Wasserstein stability estimates for covariance-preconditioned Fokker-Planck equations

J. A. Carrillo; U. Vaes

doi:10.1088/1361-6544/abbe62

Wasserstein stability estimates for covariance-preconditioned Fokker-Planck equations

J. A. Carrillo
, U. Vaes

Research output: Contribution to journal › Article › peer-review

Abstract

We study the convergence to equilibrium of the mean field PDE associated with the derivative-free methodologies for solving inverse problems that are presented by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412-41), Herty and Visconti (2018 arXiv:1811.09387). We show stability estimates in the Euclidean Wasserstein distance for the mean field PDE by using optimal transport arguments. As a consequence, this recovers the convergence towards equilibrium estimates by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412-41) in the case of a linear forward model.

Original language	English
Pages (from-to)	2275-2295
Number of pages	21
Journal	Nonlinearity
Volume	34
Issue number	4
DOIs	https://doi.org/10.1088/1361-6544/abbe62
Publication status	Published - 1 Apr 2021
Externally published	Yes

Keywords

Ensemble Kalman inversion
Mean-field Fokker-Planck equation
Wasserstein stability estimates

Access to Document

10.1088/1361-6544/abbe62

Cite this

@article{e2d2814bd7d14529a84a1e08e92ca5c6,

title = "Wasserstein stability estimates for covariance-preconditioned Fokker-Planck equations",

abstract = "We study the convergence to equilibrium of the mean field PDE associated with the derivative-free methodologies for solving inverse problems that are presented by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412-41), Herty and Visconti (2018 arXiv:1811.09387). We show stability estimates in the Euclidean Wasserstein distance for the mean field PDE by using optimal transport arguments. As a consequence, this recovers the convergence towards equilibrium estimates by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412-41) in the case of a linear forward model.",

keywords = "Ensemble Kalman inversion, Mean-field Fokker-Planck equation, Wasserstein stability estimates",

author = "Carrillo, \{J. A.\} and U. Vaes",

note = "Publisher Copyright: {\textcopyright} 2021 IOP Publishing Ltd.",

year = "2021",

month = apr,

day = "1",

doi = "10.1088/1361-6544/abbe62",

language = "English",

volume = "34",

pages = "2275--2295",

journal = "Nonlinearity",

issn = "0951-7715",

number = "4",

}

TY - JOUR

T1 - Wasserstein stability estimates for covariance-preconditioned Fokker-Planck equations

AU - Carrillo, J. A.

AU - Vaes, U.

PY - 2021/4/1

Y1 - 2021/4/1

N2 - We study the convergence to equilibrium of the mean field PDE associated with the derivative-free methodologies for solving inverse problems that are presented by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412-41), Herty and Visconti (2018 arXiv:1811.09387). We show stability estimates in the Euclidean Wasserstein distance for the mean field PDE by using optimal transport arguments. As a consequence, this recovers the convergence towards equilibrium estimates by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412-41) in the case of a linear forward model.

AB - We study the convergence to equilibrium of the mean field PDE associated with the derivative-free methodologies for solving inverse problems that are presented by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412-41), Herty and Visconti (2018 arXiv:1811.09387). We show stability estimates in the Euclidean Wasserstein distance for the mean field PDE by using optimal transport arguments. As a consequence, this recovers the convergence towards equilibrium estimates by Garbuno-Inigo et al (2020 SIAM J. Appl. Dyn. Syst. 19 412-41) in the case of a linear forward model.

KW - Ensemble Kalman inversion

KW - Mean-field Fokker-Planck equation

KW - Wasserstein stability estimates

UR - https://www.scopus.com/pages/publications/85105046681

U2 - 10.1088/1361-6544/abbe62

DO - 10.1088/1361-6544/abbe62

M3 - Article

AN - SCOPUS:85105046681

SN - 0951-7715

VL - 34

SP - 2275

EP - 2295

JO - Nonlinearity

JF - Nonlinearity

IS - 4

ER -

Wasserstein stability estimates for covariance-preconditioned Fokker-Planck equations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this