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

2026-03-05

AI Summary

This work addresses the challenges of high computational cost, rapid error accumulation, and energy drift in long-term ocean state prediction by proposing a novel approach based on continuous-time Koopman autoencoders. The method embeds the nonlinear ocean dynamical system into a latent space governed by linear ordinary differential equations, enabling time-resolution-independent inference through matrix exponential evolution. Evaluated over a 2083-day rolling forecast, the model maintains bounded prediction errors and stable large-scale statistical properties, achieving inference speeds several orders of magnitude faster than conventional numerical solvers and significantly outperforming autoregressive Transformer baselines.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• ocean state forecasting
• long-horizon prediction
• error growth
• energy drift
• stability

Innovation

• Continuous-Time Koopman
• Ocean State Forecasting
• Linear Latent Dynamics
• Resolution-Invariant Forecasting
• Hybrid Physics-ML Models