Efficient Graph Design for GNN Surrogates of Flexible Unstructured Coastal Models in Complex Geometries

  • Schäfer, Faro (DHI A/S)
  • Cremer, Clemens (DHI A/S)
  • Mariegaard, Jesper (DHI A/S)

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Graph Neural Networks (GNNs) have shown strong potential as surrogate models for traditional numerical solvers, particularly in weather forecasting where GNN-based approaches are already deployed in operational services. These surrogates typically rely on structured computational grids that map naturally to grid-like graphs. This architecture has already been successfully adapted to ocean simulations on grids. However, high-resolution coastal models often favor flexible unstructured meshes to capture complex coastlines and bathymetry and the resulting non-linear dynamics. Although recent ocean surrogates have demonstrated benefits of adaptive, non-gridded graph designs, effective strategies for constructing such graphs directly from existing complex computational meshes have not yet been systematically studied. This work addresses this gap by proposing two mesh-guided strategies for constructing GNN surrogates that leverage the domain knowledge embedded in the original numerical model. First, we explore density-aware graphs, which account for spatially varying mesh resolution, mitigating biases caused by non-uniform mesh-to-graph connections. Second, we study topology-aware graphs that directly exploit the computational mesh topology, typically carefully encoded by the modeller during mesh generation. This preserves physical boundaries and channels information flow to physically meaningful neighborhoods. We systematically compare the approaches against commonly used baselines, including Keisler-type graphs, GraphCast-type graphs, and hierarchical graphs, which underpin state-of-the-art AI weather models. The graphs are evaluated on highly dynamic coastal systems under strong wind and tidal boundary forcing. The training data is generated using MIKE21 FM and is openly available as part of the DHI WaterBench case library. Results demonstrate that mesh-guided graph generation not only improves physical consistency but offers a key workflow advantage: it enables the efficient and robust setup of GNN surrogates directly from existing simulations, eliminating the need for complex remeshing or dedicated data generation. Thereby the proposed approach lowers the effort of building application-oriented surrogates in coastal engineering.