Reduced-Order Surrogates for Forced Flexible Mesh Coastal-Ocean Models

Abstract: While POD-based surrogates are widely explored for hydrodynamic applications, the use of Koopman Autoencoders for real-world coastal-ocean modelling remains relatively limited. This paper introduces a flexible Koopman autoencoder formulation that incorporates meteorological forcings and boundary conditions, and systematically compares its performance against POD-based surrogates. The Koopman autoencoder employs a learned linear temporal operator in latent space, enabling eigenvalue regularization to promote temporal stability. This strategy is evaluated alongside temporal unrolling techniques for achieving stable and accurate long-term predictions. The models are assessed on three test cases spanning distinct dynamical regimes, with prediction horizons up to one year at 30-minute temporal resolution. Across all cases, the Koopman autoencoder with temporal unrolling yields the best overall accuracy compared to the POD-based surrogates, achieving relative root-mean-squared-errors of 0.01-0.13 and $R^2$-values of 0.65-0.996. Prediction errors are largest for current velocities, and smallest for water surface elevations. Comparing to in-situ observations, the surrogate yields -0.65% to 12% change in water surface elevation prediction error when compared to prediction errors of the physics-based model. These error levels, corresponding to a few centimeters, are acceptable for many practical applications, while inference speed-ups of 300-1400x enables workflows such as ensemble forecasting and long climate simulations for coastal-ocean modelling.