EYAWKADANAJKOS

Contribution List

1. Discretizing the Fokker-Planck equation with second-order accuracy: a dissipation driven approach

Clément Cancès (Inria)

4/16/25, 10:30 AM

We propose a fully discrete finite volume scheme for the standard Fokker-Planck equation. The space discretization relies on the well-known square-root approximation, which falls into the framework of two-point flux approximations. Our time discretization is novel and relies on a tailored nonlinear mid-point rule, designed to accurately capture the dissipative structure of the model. We...

2. Lagrangian scheme for nonlinear Fokker-Planck-type equations

Bertram Düring

4/16/25, 11:25 AM

Many nonlinear diffusion equations can be interpreted as gradient flows whose dynamics are driven by internal energies and given external potentials, examples include the heat equation and the porous medium equation. When solving these equations numerically, schemes that respect the equations’ special structure are of particular interest. In this talk we present a Lagrangian scheme for...

3. Vector valued optimal transport: from dynamic to Kantorovich formulations

Katy Craig

4/16/25, 1:45 PM

Motivated by applications in multispecies PDE and classification of vector valued measures, we develop a unified theory that connects four existing notions of vector valued optimal transport. We prove a sharp inequality relating the four notions, showing they are bi-Holder equivalent, and compare and contrast the properties of each metric from the perspective of gradients flows and linearization.

4. The Riemannian geometry of Sinkhorn divergences

Bernhard Schmitzer

4/16/25, 2:40 PM

Optimal transport provides an intuitive and robust way to compare probability measures with applications in many areas of mathematics. This holds in particular for the Wasserstein-2 distance with its formal Riemannian structure. While entropic regularization of optimal transport has several favourable effects, such as improved statistical sample complexity, it destroys this metric structure....

5. Remarks on JKO steps for the Fisher information

Guillaume Carlier

4/16/25, 4:00 PM

It is by now well-known that the quantum drift diffusion equation which is a highly nonlinear fourth-order evolution equation is the Wasserstein gradient flow of the Fisher information. It is therefore natural to investigate whether JKO steps are tractable both from an analytical and computational viewpoint. In this talk, based on a joint work with Daniel Matthes and Jean-David Benamou, I will...

6. Particle discretization of Wasserstein gradient flows

Quentin Merigot

4/16/25, 4:55 PM

In this talk, I will present an approach to particle-based discretizations of Wasserstein gradient flows based on the Moreau-Yosida regularization of the underlying energies. This approach allows to approximate some evolution PDEs (such as Fokker-Planck, porous media or crowd motion models) with interacting particle systems, the interaction being through a mesh which is canonically associated...

7. From inverse optimal transport to global trade

Marie-Therese Wolfram

4/17/25, 9:10 AM

In this talk I will focus on two challenging problems in applied optimal transport: inferring unknown cost functions in noisy optimal transport plans and leveraging deep learning to infer trading barriers in international commodity trade.

We start by discussing the classic optimal transportation problems studied by Gaspard Monge and Leonid Kantorovich, before focusing on the respective...

8. Diffusion: not just discretized, but also quantized

Daniel Matthes

4/17/25, 10:30 AM

Around 2005, Degond, Mehats and Ringhofer proposed a novel approach for the derivation of quantum fluid models (known as QHD, QET etc) from first principles: they apply a moment method to the quantum Boltzmann equation, using a BGK collision operator for moment closure. In the simplest case, the resulting fluid model is the non-local quantum drift diffusion equation nlQDD. It turns out that...

9. Derivation of the fourth order DLSS equation with nonlinear mobility via chemical reactions

André Schlichting

4/17/25, 11:25 AM

We provide a derivation of the fourth-order DLSS equation based on an interpretation as a chemical reaction network. We consider on the discretized circle the rate equation for the process where pairs of particles sitting on the same side jump simultaneously to the two neighboring sites, and the reverse jump where a pair of particles sitting on a common site jump simultaneously to the side in...

10. Finding Wasserstein saddle points "without" optimal transport

Rafael Bailo

4/17/25, 1:45 PM

In this talk, we will present a numerical scheme to approximate the saddle points of a Wasserstein gradient flow. Our approach is based on known techniques for Hilbert spaces and is derived from a formal JKO scheme. Unlike geodesic approaches, ours does not require solving any optimal transport problems. We will showcase the performance of the method and validate it over several examples. This...

11. Hilbertian degenerations and inhibition models

Bertrand Maury

4/17/25, 2:40 PM

Gradient flows in Hilbert spaces are conditioned by the choice of an underlying metric so that a given functional may give rise to infinitely many gradient flows. We shall investigate in this talk the possible limit behaviors of the associated evolution problems when the metric degenerates, by considering sequences of metrics which are « less and less equivalent » to the canonical one. In...