KineFlow: Kinematic Second-Order Flow Matching for Time-Series Forecasting

Conventional time-series discriminative forecasting relies on point-wise regression, which inherently induces over-smoothing and fails to capture stochastic volatility in complex systems. While first-order generative flow matching methods mitigate this issue, they ignore system inertia, resulting in phase-space ambiguities and high sensitivity to noise. We introduce KineFlow, a generative time-series forecasting framework that augments flow matching with a phase-space Neural Acceleration Field, treating exogenous inputs as driving forces that produce gradual momentum shifts rather than abrupt state perturbations. This second-order formulation serves as a structural filter via double integration, suppressing high-frequency noise and producing robust, physically consistent predictions. Extensive experiments on six real-world benchmarks demonstrate that KineFlow achieves an average 15% MSE improvement over discriminative baselines and an 8% gain in CRPS compared to state-of-the-art generative methods.

Predicting complex dynamical systems such as electricity demand, traffic flows, and weather remains a significant challenge. Existing AI models often generate overly smoothed forecasts that fail to capture abrupt changes or neglect the system’s intrinsic momentum, resulting in predictions that are overly sensitive to noise and physically implausible. To address these limitations, we propose KineFlow, a physics-informed forecasting framework that explicitly models not only the system’s future state but also its velocity and acceleration. In our formulation, exogenous factors such as heavy rainfall or other external disturbances are treated as forces that influence the system’s momentum in a gradual and physically consistent manner. By embedding these dynamical constraints into the model, KineFlow serves as a principled regularizer against noisy observations and produces more accurate and realistic forecasts, with particularly strong performance in critical infrastructure applications, including power systems.