Operator Flow Matching for Timeseries Forecasting

Yolanne Yi Ran Lee, Kyriakos Flouris

Keywords: Flow matching, neural operators, PDEs, forecasting

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 propose TempO, a time-conditioned latent flow matching method mimicking classical PDE evolution operators. We introduce an attention-based multiscale autoencoder, a latent Fourier vector field regressor, and decoupled spatial and temporal processing for temporally coherent and accurate rollouts. We prove an upper bound on FNO approximation error and empirically show that 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.

Primary Area: generative models

Submission Number: 22218