Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations
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...
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| Format: | Journal article |
| Language: | English |
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IOP Publishing
2021
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| _version_ | 1797066676627308544 |
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| author | Carrillo, JA Vaes, U |
| author_facet | Carrillo, JA Vaes, U |
| author_sort | Carrillo, JA |
| collection | OXFORD |
| description | 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.
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| first_indexed | 2024-03-06T21:45:26Z |
| format | Journal article |
| id | oxford-uuid:496a0591-90de-472a-94c5-b8765ecac5fb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:45:26Z |
| publishDate | 2021 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | oxford-uuid:496a0591-90de-472a-94c5-b8765ecac5fb2022-03-26T15:31:27ZWasserstein stability estimates for covariance-preconditioned Fokker–Planck equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:496a0591-90de-472a-94c5-b8765ecac5fbEnglishSymplectic ElementsIOP Publishing2021Carrillo, JAVaes, UWe 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. |
| spellingShingle | Carrillo, JA Vaes, U Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations |
| title | Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations |
| title_full | Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations |
| title_fullStr | Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations |
| title_full_unstemmed | Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations |
| title_short | Wasserstein stability estimates for covariance-preconditioned Fokker–Planck equations |
| title_sort | wasserstein stability estimates for covariance preconditioned fokker planck equations |
| work_keys_str_mv | AT carrilloja wassersteinstabilityestimatesforcovariancepreconditionedfokkerplanckequations AT vaesu wassersteinstabilityestimatesforcovariancepreconditionedfokkerplanckequations |