Two-Parameter Flows for Learning Population Dynamics of Physical Systems
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Computer Science > Machine Learning
Title:Two-Parameter Flows for Learning Population Dynamics of Physical Systems
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.
| Subjects: | Machine Learning (cs.LG); Numerical Analysis (math.NA) |
| Cite as: | arXiv:2605.26285 [cs.LG] |
| (or arXiv:2605.26285v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.26285
arXiv-issued DOI via DataCite (pending registration)
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Submission history
From: Benjamin Peherstorfer [view email][v1] Mon, 25 May 2026 19:16:22 UTC (1,307 KB)
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