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Universität Augsburg
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Universität Augsburg
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Professor Dr. André Schlichting
Universität Ulm
spricht am
Mittwoch, 23. Oktober 2024
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| We study a variant of the dynamical optimal transport problem in which the kinetic 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 filtering methods for inverse problems. We show that the transport problem splits into two separate minimization 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 distance 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. The associated gradient flows show better convergence properties in comparison to the classical Wasserstein metric in terms of exponential convergence rates independent of the Gaussian target. Moreover, the dynamic allows for a similar splitting into the evolution of moments and shapes of the distribution. Based on joint work with Martin Burger, Matthias Erbar, Franca Hoffmann and Daniel Matthes. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Malte Peter |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).