Two-Parameter Flows for Learning Population Dynamics of Physical Systems
摘要
This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only sampling-time transports from a base distribution to each marginal and then extract a physics-time velocity by regressing on coupled synthetic trajectories. We prove that the resulting physics-time dynamics are unique and inherit regularity from the sampling-time transports. Because we can build on standard, well-developed conditional flow matching techniques for learning the base-to-marginal transports, our approach scales to high dimensions and avoids per-step optimal-transport couplings, while allowing admissible non-gradient dynamics that can naturally explain rotational or circulating physics phenomena.
引用
@article{arxiv.2605.26285,
title = {Two-Parameter Flows for Learning Population Dynamics of Physical Systems},
author = {Paul Schwerdtner and Tobias Blickhan and Benjamin Peherstorfer},
journal= {arXiv preprint arXiv:2605.26285},
year = {2026}
}