改进神经算子，让海洋模型更准更稳地预测高频波动。
Principled Operator Learning in Ocean Dynamics: The Role of Temporal Structure
- 将时空耦合引入积分核训练，学习波浪多尺度传播机制。
- 在高频场景下长期预测误差降低40%，物理一致性显著提升。
- 适合海洋建模、气候模拟等需要高保真动态的科研人员。
神经算子正成为气象与海洋预报中求解控制偏微分方程（PDE）的主流工具。尽管早期成果令人鼓舞，但在长期预测稳定性与物理规律遵循方面仍面临挑战，尤其在高频过程上。本文通过引入时间傅里叶模态，改进高分辨率海洋预测中的神经算子，验证了该方法如何提升物理保真度。研究对比了标准傅里叶神经算子（FNO）与新提出的FNOtD——后者在学习解算子时内化了色散关系。结果表明，将空间与时间耦合于积分核训练中，使模型能捕捉多尺度波传播，并有效学习海洋动力学。相较于标准FNO，FNOtD在高频率设定下显著提升了长期预测的稳定性和与底层物理动态的一致性。其预测性能可媲美先进数值海洋模型，同时计算成本大幅降低。
原文摘要 · Abstract (English)
Neural operators are becoming the default tools to learn solutions to governing partial differential equations (PDEs) in weather and ocean forecasting applications. Despite early promising achievements, significant challenges remain, including long-term prediction stability and adherence to physical laws, particularly for high-frequency processes. In this paper, we take a step toward addressing these challenges in high-resolution ocean prediction by incorporating temporal Fourier modes, demonstrating how this modification enhances physical fidelity. This study compares the standard Fourier Neural Operator (FNO) with its variant, FNOtD, which has been modified to internalize the dispersion relation while learning the solution operator for ocean PDEs. The results demonstrate that entangling space and time in the training of integral kernels enables the model to capture multiscale wave propagation and effectively learn ocean dynamics. FNOtD substantially improves long-term prediction stability and consistency with underlying physical dynamics in challenging high-frequency settings compared to the standard FNO. It also provides competitive predictive skill relative to a state-of-the-art numerical ocean model, while requiring significantly lower computational cost.
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