Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approach
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914407989116928 |
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| author | Grozavescu, Rares Zhang, Pengyu Girolami, Mark Meunier, Etienne |
| author_facet | Grozavescu, Rares Zhang, Pengyu Girolami, Mark Meunier, Etienne |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05560 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approach Grozavescu, Rares Zhang, Pengyu Girolami, Mark Meunier, Etienne Machine Learning Artificial Intelligence Applied Physics Computational Physics Geophysics 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. |
| title | Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approach |
| topic | Machine Learning Artificial Intelligence Applied Physics Computational Physics Geophysics |
| url | https://arxiv.org/abs/2603.05560 |