## Séminaire Modélisation, Analyse et Calcul

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Organisateurs : Nicolas Godet & Ariane Trescases

Horaires et lieux habituels : mardi à 11h en amphi Schwartz (Bât. 1R3)

• ### Mardi 22 octobre 11:00-12:00 -

Pas de séminaire

• ### Mardi 29 octobre 11:00-12:00 -

Pas de séminaire - Vacances

• ### Mardi 5 novembre 11:00-12:00 - Antonio Esposito - Friedrich-Alexander Universität Erlangen-Nürnberg

On systems of PDEs with nonlinear cross-diffusion and nonlocal interactions

Résumé : I will discuss recent results obtained in collaboration with J. A. Carrillo, M. Di Francesco, S. Fagioli and M. Schmidtchen on some systems of partial differential equations modelling aggregation-diffusion phenomena with many species. First, I will talk about a class of systems of PDEs with nonlinear degenerate cross-diffusion and nonlocal interactions, for which we prove global-in-time existence of weak solutions under a uniform “coerciveness” assumption on the diffusion part, and by means of a semi-implicit version of the Jordan-Kinderlehrer-Otto scheme. Our approach allows to consider nonlocal interaction terms not necessarily yielding a formal gradient flow structure. This work is co-authored with M. Di Francesco and S. Fagioli, both from the University of L’Aquila. Further collaboration with J. A. Carrillo (Imperial College London) and M. Schmidtchen (LJLL, Sorbonne Université) led to a recent work where we deal with a system of continuity equations driven by Newtonian nonlocal interaction in one dimension. We provide global-in-time existence and uniqueness either of measure solutions or $L^p$ densities, for $p\in(1,+\infty]$. In the latter case we also provide a characterisation of equilibria and prove that they are achieved (up to time subsequences) in the large time asymptotics.

Lieu : Amphithéâtre Laurent Schwartz

• ### Mardi 12 novembre 11:00-12:00 - Anthony Nouy - Centrale Nantes

Approximation with tree tensor networks

Résumé : Many problems in computational science require the approximation of high-dimensional functions. Examples of such problems can be found in physics, stochastic analysis or statistical learning. Other examples include parametric or uncertainty analyses for parameter-dependent models.
The approximation of a high-dimensional function requires the introduction of specific approximation formats with a low number of parameters that can be estimated using limited information on the function. In this talk, we will first review some classical tools for high-dimensional approximation. We will then give an introduction to low-rank approximation formats, including tree tensor networks, and make the connection between these formats and a particular family of deep neural networks.
Finally, we will present some approximation results for tree tensor networks.

Lieu : Salle MIP

• ### Mardi 19 novembre 11:00-12:00 -

Pas de séminaire - Journée HCERES

• ### Mardi 26 novembre 11:00-12:00 - Joackim Bernier - Université Toulouse 3

Exact splitting methods for semigroups generated by inhomogeneous quadratic differential operators

Résumé : I will present some general tools to factorize semigroups generated by inhomogeneous quadratic differential operators as product of more elementary semigroups. On the one hand, I will explain how such a factorization can be used to characterize the regularizing effects of these semigroups. On the other hand, from a numerical point of view, we will see how it can be used to get some efficient and accurate splitting methods. I will highlight the efficiency of these new methods on the example of the magnetic Schrödinger equations with harmonic potentials. This talk will rely on some joint works with Paul Alphonse, Nicolas Crouseilles, Fernando Casas and Yingzhe Li.

Lieu : Salle MIP

• ### Mardi 3 décembre 11:00-12:00 - Kévin Le Balc'h - Institut de Mathématiques de Bordeaux

TBA

Lieu : Amphithéâtre Laurent Schwartz

• ### Mardi 10 décembre 11:00-12:00 - TBA

Date libre

Lieu : Salle MIP

• ### Mardi 17 décembre 11:00-12:00 - Emeric Bouin - Université Paris-Dauphine

TBA

Lieu : Amphithéâtre Laurent Schwartz

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