Conférence pour les 50 ans du CMAP

Europe/Paris
Amphi Faurre (Ecole Polytechnique)

Amphi Faurre

Ecole Polytechnique

Description

            Conférence pour les 50 ans du CMAP 

                    Du 11 au 13 Septembre 2024

 

Cette conférence a pour but de célébrer les 50 ans d'existence du Centre de Mathématiques Appliquées de l'Ecole Polytechnique.

Cet évènement à la fois festif et scientifique permettra de présenter un panorama large des thématiques couvertes au sein du laboratoire depuis sa création.  

 

Orateurs :

  • S. Allassonnière (U. Paris-Cité)
  • H. Ammari (ETH Zurich)
  • T. Bodineau (CNRS & IHES)
  • A. Chambolle (CNRS & CEREMADE, PSL)
  • C. Dapogny (CNRS & U. Grenoble-Alpes)
  • R. Douc (Telecom SudParis)
  • C. Hillairet (ENSAE)
  • J. Josse (INRIA)
  • S. Mallat (Collège de France)
  • E. Moulines (CMAP, Polytechnique)
  • J.M. Roquejoffre (IMT Toulouse)
  • N. Spillane (CNRS & CMAP, Polytechnique)
  • N. Touzi (NYU, New York)
  • A. Veber (CNRS & U. Paris-Cité)
  • D. Villemonais (U. Lorraine)

 

 

Comité d'organisation :

E. Abi-Jaber, C. Bertucci,  V. Giovangigli, M. Goldman, C. Graham, A. Oliviero-Durmus, M. Tomasevic 

 

Lien vers le site web du CMAP :

https://cmap.ip-paris.fr/

 

    • 1
      Ouverture et mot des tutelles Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

    • 2
      T. Bodineau : Statistical properties of a hard sphere gas Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      A gas dynamics can be modelled by a billiard made of hard spheres, moving according to the laws of classical mechanics. Initially the spheres are randomly distributed according to a probability measure which is then transported by the flow of the deterministic dynamics. Since the seminal work of Lanford, it is known that the gas density converges in the kinetic limit towards the Boltzmann equation (at least for a short time). In this talk, we are going to review several results on the fluctuations of the particle system density around the Boltzmann equation. This is based on joint works with I. Gallagher, L. Saint-Raymond and S. Simonella.

    • 3
      N. Spillane : Convergence and acceleration of GMRES for solving linear systems Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      The GMRES linear solver, introduced by Y. Saad et M. H. Schultz is the go-to solver for non-symmetric systems that are too large to be factorized. For general matrices, the convergence behaviour of GMRES is not fully understood. Theoretical analysis is a challenge in itself but it also has very important practical implications.

      In this talk I will present some existing convergence results for GMRES as well as their limitations. For matrices that have positive-definite symmetric part, I will analyze GMRES in a way that makes explicit the influence of three GMRES accelerators:
      - weighting (i.e., changing the inner product),
      - preconditioning (i.e., providing a cheap approximate inverse of the matrix),
      - deflation (i.e., solving exactly the problem on part of the solution space).

      These results provide us with a strategy for accelerating GMRES in the case of positive-definite problems.

      This is joint work with Daniel Szyld from Temple University in Philadelphia.

    • 3:00 PM
      Pause Café Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

    • 4
      S. Allassonnière : Intelligence artificielle en santé : actualités et perspectives. Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      Along my years in the CMAP, I have been able to work with my students on several projects that I will quickly describe here.

      First we have provided coherent framework for studying cross-sectional, multimodal and longitudinal manifold-valued data. We have introduced Bayesian mixed-effect models which allow to estimate both a group-representative piecewise-geodesic trajectory in the Riemannian space of shape and inter-individual variability. We have proved theoretical guarantees of the models and the optimisation algorithms. The practical use of these models has led to the creation of a startup named Qairnel.

      In this second work we investigate a model-based reinforcement learning approach for a sequential decision making problem in a rare obstetrical disease diagnostic task. The specificities of our case study, namely the data scarcity, the lack of expert demonstration from which we could learn, and the importance of domain knowledge combined with high-dimensionnal issues lead us to an original model learning algorithm proposition. This led to the creation of Sonio.

      I will end with a new research topic about data augmentation to accelerate clinical trials.

    • 5
      S. Mallat Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

    • 6
      Session Poster Grand Hall

      Grand Hall

      Ecole Polytechnique

    • 7
      C. Hillairet : Actuarial modeling for the systemic component of Cyber-risk Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      With the rise of digital economy, cyber risk has become a major threat for the financial system, while the scale of losses linked to cyber-risk is rising sharply (more than 1% of the global GDP). Facing this risk, cyber insurance is an essential lever for economic resilience, but its development encounters some pitfalls, with important uncertainties. Indeed the emerging and evolving nature of cyber-risk and its potential systemic component questions its insurability. After an introduction to the specificities on cyber risk, we present a stochastic model to capture the cluster features in the arrival of cyber-events, namely Marked Hawkes processes. These mathematical objects turn out to be difficult to study. Using new technics at the crossroad of the so-called Poisson imbedding and Malliavin’s calculus, we develop theoretical results on such processes and present several applications in terms of risk quantification.

      This talk is based on joint works with Anthony Réveillac, Mathieu Rosenbaum, and Thomas Peyrat

    • 8
      J.-M. Roquejoffre : Large time dynamics in the Fisher-KPP equation Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      The Fisher-KPP equation (the acronym KPP standing for Kolmogorov, Petrovskii and Piskunov) is an ubiquitous model that arises in the applied sciences, such as ecology or combustion science, but also in probability theory. When solved with a a compactly supported initial datum, its level sets advance at asymptotically constant speed, corrected by a term that is logarithmic in time. The correction was discovered by Bramson at the beginning of the 80's, with the aid of probabilistic arguments. This is an intriguing behaviour, as many models of front propagation do not exhibit it.

      The goal of the talk is to explain the mechanism leading to this asymptotic behaviour with a simple PDE argument, that was proposed in collaboration with J. Nolen and L. Ryzhik in 2017. I will then discuss how these ideas can be used to explore less standard models, such as, for instance, equations with integral diffusion or nonlocal models in epidemiology.

    • 10:50 AM
      Pause Café Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

    • 9
      D. Villemonais : Processus de Galton-Watson bi-sexués et multi-types Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      Le modèle de Galton-Watson bi-sexué multi-type permet de modéliser l'évolution d'une population genrée. Cette propriété, qui permet de palier une restriction essentielle des processus de Galton Watson classiques, fait perdre au processus sa propriété de branchement. En l'absence d'un opérateur de reproduction linéaire, qui est la clé pour comprendre le comportement du modèle dans le cas asexué, nous construisons un opérateur de reproduction concave et utilisons une théorie de Perron-Frobenius concave pour démontrer des conditions nécessaires et suffisantes d'extinction et de comportement malthusien, sous des hypothèses de super-additivité. Il s'agit d'un travail en collaboration avec Coralie Fritsch et Nicolas Zalduendo.

    • 10
      H. Ammari : 50 ans d'ondes au CMAP Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      Les ondes ont été et continuent d'être un domaine de recherche majeur au CMAP. L'objectif de cette présentation est de retracer l'histoire des ondes au CMAP et de présenter les derniers développements dans ce domaine.

    • 12:40 PM
      Pause déjeuner Salon d'honneur

      Salon d'honneur

      Ecole Polytechnique

    • 11
      J. Josse : Leveraging causal inference to generalize trial results to diverse population. Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      Randomized Controlled Trials (RCTs) are pivotal in evidence-based medicine, estimating average treatment effects by avoiding confounding factors. However, concerns about RCT limitations—strict eligibility criteria, real-world impracticality, and small sample sizes—threaten their generalization to diverse populations. In this talk, I will first present transportability methods by integrating non-randomized observational data to extend trial findings to other populations, potentially facing distributional shifts. Then, I will focus on which causal measure is easier to generalize, whether absolute as the Risk Difference or relative as the Risk Ratio, Odds Ratio, etc. In particular, I will demonstrate that only the Risk difference can disentangle the treatment effect from the baseline risk at both population and strata levels.

    • 12
      N. Touzi Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

    • 3:30 PM
      Pause Café Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

    • 13
      C. Dapogny : Optimisation de la forme des régions portant les conditions aux limites d’un problème physique Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      Très généralement, l'optimisation de formes vise à optimiser le design d'un domaine du plan ou de l'espace au regard d'un objectif et en respectant certaines contraintes, exprimés comme des fonctions du domaine.

      Dans les applications, ces fonctions dépendent de la forme par la solution d'une équation aux dérivées partielles décrivant la physique du problème en jeu, qui est complémentée par des conditions aux limites décrivant l'influence du milieu extérieur. Ainsi une structure mécanique est caractérisée par son déplacement, solution du système de l'élasticité linéaire, équipé de conditions aux limites de Dirichlet homogènes (correspondant aux zones d'attache de la structure), ou de Neumann homogènes (bord libres d'effort) ou inhomogènes (bords sur lesquels une force est appliquée).

      Le plus souvent, une seule partie du bord de la forme est optimisée -- typiquement, le bord libre en mécanique des structures. L'objectif de ce travail est, au contraire, d'optimiser la répartition des régions du bord de la forme portant les conditions aux limites du problème physique en jeu.

      Cette question est abordée sous deux aspects complémentaires :
      - D'une part, on étudie la dérivée de forme d'une fonction du domaine au sens de Hadamard lorsque les déformations en jeu ne s'annulent pas au changement des conditions aux limites : on optimise ainsi comment les régions portant les conditions aux limites peuvent "glisser" le long du bord de la forme.
      - D'autre part, on étudie la sensibilité de la solution du problème physique en jeu (et d'une quantité d'intérêt qui en dépend) lorsque l'on fait apparaître une petite région portant un certain type de conditions aux limites (par exemple, de Dirichlet) au sein d'une région portant d'autres conditions (par exemple, de Neumann) : ceci conduit à une sorte de "dérivée topologique" décrivant le changement de conditions aux limites sur le bord d'une forme donnée.

      On discutera plusieurs applications numériques de ces développements.

      Ces travaux ont été réalisés en collaboration avec Eric Bonnetier, Carlos Brito-Pacheco, Nicolas Lebbe, Edouard Oudet et Michael Vogelius.

    • 14
      E. Moulines : Solving Bayesian Inverse Problems Using Denoising Diffusion Models Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      Solving Bayesian Inverse Problems Using Denoising Diffusion Models

      joint work with: Alain Oliviero-Durmus, Yazid Janati-El-Idrissi (post-doc), Badr Moufad (PhD), Mehdi Abou El Qassime (PhD), Ahmed Ghorbel (Ing), Lisa Bedin (Ing), Ecole polytechnique & FX-Conseil, J. Olsson, KTH, S. Le Corff, Sorbonne Université.

      The growing interest in the use of Denoising Diffusion Models (DDMs) as fundamental elements for solving inverse Bayesian problems has recently marked a significant trend. The application of DDMs in this context offers a promising way to harness complex prior distributions. However, one of the major hurdles in this approach is the difficulty of sampling from the posterior distribution that arises when DDMs are used as priors. This challenge is primarily due to the complicated dynamics and high-dimensional nature of the diffusion processes involved.

      To overcome this obstacle, previous research efforts have focused on developing strategies to modify the drift term within the diffusion process. These modifications aim to better approximate the true posterior distribution, albeit often at the cost of introducing bias or increased computational complexity. While useful, such methods do not target the "true" posterior.

      Our work introduces a novel paradigm that takes advantage of the unique structural properties of DDMs. We propose a systematic decomposition of the posterior sampling into a sequence of more manageable intermediate tasks. Each of these tasks is designed to progressively refine the approximation of the posterior distribution, utilizing the structure of the DDM prior to effectively guide the sampling process. With this methodology, we can achieve a more accurate approximation of the posterior distribution and significantly reduce the approximation error compared to previous approaches.

      Our empirical investigations emphasize the effectiveness of our proposed method in a wide range of applications, ranging to image restoration, ECG reconstruction to urban mobility simulation.
      This work therefore sets a new benchmark for the use of denoising-diffusion models in solving inverse Bayesian problems and provides both theoretical insights and practical advances in the field.

    • 5:20 PM
      Pause de retrouvailles Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

    • 15
      Séance d'interventions historiques : Jean-Claude Nédélec, Claire Mouradian, Geo Boléat, Jeanne Bailleul, Marc Schoenauer, Laurence Halpern, Nicole El Karoui, Jean-François Colonna, Robert Brizzi, Éric Bonnetier, François Jouve, et al. Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

    • 7:00 PM
      Cocktail dinatoire Salon d'honneur

      Salon d'honneur

      Ecole Polytechnique

    • 16
      R. Douc -- Sampling by auxiliary target distributions: from the teleportation algorithm to the importance sampling Markov chain. Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      This review presentation brings together several works conducted in collaboration with Alain Durmus, Jimmy Olsson, Aurélien Enfroy, Charly Andral, Christian Robert, and Yazid Janati.

      In this presentation, we will introduce the teleportation algorithm and the importance sampling algorithm by Markov chains. These two algorithms share the common principle of obtaining a chain targeting a given distribution from a simple transformation of a Markov chain aimed at an auxiliary distribution. Importance sampling by Markov chain is based on decimation and reproduction procedures that enable transitions between modes while reproducing points in the vicinity of the modes. The teleportation algorithm helps to diversify points around the modes and thus acts complementarily to importance sampling by Markov chain. We demonstrate that under weak conditions, essential properties such as the law of large numbers, geometric ergodicity, and the central limit theorem are preserved through these two operations. We will also present some approaches for sequentially combining these two algorithms to gradually transition through a sequence of intermediate laws, from a Markov chain targeting a standard distribution to a chain targeting the desired distribution, thereby providing a promising alternative to sequential Monte Carlo methods.

    • 17
      A. Veber Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

    • 10:50 AM
      Pause Café Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

    • 18
      A. Chambolle : Discrete to continuous crystalline curvature flow Amphi Faurre

      Amphi Faurre

      Ecole Polytechnique

      In this joint work with Daniele DeGennaro (CEREMADE, Parma) and Massimiliano Morini (Parma) we study a fully space and time discrete implicit approximation of the curvature flow, for a surface tension defined by pairwise interactions on the discrete lattice (with bounded range). We study the convergence as the space and time steps go to zero (with different possible regime) and find, surprisingly, that in some cases we get a limiting crystalline curvature flow in any convergence regime.

    • 12:00 PM
      Repas Salon d'honneur

      Salon d'honneur

      Ecole Polytechnique