KFTD: Koopman-Fourier Time-Differentiable Network for Continuous Ocean Spatiotemporal Forecasting

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 timecontinuous two-stage 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 speed-up. We further introduce a D-PP 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%.