Two-Parameter Flows for Learning Population Dynamics of Physical Systems

• URL: http://arxiv.org/abs/2605.26285v1
• Date: Mon, 25 May 2026 19:16:22 GMT
• Title: Two-Parameter Flows for Learning Population Dynamics of Physical Systems
• Abstract summary: We learn the dynamics of high-dimensional probability densities over time using unlabeled samples.<n>We prove that the resulting physics-time dynamics are unique and inherit regularity from the sampling-time transports.
• Score: 6.973074865500705
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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