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

TL;DR

This paper develops a Koopman autoencoder surrogate model for coastal-ocean simulations, incorporating forcings and boundary conditions, and demonstrates its high accuracy and significant speed-up over traditional models across multiple test cases.

Contribution

It introduces a novel Koopman autoencoder formulation with temporal unrolling for stable long-term predictions, outperforming POD-based surrogates in some cases.

Findings

Achieves relative RMSE of 0.0068-0.14 across test cases.

Provides 300-1400x inference speed-up enabling efficient long-term simulations.

Koopman autoencoder outperforms POD in two of three test cases.

Abstract

While proper orthogonal decomposition (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 reduced order surrogates with temporal unrolling achieve high accuracy with relative root-mean-squared-errors of 0.0068-0.14 and $R^2$-values of 0.61-0.995, where prediction errors are largest for current velocities, and smallest for water surface elevations. In two of the three cases, the Koopman Autoencoder have higher accuracy than the POD-based surrogates. Comparing to in-situ observations, the surrogate yields -0.64% to 12% increase 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.