Learning to Control on the Fly: Online Meta Flow Matching across Unknown Dynamics

The control of complex physical systems is a fundamental challenge in science and engineering, requiring effective finite-horizon planning under unknown and varying dynamics. While deep learning provides a promising framework for optimizing control sequences, most learning-based approaches assume a fixed distribution of system dynamics. This assumption limits their ability to adapt efficiently when system dynamics are either unknown in advance or vary across environments. To address this limitation, we propose OnlineMeta Flow Matching (OMFM), a generative control framework that continuously adapts control generation from streaming interactions without requiring explicit knowledge of governing equations or dynamical parameters. For each encountered environment, OMFM encodes observed trajectories into a shared context that adapts both control generation and candidate evaluation to the underlying dynamics. The generator learns to produce control sequences from a Gibbs-weighted empirical distribution of observed trajectories, while the predictor estimates future state evolution for candidate evaluation. During deployment, multiple candidates are generated, evaluated by a learned dynamics predictor, and ranked by their predicted objectives without additional environment interaction. We evaluate OMFM on five diverse control tasks involving dynamical systems of varying complexity. The results indicate that OMFM consistently outperforms strong baselines, achieving 25.01% improvement in control performance and converging significantly faster during online adaptation. Our code is available at https://anonymous.4open.science/r/OMFM-473B