PathFM: Generative Forecasting of Multivariate Trajectories with Flow Matching
PathFM is a novel generative forecasting model designed to predict entire future trajectories of multivariate time series, unlike traditional models that often only predict marginal quantiles. By using flow matching, it captures the complex dependencies between different parts of a future path, which is crucial for applications sensitive to the sequence and interaction of events. This approach makes generative time series forecasting both competitive and practical for diverse real-world problems.
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PathFM is a novel generative forecasting model designed to predict entire future trajectories of multivariate time series, unlike traditional models that often only predict marginal quantiles. By using flow matching, it captures the complex dependencies between different parts of a future path, which is crucial for applications sensitive to the sequence and interaction of events. This approach makes generative time series forecasting both competitive and practical for diverse real-world problems.
Imagine trying to predict the exact path a river will take, including all its twists and turns, not just how high the water will be at a few points. Traditional forecasting might tell you the water level at specific locations (marginal quantiles), but PathFM aims to predict the entire 'flow' or trajectory of the river, capturing how changes in one part affect the others. This is like predicting the full solution to a differential equation, not just a few points on its curve.
How PathFM Generates Future Paths
- 1PathFM uses a technique called flow matching to learn a continuous transformation that maps a simple noise distribution to the complex distribution of future time series trajectories. This allows it to generate diverse and realistic future paths.
- 2The model is distilled into one or two steps, and attention caches are shared across multiple generated paths. This optimization significantly speeds up the generation process, making it comparable to the time needed for a single query to a quantile model.
- 3By directly optimizing a calibration loss, PathFM ensures that its generated paths accurately reflect the true uncertainty and variability of the future, even in chaotic systems where other models might fail.
pₜ(x) = (∂)/(∂ x) Pₜ(x)
This represents the probability density function of a time series at time $t$, where $P_t(x)$ is the cumulative distribution function. PathFM aims to model the entire path distribution, not just individual points.
In supply chain management, predicting the full trajectory of demand for multiple interdependent products (e.g., a phone, its charger, and its case) is critical. PathFM can generate consistent future demand scenarios, allowing businesses to optimize inventory, production, and logistics more effectively than if they only predicted individual product demands in isolation.
PathFM's use of flow matching for trajectory-based forecasting provides a powerful way to model the full dependence structure of multivariate time series, leading to more robust and practical generative predictions.