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Can I read Hessian Metric via Transport Information Geometry on EtoBox?
Hessian Metric via Transport Information Geometry by Wuchen Li is a Physics and Astronomy article available to read on EtoBox.
What is Hessian Metric via Transport Information Geometry about?
We propose to study the Hessian metric of a functional on the space of probability measures endowed with the Wasserstein-2 metric. We name it transport Hessian metric, which contains and extends the classical Wasserstein-2 metric. We formulate several dynamical systems associated with transport Hessian metrics. Several connections between transport Hessian metrics and mathematical physics equations are discovered. For example, the transport Hessian gradient flow, including Newton's flow, formulates a mean-field kernel Stein variational gradient flow; the transport Hessian Hamiltonian flow of Boltzmann-Shannon entropy forms the shallow water equation; and the transport Hessian gradient flow of Fisher information leads to the heat equation. Several examples and closed-form solutions for transport Hessian distances are presented.
Who reads Hessian Metric via Transport Information Geometry?
It is typically read by researchers, students, and practitioners in Physics and Astronomy.
- Author
- Wuchen Li
- Publisher
- AIP Publishing
- Published
- 2021
- Language
- EN
- Field
- Physics and Astronomy (Physical Sciences)