用连续时间建模提升海洋时空预测精度与速度
KFTD: Koopman-Fourier Time-Differentiable Network for Continuous Ocean Spatiotemporal Forecasting
- 分两阶段建模：先映射到线性空间，再用傅里叶分析实现任意时间步插值
- 相比传统方法平均降低5.6%误差，最高达12.7%，推理速度提升76.25%
- 支持任意微分方程约束，适合需物理一致性高精度的气候预测场景
精准的海洋预报对气候监测和灾害预警至关重要。然而，海洋时空预测面临建模复杂动力系统与保证计算效率的双重挑战。我们提出Koopman-Fourier时变网络（KFTD），一种连续时间两阶段范式，将插值与预测解耦，实现高效可扩展的时空建模。通过将复杂非线性动力学映射至Koopman线性空间，并利用傅里叶分析实现任意子步长的连续时间插值，轻量级残差网络基于高保真中间状态生成最终预报。不同于扩散模型，KFTD无需多步噪声采样，直接在连续时间演化系统，实现4倍计算加速。我们进一步引入DPP损失，以端到端方式支持任意偏微分方程约束，突破纯数据驱动方法的物理一致性瓶颈。在四个海洋数据集上的实验表明，该连续时间框架平均降低均方误差5.6%（海表温度最高降低12.7%），相较MCVD效率提升76.25%。
原文摘要 · Abstract (English)
Accurate oceanic forecasting is critical for climate monitoring and disaster early warning. However, ocean spatiotemporal forecasting encounters the double challenges of modeling complex dynamical systems and ensuring computational efficiency. We present Koopman Fourier Time-Differentiable (KFTD) Network, a time continuous twostage paradigm that decouples interpolation from prediction to achieve efficient and scalable spatiotemporal modeling. We map complex nonlinear dynamics into the Koopman linear space and exploit Fourier analysis to enable continuous time interpolation at arbitrary sub-steps. A lightweight residual network consumes the high fidelity intermediate states to yield the final forecast. Unlike diffusion models, KFTD eliminates multi step noise sampling and directly evolves the system in continuous time, yielding a 4 computational speedup. We further introduce a DPP Loss that supports arbitrary PDE constraints in an endtoend manner, breaking the physical consistency bottleneck of pure data-driven approaches. Empirical results on four ocean datasets confirm that our continuous time framework reduces MSE by an average of 5.6% (up to 12.7% for SST) and improves efficiency over MCVD by 76.25%.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。