| Abstract: |
| Flow matching has emerged as a powerful paradigm for generative modeling. From the viewpoint of dynamical measure transport, it constructs continuous-time ODE samplers by prescribing probability paths that connect a base and a target distribution. In this talk, we discuss both the potential and pitfalls of flow matching for probabilistic forecasting of dynamical systems. We observe that forecasting performance is highly sensitive to the choice of probability path, motivating principled constructions that lead to improved computational efficiency and predictive performance on spatio-temporal dynamical system benchmarks. We then revisit flow matching in the empirical setting and analyze the structure of the induced velocity fields, uncovering connections between flow matching, memory effects, and nonparametric dynamical systems. This perspective leads to new sampling strategies and raises questions about the role of parameterization in learning dynamical systems from data. |
|