H.B. Keller Colloquium

Monday, January 30, 2023
4:00pm to 5:00pm
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Annenberg 105
Covariance-modulated optimal transport and gradient flows
Franca Hoffmann, Assistant Professor, Computing and Mathematical Sciences Department, California Institute of Technology,

We present 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 certain ensemble Kalman methods for solving inverse problems.
We show that the transport problem splits into two coupled minimization problems up to degrees of freedom given by rotations: one for the evolution of mean and covariance of the interpolating curve, and one for its shape.

Similarly, on the level of the gradient flows a similar splitting into the evolution of moments and shapes of the distribution can be observed. 

Those show better convergence properties in comparison to the classical Wasserstein metric in terms of exponential convergence rates independent of the Gaussian target.

For more information, please contact Diana Bohler by phone at 16263951768 or by email at [email protected].