Operator Flow Matching for Timeseries Forecasting

• URL: http://arxiv.org/abs/2510.15101v1
• Date: Thu, 16 Oct 2025 19:40:56 GMT
• Title: Operator Flow Matching for Timeseries Forecasting
• Authors: Yolanne Yi Ran Lee, Kyriakos Flouris,
• Abstract summary: Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long, physically consistent forecasts.<n>We prove an upper bound on FNO error and propose TempO, a latent flow matching model leveraging sparse conditioning with channel folding.
• Score: 2.406359246841227
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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