Responsabilités

Membre du Conseil Scientifique du GDR Calcul

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Editeur associé de BIT Numerical Mathematics (10.2021 - now)

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Co-organisateur du séminaire en ligne One World Stochastic Numerics and Inverse Problems. (09.2020 - now)

Information about the seminar

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Organisation d'événements:

- août 2023: mini-symposium "Numerical methods for stochastic partial differential equations", ICIAM 2023, co-organisé avec Jianbo Cui (Hong-Kong).

- juin 2023: mini-symposium "Numerics for stochastic partial differential equations", International Conference on Monte Carlo Methods and Applications MCM2023, Paris.

- 8-9 décembre 2022: journées "Rough Paths et Méthodes numériques", Pau, co-organisé avec J. Cresson. Sponsor: GDR TRAG.

- 4-5 novembre 2021: conférence internationale NASPDE: Numerical Analysis of Stochastic Partial Differential Equations. Au CIRM (Marseille), co-organisé avec C. Bauzet et J. Charrier (Aix-Marseille Université), L. Goudenège et A. Richard (CentraleSupélec). Sponsor: projet ANR SIMALIN.

- 24-25 avril 2019: Journées Calcul et Apprentissage. A Lyon, co-organisé avec B. Fabrèges et R. Denis. Sponsors: GdR Calcul et Labex MiLyon. Programme détaillé et documents : page indico.

Thèmes de recherche

Méthodes numériques pour les Equations aux Dérivées Partielles Stochastiques  : construction, analyse d'erreur et implémentation. Approximation de distributions invariantes. Schémas de splitting.
Analyse d'erreur faible : équations de Kolmogorov et de Poisson en dimension infinie.

Problèmes stochastiques multi-échelles : principe de moyennisation, ordres de convergence. Méthodes numériques: schémas préservant l'asymptotique.

Simulation d'événements rares & de processus métastables : Adaptive Multilevel Splitting ; Adaptive Biasing Potential, Adaptive Biasing Force.

Applications: collaborations avec des physiciens, astrophysiciens et biologistes. 

Encadrement

Offre de thèse:

Stochastic models for natural dispersion of aerosols, particles and pollutants in turbulent conditions.
Financement par l'Université Lyon 1 et l'Institut des Mathématiques pour la Planète Terre (IMPT),

Projet avec Mickaël Bourgoin, Laurent Chevillard et Romain Volk (ENS Lyon). Nous contacter pour plus d'informations.

Doctorat

• 2018-2021 : Shmuel Rakotonirina-Ricquebourg. Co-supervision avec Julien Vovelle. Soutenance : 05 juillet 2021. Etude théorique et numérique d'équations cinétiques stochastiques multi-échelles.

Post-doctorat

• 2023: Jules Pertinand. Financement: ANR SIMALIN. Co-supervision avec Ludovic Goudenège.
• 2021-2022 :  Raphael Winter. Financement : projet IDEXLYON TurBullet.
• 20219-2020 :  Marta Leocata. Financement : projet IDEXLYON TurBullet. Co-supervision avec Julien Vovelle.

Stages

• 2021 : Vincent Martos, ENS Lyon (Département de Physique), M2. Co-supervision avec Laurent Chevillard.
• 2020 : Schayma Ben Marzougui, ENSTA ParisTech, 2A.
• 2020 : Charles Minier, ENS Lyon, M1.
• 2018 : Shmuel Rakotonirina-Ricquebourg, ENS Paris-Saclay, M2. Co-supervision avec Julien Vovelle.
• 2014 : Loïc Tudela, ENSAE, M1. Co-supervision avec Ludovic Goudenège.

Projets

Projets ANR

• ADA : Moyennisation, approximation-diffusion en dimension infinie - téorie et approximation numérique. ANR-19-CE40-0019.
  Porteur : Julien Vovelle (CNRS & ENS Lyon).
• SIMALIN : Simulation aléatoire en dimension infinie. ANR-19-CE40-0016.
  Porteur : Ludovic Goudenège (CNRS & CentraleSupélec).
• BORDS : Bords, oscillations et couches limites dans les systèmes différentiels . ANR-16-CE40-0027.
  Porteur : Christophe Prange (CNRS & Cergy Paris Université)

IDEX LYON - Scientific Breakthrough Program (2018)

• TurBullet : Sédimentation et propulsion de particules en écoulements turbulents. Porteur : Mickaël Bourgoin (CNRS & ENS Lyon).
• ACADEMICS : Machine Learning & Data Science for Complex and Dynamical Models . Porteur : Pierre Borgnat (CNRS & ENS Lyon)

MITI CNRS - Mission pour les initiatives transverses et interdisciplinaires - Appel à projets Evévénements rares (2021)

• Coupling in-vivo meA foot printing with quantitative modeling to better understand the role of rare contacts between Sir3 and euchromatic genes in the global regulation of gene expression.
  Avec Marta Radman-Livaja (Montpellier) et Daniel Jost (ENS Lyon).
• La nucléation un phénomène rare ?
  Avec Stéphane Veesler et collaborateurs (CINam, Marseille).

Institut des Mathématiques pour la Planète Terre Appel à projets 2022

• Natural dispersion of aerosols, particles and pollutants: The role of turbulent fluctuations. Avec: Mickaël Bourgoin, Laurent Chevillard et Romain Volk (ENS Lyon)

Publications

Liste des publications

HALTOOLS

PREPRINTS

Analysis of a positivity-preserving splitting scheme for some nonlinear stochastic heat equations.
CEB, David Cohen & Johan Ulander. 2023. arxiv:2302.08858

Uniform strong and weak error estimates for numerical schemes applied to multiscale SDEs in a Smoluchowski-Kramers diffusion approximation regime.
CEB. 2022. arxiv:2208.00447 ; hal-03741115
 
Uniform error bounds for numerical schemes applied to multiscale SDEs in a Wong-Zakai diffusion approximation regime.
CEB. 2022. arxiv:2208.00448 ; hal-03741112

Splitting schemes for FitzHugh--Nagumo stochastic partial differential equations.
CEB, David Cohen & Giuseppe Giordano. 2022. arxiv:2207.10484 ; hal-03735693

Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation.
CEB, Jianbo Cui & Xiaojie Wang. 2022. arxiv:2207.09266 ; hal-03727797

Uniform weak error estimates for an asymptotic preserving scheme applied to a class of slow-fast parabolic semilinear SPDEs.
CEB. 2022. arxiv:2203.10600 ; hal-03614537

Analysis of a modified Euler scheme for parabolic semilinear stochastic PDEs.
CEB. 2022. arxiv:2203.10598 ; hal-03614530

Asymptotic behavior of a class of multiple time scales stochastic kinetic equations.
CEB & Shmuel Rakotonirina-Ricquebourg. 2021. arxiv:2106.06417 ; hal-03258628

Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme.
CEB. 2020. arxiv:2010.00512 ; hal-02955371

ARTICLES

Splitting integrators for stochastic Lie-Poisson systems.
CEB, David Cohen & Tobias Jahnke. 2023+.
Mathematics of Computation. to appear

Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations.
CEB & David Cohen. 2022.
Applied Numerical Mathematics. DOI:10.1016/j.apnum.2023.01.002

Phoresis in cellular flows: from enhanced dispersion to blockage.
Romain Volk, Mickaël Bourgoin, CEB & Florence, Raynal. 2022.
Journal of Fluid Mechanics. DOI: 10.1017/jfm.2022.730

The averaging principle for stochastic differential equations driven by a Wiener process revisited.
CEB. 2022.
Comptes Rendus de l'Académie des Sciences - Série Mathématique. DOI: 10.5802/crmath.297

Strong rates of convergence of a splitting scheme for Schrödinger equations with nonlocal interaction cubic nonlinearity and white noise dispersion.
CEB & David Cohen. 2022.
SIAM / ASA Journal on Uncertainty Quantification (JUQ). DOI: 10.1137/20M1378168

On Asymptotic Preserving schemes for a class of Stochastic Differential Equations in averaging and diffusion approximation regimes.
CEB & Shmuel Rakotonirina-Ricquebourg. 2022.
 Siam Multiscale Modeling and Simulation. DOI: 10.1137/20M1379836

Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme.
CEB. 2022.
ESAIM: M2AN. DOI : 10.1051/m2an/2021089

Asymptotic preserving schemes for SDEs driven by fractional Brownian motion in the averaging regime.
CEB. 2022.
Journal of Mathematical Analysis and Applications. DOI : 10.1016/j.jmaa.2021.125940

Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs.
Assyr Abdulle, CEB & Gilles Vilmart. 2021.
IMA Journal of Numerical Analysis. DOI : 10.1093/imanum/drab090

Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastability.
Elias Ventre, Thibault Espinasse, CEB, Vincent Calvez, Thomas Lepoutre & Olivier Gandrillon. 2021.
Journal of Mathematical Biology. DOI : 10.1007/s00285-021-01684-1

Analysis of an Adaptive Biasing Force method based on self-interacting dynamics.
Michel Benaïm, CEB & Pierre Monmarché. 2020.
Electronic Journal of Probability. DOI : 10.1214/20-EJP490

On the settling of small grains in dusty discs: analysis and formulas.
Guillaume Laibe, CEB & Maxime Lombart. 2020.
Monthly Notices of the Royal Astronomical Society. DOI : 10.1093/mnras/staa994

On parareal algorithms for semilinear parabolic Stochastic PDEs.
CEB & Xu Wang. 2020.
Siam Journal on Numerical Analysis. DOI : 10.1137/19M1251011

Weak convergence rates of splitting schemes for the stochastic Allen-Cahn equation.
CEB & Ludovic Goudenège. 2019.
BIT Numerical Mathematics. DOI : 10.1007/s10543-019-00788-x

Orders of convergence in the averaging principle for SPDEs: the case of a stochastically forced slow component.
CEB. 2019.
Stochastic Processes and their Applications. DOI : 10.1016/j.spa.2019.09.015

Influence of the regularity of the test functions for weak convergence in numerical discretization of SPDEs.
CEB. 2019.
Journal of Complexity. DOI : 10.1016/j.jco.2019.101424

Analysis of some splitting schemes for the stochastic Allen-Cahn equation.
CEB & Ludovic Goudenège. 2019.
Discrete and Continuous Dynamical Systems - Series B (Special issue in honor of Dr. Peter E. Kloeden on the occasion of his 70th birthday). DOI : 10.3934/dcdsb.2019077

Convergence analysis of Adaptive Biasing Potential methods for diffusion processes.
Michel Benaïm & CEB. 2019.
Communications in Mathematical Sciences.
DOI : 10.4310/CMS.2019.v17.n1.a4

On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting.
CEB & Tony Lelièvre. 2019.
Chaos (Special Issue "Rare Event Sampling Methods: Development, Analysis and Application"). DOI : 10.1063/1.5081440

Kolmogorov equations and Weak order analysis for SPDEs with nonlinear diffusion coefficient.
CEB & Arnaud Debussche. 2018.
Journal de Mathématiques Pures et Appliquées. DOI : 10.1016/j.matpur.2018.08.010

Strong convergence rates of semi-discrete splitting approximations for stochastic Allen-Cahn equation.
CEB, Jianbao Cui & Jialin Hong. 2018.
IMA Journal of Numerical Analysis. DOI : 10.1093/imanum/dry052

Computing return times or return periods with rare event algorithms.
Thibault Lestang, Francesco Ragone, CEB, Corentin Herbert & Freddy Bouchet. 2018.
Journal of Statistical Mechanics: Theory and Experiment. DOI : 10.1088/1742-5468/aab856

Weak error estimates for trajectories of SPDEs for Spectral Galerkin discretization.
CEB, Martin Hairer & Andrew Stuart. 2018.
Journal of Computational Mathematics (Special Issue "Numerics for SPDEs"). DOI : 10.4208/jcm.1607-m2016-0539

Unbiasedness of some Generalized Adaptive Multilevel Splitting algorithms.
CEB, Maxime Gazeau, Ludovic Goudenège, Tony Lelièvre & Mathias Rousset. 2016.
The Annals of Applied Probability. DOI : 10.1214/16-AAP1185

High-order integrator for sampling the invariant distribution of a class of parabolic SPDEs with additive space-time noise.
CEB & Gilles Vilmart. 2016.
Siam Journal of Scientific Computing. DOI : 10.1137/15M1021088

Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme.
CEB & Marie Kopec. 2016.
IMA Journal of Numerical Analysis. DOI : 10.1093/imanum/drw030

Convergence of Adaptive Biaising Potential methods for diffusions.
Michel Benaïm & CEB. 2016.
Comptes Rendus de l'Académie des Sciences - Série Mathématique. DOI : 10.1016/j.crma.2016.05.011

Large deviations principle for the Adaptive Multilevel Splitting Algorithm in an idealized setting.
CEB. 2015.
Alea – Latin American Journal of Probability and Mathematical Statistics. Link : alea.impa.br/articles/v12/12-27

Analysis of the Monte-Carlo error in a hybrid semi-lagrangian scheme.
CEB & Erwan Faou. 2015.
Applied Mathematics Research Express. DOI : 10.1093/amrx/abv001

Analysis of Adaptive Multilevel Splitting algorithms in an idealized case.
CEB, Tony Lelièvre & Mathias Rousset. 2015.
ESAIM Probability and Statistics. DOI : 10.1051/ps/2014029

Approximation of the invariant measure via an Euler scheme for SPDEs driven by space-time white noise.
CEB. 2014.
Potential Analysis. DOI : 10.1007/s11118-013-9338-9

Analysis of an HMM time-discretization scheme for a system of Stochastic PDEs.
CEB. 2013.
Siam Journal on Numerical Analysis. DOI : 10.1137/110853078

Strong and Weak orders in Averaging for SPDEs.
CEB. 2012.
Stochastic Processes and their Applications. DOI : 10.1016/j.spa.2012.04.007

PROCEEDINGS

Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting.
CEB, Ludovic Goudenège & Loïc Tudela. 2016.
Monte Carlo and Quasi Monte Carlo Methods 2014. DOI :10.1007/978-3-319-33507-0_10

Recent advances in various fields of numerical probability.
CEB, Paul-Eric Chaudru de Raynal, Vincent Lemaire, Fabien Panloup & Clément Rey. 2015.
ESAIM: Proceedings and Surveys (Journées MAS 2014). DOI : 10.1051/proc/201551015

Analysis and simulation of rare events for SPDEs
CEB, Maxime Gazeau, Ludovic Goudenège & Mathias Rousset. 2015.
ESAIM: Proceedings and Surveys (CEMRACS 2013). DOI : 10.1051/proc/201448017