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

arXiv: https://arxiv.org/abs/2606.17070 · HTML: https://mlsanity.com/paper/2606.17070/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 62 references that are in the map.
- First posted on arXiv 6 Jun 2026.

## Builds on (most cited first, 12 of 12)

- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [UniST: A Prompt-Empowered Universal Model for Urban Spatio-Temporal Prediction](https://mlsanity.com/paper/2402.11838/) (2024)
- [VMRNN: Integrating Vision Mamba and LSTM for Efficient and Accurate Spatiotemporal Forecasting](https://mlsanity.com/paper/2403.16536/) (2024)
- [Optimizing Neural Networks via Koopman Operator Theory](https://mlsanity.com/paper/2006.02361/) (2020)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Learning Vertex Representations for Bipartite Networks](https://mlsanity.com/paper/1901.09676/) (2019)
- [Non-Imaging Medical Data Synthesis for Trustworthy AI: A Comprehensive Survey](https://mlsanity.com/paper/2209.09239/) (2022)
- [Distilled Large Language Model-Driven Dynamic Sparse Expert Activation Mechanism](https://mlsanity.com/paper/2603.26735/) (2026)
- [A spatio-temporal LSTM model to forecast across multiple temporal and spatial scales](https://mlsanity.com/paper/2108.11875/) (2021)
- [Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties](https://mlsanity.com/paper/2106.06033/) (2021)
- [STEMO: Early Spatio-temporal Forecasting with Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2406.04035/) (2024)

## Built on by (most cited first, 2 of 2)

- [Content-Induced Spatial-Spectral Aggregation Network for Change Detection in Remote Sensing Images](https://mlsanity.com/paper/2606.10328/) (2026)
- [Building Change Detection in Earthquake: A Multi-Scale Interaction Network and A Change Detection Dataset](https://mlsanity.com/paper/2606.10329/) (2026)

## Abstract (arXiv)

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%.