用双参数流学习物理系统概率密度演化，无需轨迹信息。
Two-Parameter Flows for Learning Population Dynamics of Physical Systems
- 通过采样时间传输建模各时刻分布，再回归合成轨迹得物理时间速度。
- 在高维下有效，避免逐步最优传输，支持旋转等非梯度动力学。
- 适合研究无轨迹数据的物理系统演化，如流体或粒子群行为。
本文解决仅通过无标签样本学习高维概率密度随时间演化的难题，无需轨迹信息。提出双参数流方法：仅从基分布到各边际分布学习采样时间传输，并通过回归耦合合成轨迹得到物理时间速度。证明所得物理时间动力学唯一且继承采样时间传输的正则性。由于可利用成熟的条件流匹配技术学习基分布到边际的传输，该方法能扩展至高维，避免每步最优传输耦合，同时允许非梯度动力学，自然描述旋转或循环等物理现象。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。