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About this paper
Qiangwei Peng, Zihan Wang, Junda Ying, Yuhao Sun, Qing Nie, Lei Zhang, Tiejun Li, Peijie Zhou
A new method, WFR-FM, reconstructs continuous, unbalanced dynamics from discrete data by unifying the Wasserstein–Fisher–Rao metric with a simulation-free flow matching paradigm. It simultaneously models particle displacement and population growth/death, achieving low 1-Wasserstein distance for distribution matching and near-zero relative mass error.
Key insights
- The Wasserstein–Fisher–Rao (WFR) metric offers a theoretically sound geometry for modeling systems with evolving states and changing mass, such as cell proliferation and apoptosis.
- Simulation-free flow matching can be extended to unbalanced optimal transport by constructing analytical conditional measure paths, derived from WFR geodesics, to provide target velocity and growth rate fields.
- Simultaneously learning explicit neural networks for both the transport velocity field and the scalar growth rate function, weighted by conditional mass, enables comprehensive and robust modeling of unbalanced dynamic systems.
Summary by alphaXiv.
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