Operator Flow Matching for Timeseries Forecasting
This addresses forecasting problems in physics and engineering where cumulative errors and discretisation artifacts limit long, physically consistent predictions.
The paper tackles the challenge of forecasting high-dimensional, PDE-governed dynamics by proposing TempO, a latent flow matching model that outperforms state-of-the-art baselines across three benchmark PDE datasets with superior recovery of multi-scale dynamics.
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.