Two-Parameter Flows for Learning Population Dynamics of Physical Systems
For researchers modeling physical systems with high-dimensional densities, this method enables learning dynamics from marginal samples without trajectories, addressing a key bottleneck in data-driven physics simulation.
This work introduces two-parameter flows to learn population dynamics of high-dimensional probability densities from unlabeled samples without trajectory data, achieving unique and regular dynamics that scale to high dimensions and capture rotational phenomena.
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.