  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 transfer operators derived from GW transport
plans, when merely the initial and final states are known. We focus on entropy
regularized GW transport, which allows to utilize the fast Sinkhorn algorithm
and a spectral clustering procedure to extract coherent structures. Moreover,
the GW framework provides a natural quantitative assessment on the
shape-coherence of the extracted structures. We discuss fused and unbalanced
variants of GW transport for labelled and noisy data, respectively. Our models
are verified by three numerical examples of dynamical systems with governing
rotational forces.
