Temporal stability in reduced order model prediction of sea states: A surrogate model case study

Freja Petersen, Allan Peter Engsig-Karup, Rocco Palmitessa, Jesper Sandvig Mariegaard

Keywords: surrogate, machine learning, stability, temporal stability, koopman autoencoder, proper orthogonal decomposition, differentiable, sea state, forecast, temporal unrolling

TL;DR: A case study comparing techniques for ensuring long-term numerical stability in reduced order machine learning models for predicting sea states.

Abstract: Physics-based hydrodynamic models provide accurate forecasts of sea surface elevations and currents but are often too computationally demanding for real-time or ensemble predictions. This study investigates linear reduced-order machine learning surrogates as efficient alternatives, focusing on methods to ensure temporal stability in long-term forecasts. Two models are compared: a partly differentiable approach based on proper orthogonal decomposition and linear regression (PODLR), and a fully differentiable linear Koopman autoencoder (LKAE). The effects of eigenvalue constraints and temporal unrolling during training are evaluated using a large-scale hydrodynamic dataset from the Øresund region. Results show that PODLR suffers from severe stability issues, which are effectively mitigated by eigenvalue constraints and temporal unrolling, achieving high accuracy relative to the full hydrodynamic model. The LKAE is inherently stable, with temporal unrolling reducing forecast errors by nearly 50%. These findings highlight that exploiting differentiable structures in machine learning surrogates enables robust and computationally efficient hydrodynamic forecasting, allowing year-long simulations to be performed within seconds.

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Submission Number: 28