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Covariance-modulated optimal transport

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Authors : Hoffmann, Franca (Author of the conference)
CIRM (Publisher )

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Abstract : We study a variant of the dynamical optimal transport problem in which the energy to be minimized is modulated by the covariance matrix of the current distribution. Such transport metrics arise naturally in mean field limits of recent particle methods for inverse problems. We show that the transport problem splits into two separate minimisation problems: one for the evolution of mean and covariance of the interpolating curve and one for its shape. The latter consists in minimizing the usual Wasserstein length under the constraint of maintaining fixed mean and covariance along the interpolation. We analyze the geometry induced by this modulated transport distance on the space of probabilities as well as the dynamics of the associated gradient flows. This is joint work with Martin Burger, Matthias Erbar, Daniel Matthes and André Schlichting.

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    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 10/05/2022
    Conference Date : 25/04/2022
    Subseries : Research talks
    arXiv category : Dynamical Systems
    Mathematical Area(s) : Dynamical Systems & ODE
    Format : MP4 (.mp4) - HD
    Video Time : 00:52:32
    Targeted Audience : Researchers ; Graduate Students
    Download : https://videos.cirm-math.fr/2022-04-25_Hoffman.mp4

Information on the Event

Event Title : Probability/PDE Interactions: Interface Models and Particle Systems / Interactions EDP/Probabilités : interfaces et systèmes de particules
Event Organizers : Duerinckx, Mitia ; Gess, Benjamin ; Fathi, Max ; Guillin, Arnaud ; Simon, Marielle
Dates : 25/04/2022 - 29/04/2022
Event Year : 2022
Event URL : https://conferences.cirm-math.fr/2557.html

Citation Data

DOI : 10.24350/CIRM.V.19910203
Cite this video as: Hoffmann, Franca (2022). Covariance-modulated optimal transport. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19910203
URI : http://dx.doi.org/10.24350/CIRM.V.19910203

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