Elia Parolari
Flow Matching for Time-Series Forecasting: Scaling Laws in a Controlled Setting.
Rel. Alfredo Braunstein, Leonardo Petrini. Politecnico di Torino, Master of science program in Physics Of Complex Systems, 2026
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Abstract
Probabilistic forecasters, in contrast to point forecasters that output a single predicted value, produce a full distribution over possible outcomes, explicitly capturing uncertainty and enabling risk-aware decision-making. This approach is relevant in any domain where decisions depend on uncertain futures, such as energy systems, finance, and healthcare, where it is used to quantify variability in demand, outcomes, and risks. One way to construct such forecasts is through generative models. These models learn to sample from an unknown distribution given observations drawn from it. In forecasting settings, they can be applied autoregressively by sampling from the conditional distribution of the future given the past.
A particularly successful class of generative models are flow-based methods, including diffusion models and the more recent flow matching, which learn to transport samples from a simple source distribution (e.g., Gaussian) to the target distribution by means of a learned velocity field
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