Wasserstein-Fisher-Rao样条
Wasserstein-Fisher-Rao Splines
摘要：
研究了具有不同总质量测度的Wasserstein-Fisher-Rao（WFR）空间上的插值样条函数.为了实现这一点，我们得到的共变导数和曲率的绝对连续曲线在WFR空间。我们证明，这个几何概念的曲率是等价的拉格朗日概念的曲率的粒子的锥。最后，我们提出了一个实用的算法来计算样条扩展arXiv的工作：2010.12101。
英文摘要：
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.
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