Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approach
arXiv:2603.05560v1 Announce Type: cross 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, su
arXiv:2603.05560v1 Announce Type: cross 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 hybrid physical-machine learning climate models.
Executive Summary
The article introduces the Continuous-Time Koopman Autoencoder (CT-KAE) as a novel lightweight surrogate model for long-horizon ocean state forecasting within a two-layer quasi-geostrophic (QG) system. Leveraging the Koopman operator formalism, the CT-KAE transforms nonlinear dynamics into a linear latent-space representation, enabling efficient long-term prediction via matrix exponential formulations. The model demonstrates superior stability over long rollouts compared to autoregressive Transformer baselines, maintaining bounded error growth and preserving key bulk statistical properties such as enstrophy and autocorrelation. Notably, the CT-KAE achieves significant computational efficiency gains over numerical solvers, offering a compelling hybrid physical-machine learning alternative for climate modeling. The findings suggest a promising direction for scalable, stable forecasting systems.
Key Points
- ▸ CT-KAE uses Koopman operator formalism for nonlinear-to-linear transformation
Merits
Stability Advantage
CT-KAE exhibits bounded error growth and persistent bulk statistical properties over long horizons, unlike Transformer baselines which suffer from error amplification and energy drift.
Efficiency Gains
Orders-of-magnitude faster inference compared to numerical solvers, enabling scalable hybrid modeling.
Demerits
Fine-Scale Dissipation
Fine-scale turbulent structures are partially dissipated, potentially limiting fidelity in high-resolution phenomena.
Expert Commentary
The CT-KAE represents a sophisticated application of Koopman theory to climate dynamics, offering a rare combination of interpretability, stability, and computational efficiency. The ability to preserve bulk statistical invariants while achieving rapid inference is particularly noteworthy, as it addresses critical bottlenecks in long-horizon ocean forecasting. While the partial loss of fine-scale variability is a legitimate concern, the trade-off appears justified given the operational gains in scalability and reliability. This work bridges a critical gap between machine learning’s scalability and the physical constraints inherent in climate systems. It sets a new benchmark for surrogate modeling in environmental science and warrants replication across different climate subsystems to validate generalizability.
Recommendations
- ✓ Extend CT-KAE validation to multi-scale climate models beyond QG systems.
- ✓ Integrate CT-KAE with adaptive filtering techniques to mitigate fine-scale dissipation effects.
