Operator Flow Matching for Timeseries Forecasting
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915559244824576 |
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| author | Lee, Yolanne Yi Ran Flouris, Kyriakos |
| author_facet | Lee, Yolanne Yi Ran Flouris, Kyriakos |
| contents | Forecasting high-dimensional, PDE-governed dynamics remains a core challenge for generative modeling. Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long, physically consistent forecasts. Flow matching offers a natural alternative, enabling efficient, deterministic sampling. We prove an upper bound on FNO approximation error and propose TempO, a latent flow matching model leveraging sparse conditioning with channel folding to efficiently process 3D spatiotemporal fields using time-conditioned Fourier layers to capture multi-scale modes with high fidelity. TempO outperforms state-of-the-art baselines across three benchmark PDE datasets, and spectral analysis further demonstrates superior recovery of multi-scale dynamics, while efficiency studies highlight its parameter- and memory-light design compared to attention-based or convolutional regressors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15101 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Operator Flow Matching for Timeseries Forecasting Lee, Yolanne Yi Ran Flouris, Kyriakos Machine Learning Artificial Intelligence Forecasting high-dimensional, PDE-governed dynamics remains a core challenge for generative modeling. Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long, physically consistent forecasts. Flow matching offers a natural alternative, enabling efficient, deterministic sampling. We prove an upper bound on FNO approximation error and propose TempO, a latent flow matching model leveraging sparse conditioning with channel folding to efficiently process 3D spatiotemporal fields using time-conditioned Fourier layers to capture multi-scale modes with high fidelity. TempO outperforms state-of-the-art baselines across three benchmark PDE datasets, and spectral analysis further demonstrates superior recovery of multi-scale dynamics, while efficiency studies highlight its parameter- and memory-light design compared to attention-based or convolutional regressors. |
| title | Operator Flow Matching for Timeseries Forecasting |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2510.15101 |