用连续时间柯尔莫哥洛夫方法，实现高效稳定的海洋状态预测。
Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approach
- 将非线性动力学投影到线性微分方程主导的隐空间，提升可解释性。
- 2083天滚动预测中误差稳定增长，能量谱与涡度演化保持一致。
- 推理速度比数值求解快数个数量级，适合气候建模应用。
本文研究了连续时间柯尔莫哥洛夫自编码器（CT-KAE）在双层准地转（QG）系统中作为轻量级代理模型，用于长期海洋状态预测。通过将非线性动力学投影至由线性常微分方程控制的隐空间，模型实现了结构化且可解释的时间演化，并通过矩阵指数公式实现时间分辨率无关的预测。在2083天的滚动预测中，CT-KAE表现出误差增长有界、大尺度统计特性稳定，而自回归Transformer基线则出现渐进式误差放大和能量漂移。尽管小尺度湍流结构部分衰减，但整体能量谱、涡度演化及自相关结构在长时间内保持一致。模型推理速度相较数值求解器提升数个数量级，表明连续时间柯尔莫哥洛夫代理模型为高效、稳定的物理-机器学习气候模型提供了有力支撑。
原文摘要 · Abstract (English)
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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