Geneviève Dusson "Nonlinear Model Order Reduction via Optimal Transport"

Tuesday Oct 14, 2025, 3:15 PM → 4:15 PM Europe/Paris

Fokko du Clou (Braconnier camous la doua)

Abstract: Parametric PDEs exhibiting transport-dominated behavior pose a significant challenge for classical linear model-order reduction (MOR) techniques, which often fail to capture essential solution features such as translation or deformation. In this talk, I will first present a nonlinear MOR strategy grounded in optimal transport, where reduced solutions are constructed as Wasserstein barycenters of selected high-fidelity solutions.
Second I will introduce marginal-constrained Wasserstein barycenters, a recent development that enables efficient approximations leveraging the more easily accessible knowledge to the marginals of probability distributions, compared to the full distributions. These barycenters are defined as the solution to an optimization problem which can be analytically solved for Gaussian distributions, and requires a post-processing step for Gaussian mixtures.
This is expected to be particularly useful in high-dimensional settings where the access to full solutions is limited or expensive. As an application, we show how this approach can be used in quantum chemistry to approximate the pair density from knowledge of the electronic density alone.

joint work with Maxime Dalery and Virginie Ehrlacher