## Section: New Results

### Miscellaneous

Participants : Damiano Lombardi, Olga Mula.

In [20] an approximated formulation of the multi-marginal optimal transport problem (Kantorovich formulation) is proposed. In the formulation, called MCOT, the constraints on the marginal densities are replaced by moments of the densities. This formulation allows to deal simply with a wide spectrum of high-dimensional multi-marginal problems, with non-standard (martingale) constraints.

In [27] a reduced-order modeling framework is proposed, in which a set of model instances is part of a metric space. The introduction of the exponential and logarithmic maps (Riemannian geometry) makes it possible to reduce in an effective way solutions that are classically challenging for standard model reduction methods. Some examples on 1D hyperbolic equations and Wasserstein distance are proposed.