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- W3134669147 abstract "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. E.g., 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; 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." @default.
- W3134669147 created "2021-03-15" @default.
- W3134669147 creator A5043410025 @default.
- W3134669147 date "2021-03-01" @default.
- W3134669147 modified "2023-09-27" @default.
- W3134669147 title "Hessian metric via transport information geometry" @default.
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- W3134669147 doi "https://doi.org/10.1063/5.0012605" @default.
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