Covariance-modulated optimal transport and gradient flows
speaker: Matthias Erbar (Universiät Bielefeld)abstract: We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the current distribution. Such transport metrics arise naturally in mean field limits of recent particle filtering methods for inverse problems. We show that the transport problem splits into two coupled minimisation problems: one for the evolution of mean and covariance of the interpolating curve and one for its shape. The latter consists in minimising the usual Wasserstein length under the constraint of maintaining fixed mean and covariance along the interpolation. We analyse the geometry induced by this modulated transport distance on the space of probabilities as well as the dynamics of the associated gradient flows. Those show better convergence properties in comparison to the classical Wasserstein metric in terms of exponential convergence rates independent of the Gaussian target. This is joint work with Martin Burger, Franca Hoffmann, Daniel Matthes and André Schlichting This is joint work with Martin Burger, Franca Hoffmann, Daniel Matthes and André Schlichting
timetable:
Thu 27 Oct, 16:30 - 17:15, Aula Magna Bruno Pontecorvo
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