FlowOC: History-Informed Flow Matching with Optimal Control Calibration for Probabilistic Forecasting

Generative models provide a natural framework for probabilistic multivariate time series forecasting by modeling the conditional distribution of future trajectories rather than producing a single deterministic estimate. However, improving the alignment of generated forecasts with future observations while preserving meaningful predictive variability remains challenging. To address this issue, FlowOC adopts a two-stage training procedure. In the first stage, Conditional Flow Matching learns the predictive distribution of future trajectories from informative historical-patch source states. In the second stage, the pretrained flow is frozen, and an additive controller performs optimal control-inspired calibration using ensemble-level accuracy and distribution-shape preservation objectives, thereby improving the predictive center while maintaining the stochastic structure of the generated trajectories. Experiments on six multivariate forecasting benchmarks demonstrate that FlowOC improves point forecasting accuracy while preserving or enhancing probabilistic forecasting quality, thereby achieving a balance between forecast accuracy and faithful uncertainty characterization. Extensive ablation and qualitative analysis further validate the effectiveness of the historical-patch source distribution and the proposed optimal control calibration strategy. Code is available at https://anonymous.4open.science/r/Flow_OC-E8DA.