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This research introduces the Koopman-Fourier Time-Differentiable (KFTD) Network, a novel machine learning architecture designed to solve complex ocean spatiotemporal forecasting problems by mapping nonlinear dynamics into linear spaces. By integrating Fourier analysis with continuous time evolution and physical PDE constraints, the model achieves significant computational speedups while maintaining high fidelity in predicting sea surface temperatures without relying on multi-step noise sampling typical of diffusion models. The approach represents a meaningful advancement in applying AI to climate monitoring, demonstrating that hybrid physics-informed networks can outperform pure data-driven methods in efficiency and accuracy for dynamic system modeling.
KFTD: Koopman-Fourier Time-Differentiable Network for Continuous Ocean Spatiotemporal Forecasting
arXiv:2606.17070v1 Announce Type: cross Abstract: 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%.
Abstract: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%.
Atmospheric and Oceanic Physics (physics.ao-ph); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2606.17070 [physics.ao-ph]
(or arXiv:2606.17070v1 [physics.ao-ph] for this version)
https://doi.org/10.48550/arXiv.2606.17070 Focus to learn more arXiv-issued DOI via DataCite
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