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Dynamic Gromov-Wasserstein Optimal Transport Framework

Dynamic Generalized Gromov-Wasserstein Optimal Transport

arXiv cs.LG@Junda Ying et al. (4)
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Why we picked it

For researchers in computational biology or data science, this provides a new method for analyzing spatial transcriptomics data, which is crucial for understanding tissue dynamics.

This paper introduces TP-DATE, a theoretical and computational framework that generalizes Gromov-Wasserstein optimal transport (GW-OT) dynamically.

Body

It addresses the need for a dynamic formulation for reconstructing continuous trajectories in spatial transcriptomics, which is relevant for preserving tissue structure in addition to matching expression patterns.

The framework is tested on synthetic and real data, showing improved preservation of spatial structure and better continuous 3D dynamics reconstruction.

Original · arXiv cs.LG

Dynamic Generalized Gromov-Wasserstein Optimal Transport

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.

Industry Coordinates & Source Verification

This report is categorized under AITOP's "Papers" desk, focusing on US frontier AI labs and Silicon Valley technology leaders. Within our cross-regional analytical framework, it directly maps to AI developer toolchains, coding agents, and engineering workflows. Key entities and technical topics under continuous tracking include Gromov-Wasserstein, optimal transport, spatial transcriptomics, dynamics.

Source attribution: curated from arXiv cs.LG (@Junda Ying, Zhiwei Zeng, Peijie Zhou, Lei Zhang).

#Gromov-Wasserstein#optimal transport#spatial transcriptomics#dynamics#3D reconstruction

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