy keeps training tractable while preserving high-fidelity supervision from the original Telemac simulations, and the multimesh construction enlarges the effective spatial receptive field without increasing network depth. We further study the effect of an explicit discharge feature $Q(t)$ and of pushforward training for long autoregressive rollouts. The experiments show that conditioning on $Q(t)$ is essential in this boundary-driven setting, that multimesh connectivity brings additional gains once the model is properly conditioned, and that pushforward further improves rollout stability. Among the tested configurations, the combination of $Q(t)$, multimesh connectivity, and pushforward provides the best overall results. These gains are observed both on hydraulic variables over the surrogate mesh and on inundation maps interpolated onto a common $25\,\mathrm{m}$ regular grid and compared against the original high-resolution Telemac solution. On the studied case, the learned surrogate produces 6-hour predictions in about $0.4\,\mathrm{s}$ on a single NVIDIA A100 GPU, compared with about $180\,\mathrm{min}$ on 56 CPU cores for the reference simulation. These results support graph-based surrogates as practical complements to industrial hydraulic solvers for operational flood mapping.

Figures (8)

• Figure 1: Overview of the dataset design: (a) spatial mesh-density strategy and (b) synthetic hydrograph families used to populate the database.
• Figure 2: Distribution of unique edge lengths for the reference Telemac mesh, the projected $\times 8$ mesh, and the projected $\times 8$ + multimesh graph. The reference hydraulic mesh exhibits a broad distribution of edge lengths, reflecting its strongly inhomogeneous spatial resolution. Projection to the $\times 8$ mesh shifts the distribution toward larger local interaction scales, while multimesh connectivity adds a sparse tail of longer-range connections.
• Figure 3: Ablation of the global discharge feature $Q(t)$ on the 16 held-out floods. Left: standard mesh (E1 vs E2). Right: multimesh (E4 vs E5). Solid lines show the mean held-out $L1$ error at each lead time and shaded areas indicate one standard deviation.
• Figure 4: Ablation of multimesh connectivity on the 16 held-out floods, restricted to $Q(t)$-conditioned models. Left: no pushforward (E2 vs E5). Right: with pushforward (E3 vs E6). Solid lines show the mean held-out $L1$ error at each lead time and shaded areas indicate one standard deviation.
• Figure 5: Ablation of pushforward training on the 16 held-out floods. Left: standard mesh with $Q(t)$ (E2 vs E3). Right: multimesh with $Q(t)$ (E5 vs E6). Solid lines show the mean held-out $L1$ error at each lead time and shaded areas indicate one standard deviation.