Entropy-regularized optimal transport and its multi-marginal generalization have attracted
increasing attention in various applications, in particular due to efficient Sinkhorn-like …

We propose a new concept for the regularization and discretization of transfer and Koopman
operators in dynamical systems. Our approach is based on the entropically regularized …

Gromov–Wasserstein (GW) transport is inherently invariant under isometric transformations
of the data. Having this property in mind, we propose to estimate dynamical systems by …

Koopman operators and transfer operators represent dynamical systems through their
induced linear action on vector spaces of observables, enabling the use of operator …

Gromov–Wasserstein (GW) distances are combinations of Gromov–Hausdorff and
Wasserstein distances that allow the comparison of two different metric measure spaces …

The Gromov-Wasserstein (GW) transport problem is a relaxation of classic optimal transport,
which seeks a transport between two measures while preserving their internal geometry …

In this paper, we are concerned with estimating the joint probability of random variables $ X
$ and $ Y $, given $ N $ independent observation blocks $(\boldsymbol {x}^ i,\boldsymbol …

Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or
tropical cyclones often induce extreme weather conditions. As a consequence, their …

Over the past few decades, optimal transport (OT) has progressively shifted into the focus of
modern applied mathematics. Central to OT are various optimization problems, namely …

Abstract The Perron–Frobenius and Koopman operators provide natural dual settings to
investigate the dynamics of complex systems. In this thesis we focus on certain pertinent …