The paper introduces TP‑DATE, a dynamic framework that extends Gromov–Wasserstein optimal transport (GW‑OT) to reconstruct continuous trajectories without simulation. It formulates a broad class of static and dynamic Quadratic‑form OT (QOT) via path actions, proving static‑dynamic equivalence, and develops travelling‑pair flow matching to capture interacting conditional paths in a single vector field. Experiments on synthetic and real spatial transcriptomics data show that TP‑DATE better preserves spatial structure and improves 3D dynamics reconstruction.
By Junda Ying, Zhiwei Zeng, Peijie Zhou, Lei Zhang
arXiv:2608. 15306v1 Announce Type: cross Abstract: High-throughput single-cell and spatial transcriptomic technologies provide high-resolution snapshots of heterogeneous cellular states, but their destructive nature prevents repeated measurements of the same cells over time.
By Mary Chriselda Antony Oliver, Kaitlyn Hohmeier, Tuyen Tran, Alejandra Castillo, Caroline Moosm\"uller, Shiying Li
arXiv:2510. 01894v3 Announce Type: replace Abstract: Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots.
By Thomas Gravier, Thomas Boyer, Auguste Genovesio
arXiv:2608.21070v1 Announce Type: cross
Abstract: Inferring continuous system evolution from sparse temporal snapshots is a key challenge in generative modeling and single-cell omics. While Optimal T...
By Yuhao Sun, Zekun Wu, Zixun Huang, Peijie Zhou
Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distributions driven by an energy functional.
arXiv:2607. 04738v1 Announce Type: cross Abstract: Reconstructing population dynamics is a central problem in the physical and data sciences.
By Markus Heinonen, Yair Shenfeld, Ricardo Baptista, Daniel Waxman, Dmitry Batenkov, Tim Cooijmans, Eli Bingham