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 the Koopman Fourier Time-Differentiable (KFTD) Network, a time continuous two-stage paradigm that decouples interpolation from prediction to achieve efficient and scalable spatiotemporal modeling.
KFTD maps complex nonlinear dynamics into the Koopman linear space and exploits Fourier analysis to enable continuous time interpolation at arbitrary sub-steps. A lightweight residual network consumes 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 4x computational speedup.
We further introduce a DPP Loss that supports arbitrary PDE constraints in an end-to-end 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%.
Blogger's Review: The introduction of the KFTD network offers a fresh perspective in the field of ocean spatiotemporal forecasting. By integrating the Koopman linear space with Fourier analysis, it not only enhances prediction accuracy but also significantly boosts computational efficiency. This method shows great potential in addressing complex dynamical systems and deserves exploration in broader applications.