用最优传输势约束多边缘流匹配，提升动态系统建模精度
Multimarginal flow matching with optimal transport potentials
- 通过最优传输势软性引导流路径经过中间观测分布
- 在单细胞、海洋与气象数据上实现领先性能与高效训练
- 适合需要精确时序建模的科学领域研究者
流匹配（FM）已成为学习两个经验分布间动态传输映射的强大框架。然而，关于包含中间观测边缘分布以约束端点间流形的“多边缘”设置仍较少被探索。这一情形在许多科学领域中对动态系统的时序演化建模至关重要，因可获取序列分布样本。本文提出一种新方法，利用FM与动态最优传输（OT）的联系，通过动态OT作用中的势能项，软性引导流路径趋向中间边缘分布。通过将条件流匹配的学习目标扩展以纳入这些势能项，我们推导出一种无需模拟的高效算法，能够灵活建模所学流的时空动态。我们在单细胞RNA测序、海洋学和气象学等多种数据集上展示了基于最优传输势的流匹配（OTP-FM）达到顶尖性能并具备优异训练效率。代码已公开于https://github.com/Bexorg-Inc/OTP-FM。
原文摘要 · Abstract (English)
Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions. However, less explored is the setting with intermediate observed marginals that can help constrain the flows between the endpoints. This "multimarginal" regime is central to modeling temporal evolution in dynamical systems in many scientific domains that can sample sequential distributions. We tackle this problem with a novel approach that leverages the connection between FM and dynamic optimal transport (OT), softly steering the flow towards the intermediate marginals through potential terms in the dynamic OT action. By extending the conditional FM learning target to incorporate these potentials, we derive an efficient, simulation-free algorithm for multimarginal FM that offers considerable flexibility in the spatiotemporal dynamics of the learned flows. We demonstrate state-of-the-art performance and training efficiency of OT-potential FM (OTP-FM) on diverse single-cell RNA sequencing, oceanographic, and meteorological datasets. Our code is available at https://github.com/Bexorg-Inc/OTP-FM.
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