Dynamic Generalized Gromov-Wasserstein Optimal Transport

2026-09-17

AI Summary

本文提出了一种动态广义Gromov-Wasserstein最优传输方法TP-DATE，通过路径作用和流动匹配技术，在保持组织结构的同时改进了连续3D动态重构。

Abstract

Gromov--Wasserstein optimal transport (GW-OT) extends classical optimal transport by introducing structure-aware transport cost. This is particularly relevant for spatial transcriptomics, where dynamical reconstruction should preserve tissue structure in addition to matching expression patterns. While static formulations have been widely used for such structure-aware alignment, a general dynamic formulation for reconstructing continuous trajectories is still missing. We introduce Travelling Pair Dynamical Alignment and Trajectory Estimation (TP-DATE), a theoretical and computational framework to generalize GW-OT dynamically in a simulation-free manner. We formulate a broad class of static and dynamic Quadratic-form OT (QOT) through path actions and prove the static dynamic equivalence. We further develop travelling-pair flow matching, which allows interacting conditional paths and marginalizes their interactions into a single vector field. On synthetic and real spatial transcriptomics data, TP-DATE better preserves spatial structure and improves continuous 3D dynamics reconstruction.

Problem

• Gromov-Wasserstein
• spatial transcriptomics
• dynamic reconstruction
• structure-aware alignment
• continuous trajectories

Innovation

• Travelling Pair Dynamical Alignment and Trajectory Estimation
• dynamic generalized Gromov-Wasserstein optimal transport
• path actions
• travelling-pair flow matching
• spatial structure preservation