Time discretizations of Wasserstein–Hamiltonian flows
Time discretizations of Wasserstein–Hamiltonian flows
复制标题
Wasserstein–Hamiltonian 流的时间离散化
DOI：
10.1090/mcom/3726
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发表时间：
2022
影响因子：
2
通讯作者：
Zhou, Haomin
中科院分区：
文献类型：
--
作者：
Cui, Jianbo;Dieci, Luca;Zhou, Haomin
我们研究了概率密度流形上的Hamilton系统的离散化问题。基于离散最优输运理论，导出了图（格）上具有不同权值的几个Hamilton系统，它们可以看作是原Hamilton系统的空间离散化.我们证明了这些离散化的一致性。此外，通过正则化系统使用的Fisher信息，我们推导出一个明确的下界的密度函数，这保证了辛格式可以用来离散的时间。此外，我们还展示了这些辛格式的理想长时间行为，并在几个数值例子上证明了它们的性能。最后，我们比较了本方法与标准粘度方法。引用
We study discretizations of Hamiltonian systems on the probability density manifold equipped with the-Wasserstein metric. Based on discrete optimal transport theory, several Hamiltonian systems on a graph (lattice) with different weights are derived, which can be viewed as spatial discretizations of the original Hamiltonian systems. We prove consistency of these discretizations. Furthermore, by regularizing the system using the Fisher information, we deduce an explicit lower bound for the density function, which guarantees that symplectic schemes can be used to discretize in time. Moreover, we show desirable long time behavior of these symplectic schemes, and demonstrate their performance on several numerical examples. Finally, we compare the present approach with the standard viscosity methodology. References