论文标题
Wasserstein-Fisher-Rao花键
Wasserstein-Fisher-Rao Splines
论文作者
论文摘要
我们研究了与总质量不同的措施的Wasserstein-Fisher-Rao（WFR）空间上的插值花样。为此，我们得出了WFR空间中绝对连续曲线的协变量和曲率。我们证明，这种曲率的几何概念在锥体上的颗粒方面等于曲率的拉格朗日概念。最后，我们提出了一种用于计算流量的实用算法，该算法扩展了ARXIV的工作：2010.12101。
We study interpolating splines on the Wasserstein-Fisher-Rao (WFR) space of measures with differing total masses. To achieve this, we derive the covariant derivative and the curvature of an absolutely continuous curve in the WFR space. We prove that this geometric notion of curvature is equivalent to a Lagrangian notion of curvature in terms of particles on the cone. Finally, we propose a practical algorithm for computing splines extending the work of arXiv:2010.12101.
