Damiano Lombardi
Inria Paris – 🇫🇷 Paris (France)
Optimal transport and model reduction
In this talk we are going to recall the fundamentals of the Optimal Transport (OT) problem. In particular, we are going to highlight how the Wasserstein distance could be seen as a natural way to evaluate the distance between snapshots in phenomena dominated by transport and how the McCann interpolation provides a natural way to interpolate between them.
Moreover, we are going to discuss about how the set of snapshots, endowed with the Wasserstein distance, could appear as ‘less high-dimensional’ than the same set of snapshots when we use, as metric, Sobolev norms such as or . An analytical exemple in this respect is discussed.
Several numerical examples are described, highlighting encouraging aspects and shortcomings of the use of OT in model reduction.