应用数学青年讨论班(午餐会)-- TP-DATE: Flow Matching with Interacting Conditional Paths
报告人：应骏达（北京大学）
时间：2026-10-20 12:15-12:55
地点：智华楼-盈不足-109
摘要:
Flow matching has emerged as an efficient, simulation-free approach to solving dynamic optimal transport (OT) problems. Starting from the classical OT-CFM framework, recent developments have extended this approach to stochastic and unbalanced dynamics, including Schrödinger bridges and Wasserstein–Fisher–Rao transport. A key mathematical ingredient underlying these methods is the marginalization of conditional probability paths, which enables the construction of population-level dynamics from tractable conditional processes. However, extending this principle to interacting particle systems remains challenging, as nonlocal interaction terms generally introduce nonlinear dependence on the evolving probability distribution, preventing the direct application of standard marginalization arguments.
In this talk, we introduce TP-DATE (Travelling pair dynamical alignment and trajectory estimation), a mathematical and computational framework that addresses this challenge through travelling-pair flow matching. By lifting the dynamics to a two-particle space, we allow conditional paths to interact while retaining a linear continuity equation that supports marginalization. Building on this idea, we develop a dynamic formulation of quadratic-form optimal transport (QOT), encompassing Gromov–Wasserstein OT. We further show how interacting conditional velocities can be marginalized into a single-particle velocity field, enabling efficient simulation-free training. Finally, we demonstrate the effectiveness of TP-DATE in spatiotemporal dynamics inference and continuous three-dimensional tissue reconstruction from spatial transcriptomics data.
报告人简介：
应骏达，至尊国际
2025级博士生，导师为张磊老师，主要研究方向为最优传输理论和算法在单细胞动力学中的应用。
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