Graph Neural Networks versus Reduced-Order Models for Surrogate-Based Coastal Forecasting on Unstructured Meshes

AI-based surrogate modelling techniques are increasingly used in geoscience, with notable success in weather and climate forecasting as well as in hydrology and urban water systems. Their application to coastal and regional ocean modelling, however, remains challenging due to high spatial resolution requirements, complex geometries, and strong local dynamics. At the same time, surrogate models offer substantial benefits through fast inference, achieving speed-ups of one to three orders of magnitude compared to numerical simulations, which is particularly valuable for operational coastal forecasting where rapid decision-making and ensemble-based uncertainty quantification are essential. Many existing surrogate approaches rely on grid-like data structures that are often incompatible with the unstructured meshes required in coastal applications, highlighting the need for flexible frameworks that can operate on such data while remaining suitable for integration into operational workflows.

To address this gap, this study compares two surrogate methodologies that have been specifically adapted to the requirements of coastal modelling: Reduced Order Models (ROMs) and Graph Neural Networks (GNNs). While ROMs provide high computational efficiency, they typically treat the simulation outputs used for model training as independent data points and thus neglect the spatial structure of the computational mesh. As a result, important geometric information that is often carefully encoded in unstructured coastal models is not explicitly exploited. In contrast, GNNs offer a more flexible modelling framework that explicitly incorporates the topology of the computational mesh, enabling a more accurate representation of complex geometries and local dynamics.

Both approaches are assessed on two representative coastal domains modeled using MIKE 21 Flow Model FM software. The first is a highly dynamic estuary system influenced by anthropogenic structures, including Hamburg’s port and a complex river bifurcation. The second is the Øresund Strait, a coastal transition zone connecting the North Sea and the Baltic Sea, characterized by strong tidal currents and complex bathymetry. The surrogates are trained on the simulation inputs and outputs of these models and assessed for their forecasting of current velocities and surface elevations across varying lead times. Beyond predictive accuracy, the study examines computational efficiency and implications for real-world applicability.

The results show that both surrogate types can reproduce up to 95% of the numerical model precision, but with substantial differences in computational efficiency. ROMs achieve orders-of-magnitude faster training times, whereas GNNs demonstrate improved robustness in geometrically complex settings. These findings highlight the trade-off between mesh-aware and mesh-unaware surrogate designs and underline the importance for application-specific choices in operational coastal forecasting.