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arXiv · 2603.05560

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

Rares Grozavescu·Pengyu Zhang·Mark Girolami·Etienne Meunier
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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.

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Rares Grozavescu, Pengyu Zhang, Mark Girolami, Etienne Meunier. 2026-03-05. Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approach. https://arxiv.org/abs/2603.05560

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