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

TL;DR

This work addresses the computational bottleneck of physics-based coastal-ocean models by developing reduced-order surrogates. It introduces a forced Koopman autoencoder (KAE) that incorporates meteorological forcings and boundary conditions, and compares it to POD-based surrogates across three real-world test domains. The study demonstrates that end-to-end KAE training with temporal unrolling yields the best long-horizon accuracy (relative RMSE $0.01$–$0.13$, $R^2$ $0.65$–$0.996$) and centimeter-scale errors, with speed-ups of $300$–$1400 imes$ enabling ensemble forecasting and climate-scale simulations. Eigenvalue regularization improves stability in some cases, but temporal unrolling provides the most robust gains; results suggest strong potential for operational adoption while highlighting remaining challenges in highly resonant regimes like the Adriatic Sea.

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.

Figures (18)

• Figure 1: (a) Training of the Koopman-based Autoencoder in an end to end setting, and (b) training of POD surrogate in two steps: 1) Optimize the reconstruction loss for encoding and decoding, 2) optimize prediction loss.
• Figure 2: Graphical representation of autoencoders.
• Figure 3: The domains and the bathymetries of the three cases, Øresund (a), Southern North Sea (b), and Adriatic Sea (c). The dots indicate the location of measuring stations.
• Figure 4: Example timeseries of the surface elevation data used for training the surrogates.
• Figure 5: Reconstruction RMSEs for POD in the Adriatic test case.