2024
DOI: 10.1007/s00205-024-02065-w
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Covariance-Modulated Optimal Transport and Gradient Flows

Martin Burger,
Matthias Erbar,
Franca Hoffmann
et al.

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 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: 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 … Show more

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