Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approach

TL;DR

This paper introduces a continuous-time Koopman autoencoder for long-term ocean state forecasting that is both efficient and stable, outperforming traditional autoregressive models in error control and computational speed.

Contribution

The paper presents a novel continuous-time Koopman autoencoder that enforces linear dynamics in latent space, enabling stable, interpretable, and fast long-horizon ocean forecasts.

Findings

Bounded error growth over 2083 days

Stable large-scale ocean statistics during long rollouts

Significantly faster inference than traditional solvers

Abstract

We investigate the Continuous-Time Koopman Autoencoder (CT-KAE) as a lightweight surrogate model for long-horizon ocean state forecasting in a two-layer quasi-geostrophic (QG) system. By projecting nonlinear dynamics into a latent space governed by a linear ordinary differential equation, the model enforces structured and interpretable temporal evolution while enabling temporally resolution-invariant forecasting via a matrix exponential formulation. Across 2083-day rollouts, CT-KAE exhibits bounded error growth and stable large-scale statistics, in contrast to autoregressive Transformer baselines which exhibit gradual error amplification and energy drift over long rollouts. While fine-scale turbulent structures are partially dissipated, bulk energy spectra, enstrophy evolution, and autocorrelation structure remain consistent over long horizons. The model achieves orders-of-magnitude faster inference compared to the numerical solver, suggesting that continuous-time Koopman surrogates offer a promising backbone for efficient and stable physical-machine learning climate models.