Laboratoire J. A. Dieudonné

Séminaire de l'équipe EDP Analyse Numérique

Séminaires à venir   -   Liste complète 2023-2024   -   Archives 2009-2023

21/09/2023 
   11h
   Salle de conférences
Misha Chertkov (University of Arizona)
   Lagrangian Large Eddy Simulations via Physics Informed Machine Learning
   Traditional Large Eddy Simulations (LES) model turbulent flows using heuristics rooted in Eulerian truncation of the the Navier-Stocks (NS) equations which require assumptions about sub-grid scale impacts. We introduce an innovative Lagrangian approach, termed Lagrangian-LES, which evolves with turbulent flow particles. This method augments the Smooth Particle Hydrodynamics (SPH) formulation, leveraging Machine Learning (ML) to interpret Lagrangian data from Direct Numerical Simulation (DNS) of NS equations. L-LES offers explainable parameters, such as those for eddy-diffusivity, and uses Neural Networks (NN) to discern the effects of unresolved scales. With Differentiable Programming (DP) and Deep NN, we refine these parameters and functions, testing a variety of physics-informed loss functions. Our results demonstrate the L-LES's unique ability to depict turbulence efficiently and its proficiency in reproducing both Lagrangian and Eulerian flow statistics at the resolved scales. Based on collaborative work with Y. Tian, M. Woodward, M. Stepanov, C. Hyett, C. Fryer, and D. Livescu.
   Gestion: Florence
28/09/2023 
   8h-22h
   Salle de conférences
Journée ANR Adyct ()
   
   
   Gestion: Maxime
05/10/2023 
   11h
   
reporté (LJAD)
   
   
   Gestion: Florence
12/10/2023 
   14h
   Salle Fizeau
HDR Laurent Monasse ()
   
   
19/10/2023 
   11h
   Salle de conférences
Sam Krupa  (Max Planck Institute for Mathematics in the Sciences)
   Large Data Solutions to 1-D Hyperbolic Systems, Ill-Posedness, and Convex Integration
   For hyperbolic systems of conservation laws in one space dimension endowed with a single convex entropy, it is an open question if it is possible to construct solutions via convex integration. Such solutions, if they exist, would be highly non-unique and exhibit little regularity. In particular, they would not have the strong traces necessary for the nonperturbative $L^2$ stability theory of Vasseur. Whether convex integration is possible is a question about large data, and the global geometric structure of genuine nonlinearity for the underlying PDE. In this talk, I will discuss recent work which shows the impossibility, for a large class of 2x2 systems, of doing convex integration via the use of $T_4$ configurations. Our work applies to every well-known 2x2 hyperbolic system of conservation laws which verifies the Liu entropy condition. This talk is based on joint work with László Székelyhidi.
26/10/2023 
   14h
   Salle de conférences
Thèse Dahmane Dechicha ()
   
   
09/11/2023 
   11h
   Salle de conférences
Isabelle Tristani (LJAD)
   Autour de la notion d’hypocoercivité en théorie cinétique des gaz
   Dans cet exposé, nous présenterons la notion d’hypocoercicité en théorie cinétique des gaz qui permet d’étudier le comportement en temps long de certaines équations dont l’opérateur de collisions possède des propriétés dissipatives telles que les équations de Fokker-Planck, Boltzmann et Landau. Nous présenterons plus précisément la théorie d’hypocoercivité L^2 dans le cas de conditions au bord périodiques puis expliquerons comment étendre cela au cas de domaines bornés avec conditions au bord générales. Cette présentation reprendra notamment des résultats d’un article écrit en collaboration avec A. Bernou, K. Carrapatoso et S. Mischler.
   Gestion: Florence
16/11/2023 
   11h
   Salle de conférences
Thomas Rey (LJAD)
   Schémas d'intégration projective pour des équations cinétiques multi-échelles
   L'intégration projective a été récemment proposée comme une alternative viable aux méthodes entièrement implicites et aux méthodes micro-macro pour fournir des intégrateurs légers, non intrusifs et "presque AP" permettant de résoudre numériquement des équations cinétiques multi-échelles. Ces méthodes utilisent une suite de petits pas de temps du schéma d'Euler Explicite, intercalés avec de grands pas de temps d'extrapolation. L'approche dite télescopique itère ces extrapolations par récurrence pour des modèles ayant un grand nombre d'échelles de temps différentes. Ces approches rendent la complexité de calcul de la méthode essentiellement indépendante de la raideur du problème, ce qui permet de résoudre efficacement les équations considérées dans des régimes raréfiés ou fluides. Nous présenterons les bases de la méthode, quelques bases de théorie cinétique, ainsi qu'une série de simulations numériques permettant de valider ces schémas sur différents modèles issus de la physique et de la biologie.
   Gestion: Florence
23/11/2023 
   11h
   Salle Fizeau (?)
Chiara Simeoni  (LJAD)
   Analysis and numerics of the propagation speed for hyperbolic reaction-diffusion models
   We briefly discuss different models for reaction-diffusion phenomena based on hyperbolic equations. The standard approach makes use of parabolic systems which are, indeed, well suited to explain events such as heat transmission in close-to-equilibrium regimes. Nevertheless, such modeling is criticizable for several reasons, for instance the prediction of an infinite speed of propagation, the lack of time-delay and related inertial effects, and the exceptionality of well-posed boundary value problems. In addition, in many contexts the hyperbolic description is relevant for applications (dynamics of biological tissues, population growth, forest fire models) and more appropriate when the relaxation time required to perceive changes of the overall dynamics is sufficiently large as compared to the diffusivity coefficient. As a matter of fact, differences may emerge in the transient regimes, whose cumulations may influence significantly the final outcome. Actually, the emphasis is placed on the numerical computation of the propagation speed of traveling wave solutions. Therefore, we focus on a specific class of 2x2 systems corresponding to second order PDEs in one space dimension, which are simplified models of reaction-diffusion equations with monostable and bistable reaction terms. Beside the phase-plane algorithm which is convenient for approximating general hyperbolic reaction-diffusion systems with damping, especially in cases with available explicit formulas, we propose two numerical schemes, the so-called scout&spot algorithm - based on tracking the level curve of some intermediate value of the wave profile - and the LeVeque-Yee formula - given by the average value of the discrete advection velocity - by assessing their capability in comparative experiments of genuine predictions.
   Gestion: Thomas
30/11/2023 
   11h
   Salle 2
Yassine Laguel (LJAD)
   Robustifying Models and Algorithms in Machine Learning
   Risk-averse optimization plays a major role in ensuring safety for machine learning applications. In this talk, we will present a set of tools to enhance the resilience of models and algorithms against potentially harmful data shifts. First, we will discuss general results on modeling risk aversion and emphasize the importance of superquantile-based risk measures for enforcing robustness against worst-case scenarios. We will then show how such measures can be minimized in both the centralized and federated settings through state-of-the-art methods. Second, we will reexamine the bias-variance trade-off of first-order stochastic algorithms from a robust perspective. Specifically, we will provide a tight convergence analysis in the strongly convex/strongly concave setting for accelerated methods in solving saddle-point problems and discuss diverse robustness metrics. Finally, we will explore novel parameter selection procedures, informed by our extensive analysis of quadratics and strong convexity/concavity.
   Gestion: Florence ?
07/12/2023 
   11h
   Salle de conférences
Yves-Marie Ducimetière (EPFL)
   Non-modal amplitude equations
   In this exposé, we propose to formally derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they respond to harmonic or stochastic forcing. This approach reconciles the non-modal nature of these growth mechanisms and the need for a centre manifold to project the leading-order dynamics. Under the hypothesis of strong non-normality, small operator perturbations suffice to make the inverse resolvent singular. The adjective “small” is relative to the choice of an induced-norm, under which the systems experience a large input-output amplification. Such operator perturbation can be encompassed in a multiple-scale asymptotic expansion, closed by a standard compatibility condition. The resulting amplitude equations are tested in parallel and non-parallel two-dimensional flows, where they bring insight into the weakly nonlinear mechanisms that modify the gains as we increase the amplitude of the harmonic or stochastic forcing.
   Gestion: Florence
14/12/2023 
   11h
   Salle de conférences
Nathalie Ayi (Sorbonne Université)
   "Graph limits" de systèmes de particules en interaction sur des graphes à poids (déterministes et aléatoires)
   Dans cet exposé, nous commençons par étudier un modèle particulier de dynamique des opinions où les poids d’influence des agents évoluent dans le temps via une équation elle-même couplée à l’évolution des opinions. Nous explorons la question naturelle de la limite en grande population via deux approches : la désormais classique limite de champ moyen et la plus récente "graph limit". Après avoir rigoureusement établi la "graph limit", on définit la notion clé d'indistinguabilité, qui est un cadre nécessaire pour pouvoir considérer la limite de champ moyen. Nous prouvons alors la subordination de cette dernière à la "graph limit". Nous terminons par l'étude de systèmes de particules en interaction posés sur des graphes aléatoires à poids. Dans ce but, nous introduisons un cadre général pour la construction de ces derniers. Nous prouvons que lorsque le nombre de particules tend vers l'infini, on obtient la convergence en probabilité vers la solution d'une équation déterministe dans laquelle le graphon prescrivant l'interaction est donné par le premier moment de la loi des graphes aléatoires à poids.
   Gestion: Isabelle
25/01/2024 
   11:00
   Salle de conférences
Luca Nenna (Université Paris-Saclay)
   Convergence rate of entropy-regularized multi-marginal optimal transport costs
   We investigate the convergence rate of multi-marginal optimal transport costs that are regularized with the Boltzmann-Shannon entropy, as the noise parameter ε tends to 0. We establish lower and upper bounds on the difference with the unregularized cost of the form Cεlog(1/ε)+O(ε) for some explicit dimensional constants C depending on the marginals and on the ground cost, but not on the optimal transport plans themselves. Upper bounds are obtained for Lipschitz costs or semi-concave costs (for a finer estimate), and lower bounds for C² costs satisfying some signature condition on the mixed second derivatives that may include degenerate costs, thus generalizing results previously obtained by Carlier, Pegon and Tamanini, and by Eckstein and Nutz. We obtain in particular matching bounds in some typical situations where the optimal plan is deterministic, like in the case of Wasserstein barycenters. This is a joint work with Paul Pegon.
   E-mail: https://lucanenna.github.io/
   Gestion: Thomas
01/02/2024 
   11:00
   
Shi Jin (Shanghai Jiao Tong)
   TBA
   
08/02/2024 
   11:00
   Salle de conférences
Julien Royer (Institut de Mathématiques de Toulouse)
   Décroissance de l'énergie locale et asymptotique basse fréquence pour l'équation de Schrödinger
   On s'intéresse à la décroissance de l'énergie locale pour l'équation de Schrödinger dans un cadre asymptotiquement Euclidien. Pour cela, on s'intéresse plus précisément au comportement de la résolvante pour les basses fréquences. Nous verrons comment utiliser des idées venant de l'étude des ondes amorties pour obtenir le profil asymptotique pour la résolvante, puis celui de la solution en temps grand.
   E-mail: https://www.math.univ-toulouse.fr/~jroyer/
   Gestion: Thomas
15/02/2024 
   11:00
   Salle de conférences
Meriem Bahhi & Alba Garcia (LJAD)
   A mathematical study of a quasi-linear Schrödinger type-equation & Local behaviour of high energy eigenfunctions of polygonal domains
   We explore a Quasi-linear Schrödinger-type equation that is related to the description of the behavior of particles within atomic nuclei. Under some assumption on the parameters of the model we establish the existence and the uniqueness of positive radial solutions. Moreover we analyze the behavior of these solutions according to the parameters.
   Gestion: Thomas
22/02/2024 
   11h
   Salle de conférences
Bertrand Lods (Universita degli Studi di Torino)
   Prodi-Serrin like criteria for Landau equation with soft potentials
   The scope of the talk is to introduce Prodi-Serrin like criteria for weak solutions under which it is possible to show existence of classical solutions to the spatially homogeneous Landau equation for all classical potentials and dimensions. We establish instantaneous appearance of Lp estimates using the Prodi-Serrin criteria. This, combined with a suitable De Giorgi's argument provides appearance of pointwise bounds for such solutions. Uniqueness and regularity of solutions will also be discussed.
   Gestion: Isabelle
29/02/2024 
   11h
   
Michel Rieutord (Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse)
   Oscillations in rotating fluids: singularities of low-frequency modes in spherical shells
   Stars and planets are all rotating. Due to the conservation of angular momentum, this leads to specific oscillations known as inertial oscillations. These oscillations are low-frequency and own many peculiarities, like singularities. In this talk I will review the recent progresses in the understanding of these oscillations, especially those of a fluid in a spherical shell that are appropriate for celestial bodies and which raise many mathematical problems. I will also discuss how the properties of these waves might affect the oscillation spectrum of stars and planets, their internal dynamics or their response to a tidal forcing.
   Gestion: Florence
07/03/2024 
   11:00
   Salle de conférences
Tino Laidin (Laboratoire Paul Painlevé)
   Discrete hypocoercivity for a nonlinear kinetic reaction model.
    I will present a work in collaboration with M. Bessemoulin-Chatard and T. Rey, in which we consider a non-linear kinetic model describing a two-species generation-recombination reaction that can be considered as a simplified version of models describing the generation and recombination of electron-hole pairs in semiconductors. I will introduce a finite volume discretization of this model for which we can prove an exponential decay towards the steady state using discrete hypocoercivity methods. After presenting the ideas of the proof in the continuous framework, I will highlight the main difficulties induced by the discretization process. The properties of the method will then be illustrated by several numerical examples.
   Gestion: Thomas
14/03/2024 
   11:00
   Salle de conférences
Charlotte Perrin (Institut de Mathématiques de Marseille)
   TBA
   TBA
   E-mail: https://www.chperrin.fr/
   Gestion: Thomas
21/03/2024 
   11:00
   Salle de conférences
Pierre Ablin (Apple Machine Learning Research)
   Transformers, Dynamical Systems and Optimal Transport.
    The transformer architecture is one of the cornerstones that enables the large language models revolution. It is a neural network architecture that acts on arbitrary length sequences of vectors. At its core is the attention mechanism, which transforms a sequence into another sequence, where each element of the sequence interacts with each other. The goal of this talk is to i) give a comprehensive introduction to the transformer architecture, ii) explain its connection with interacting particles systems and optimal transport and iii) present recent results on the Lipschitz constant of attention. The talk is based on the following papers: - Sander, Michael E., Pierre Ablin, Mathieu Blondel, and Gabriel Peyré. "Sinkformers: Transformers with doubly stochastic attention." In International Conference on Artificial Intelligence and Statistics, pp. 3515-3530. PMLR, 2022. https://arxiv.org/abs/2110.11773 - Castin, Valérie, Pierre Ablin, and Gabriel Peyré. "Understanding the Regularity of Self-Attention with Optimal Transport." arXiv preprint arXiv:2312.14820 (2023). https://arxiv.org/abs/2312.14820
   E-mail: https://pierreablin.com/
   Gestion: Thomas
28/03/2024 
   11h
   Salle de conférences
Iván Moyano (LJAD)
   Existence of solutions to the fractional Vlasov-Poisson-Fokker-Planck system
   We study the existence of solutions to a kinetic system describing the dynamics of a large number of particles undergoing the effect of a self-generated field (electrical or gravitational) and the action of random jumps in velocity according to a $2\sigma$-stable Poisson process. The evolution of the corresponding system can be seen as a fractional version of the classical Valsov-Poisson-Fokker-Planck systems in which the dissipating part is described by a fractional Laplacian. We address the question of local existence in time of mild solutions for this system in all natural ranges $0 < \sigma < 1$. We also investigate the possibility of propagating the lifespan of these solutions in the range $\frac{1}{2} < \sigma < 1$ and get global solutions in $L^p$ spaces, which is possible thanks to the use of fundamental solutions combined with an approach due to Bouchut (\emph{J. Funct. Analysis} Vol 111(1) 1993 pp 239-258.).
11/04/2024 
   11:00
   TBA
André de Laire (Université de Lille/LPP)
   TBA
   TBA
   Gestion: Thomas
18/04/2024 
   11h
   Salle de conférences
Lucas Ertzbischoff (Imperial College London )
   TBA
   
   Gestion: Isabelle
16/05/2024 
   
   
 ()
   Ecole Semiclassique et Applications (13-17 mai)
   
   Gestion: Maxime
23/05/2024 
   
   
Jason Picardo ()
   TBA
   
   Gestion: Florence
30/05/2024 
   
   
Colm Caulfield (University of Cambridge)
   Rencontres Niçoises de Méca Flu
   
   Gestion: Florence
06/06/2024 
   11h
   Salle Fizeau
Salma Lahbabi (Université de Casablanca)
   
   
20/06/2024 
   11h
   Salle de conférences
Maxime Herda (Université de Lille)
   TBA
   
   Gestion: Isabelle

Contact: responsables du séminaire