Tony LELIEVRE

Organisation : Ecole des Ponts ParisTech
Laboratoire : CERMICS
Projet : Simulation moléculaire et multi-échelle
Téléphone : 33 (0)1 64 15 35 28
Fax : 33 (0)1 64 15 35 86
E-mail :
Bureau : B304, bâtiment Coriolis
Courrier :

Je suis chercheur et professeur à l'Ecole des Ponts ParisTech, directeur du CERMICS.

Je suis membre du Groupe de simulation moléculaire et multi-échelle au CERMICS et du projet Matherials d'INRIA.

Vous êtes à la recherche d'un stage, d'une thèse ou d'un post-doc ? Consultez nos offres ici.

Voici mon cv (pdf).

J'ai passé l'année 2019-2020 à Imperial College of London, au département de mathématiques et à l'UMI Abraham de Moivre.

J'ai soutenu mon Habilitation à Diriger des Recherches le 3 juin 2009 (résumé, mémoire). Sujet : Analyse mathématique et numérique de modèles pour les matériaux, de l'échelle microscopique à l'échelle macroscopique.

Pendant l'année 2004-2005, j'étais en post-doc au Centre de Recherches Mathématiques à l'Université de Montréal, dans le cadre d'une année thématique sur les mathématiques de la modélisation multiéchelle et stochastique.

J'ai soutenu ma thèse le 21 juin 2004 (résumé, mémoire). Sujet : Modèles multi-échelles pour les fluides viscoélastiques. Direction de thèse : Benjamin Jourdain et Claude Le Bris.

Centres d'intérêts principaux

Modèles micro-macro pour les fluides viscoélastiques (modèle de dumbbells, méthode CONNFFESSIT, méthodes de réduction de variance, estimées d'entropie).
Ecoulements à surface libre et magnétohydrodynamique. Application à la simulation des cuves d'électrolyse de l'aluminium (méthode Arbitrary Lagrangian Eulerian, moving contact line problem).
Simulation moléculaire (dynamique moléculaire, dynamiques avec contraintes, méthodes adaptatives, méthodes Quantum Monte Carlo, Adaptive Multilevel Splitting, Accelerated Molecular Dynamics).

Enseignement

Professeur chargé de cours à temps partiel à l'Ecole Polytechnique
Professeur à l'Ecole des Ponts ParisTech

Responsable des projets MOPSI (Modéliser Programmer Simuler)

Cours et exposés introductifs

Cours :

CEMRACS 2008 : Multiscale modelling of complex fluids: a mathematical initiation, exposé, notes de cours.
Ecole doctorale ECODOQUI 2008 : Monte Carlo methods in molecular dynamics, exposé, notes de cours.
Workshop stress tensor effects on fluid mechanics, China, 2010 : Multiscale modelling of complex fluids: a mathematical initiation, exposé, notes de cours.
Cornell University, 2010 : Free energy calculations, exposé.
IPAM tutorial, 2012 : Monte Carlo methods in molecular dynamics part 1 part 2.
ICMS tutorial, 2014: Numerical methods in molecular dynamics, or what is a metastable stochastic process ? pdf.
Computational Toolbox Winterschool 2016, Engelberg: Numerical methods in molecular dynamics, part 1 part 2.
GDR Egrin, 4ème école, Mai 2016: Model reduction techniques for stochastic dynamics, pdf.
RICAM school, December 2016, Linz: SDEs in large dimension and numerical methods, part 1 part 2.
Brummer & Partners MathDataLab, KTH, January 2021, Sampling problems in computational statistical physics, Free energy adaptive biasing methods (video), Splitting methods for rare event simulations (video), Sampling of metastable dynamics (video).
Seoul National University, Jump Markov models and transition state theory: the quasi-stationary distribution approach, 25-27th August 2021.

Exposés introductifs (vidéos) :

Horizons Maths 2012, 19 décembre 2012 : Méthodes numériques en dynamique moléculaire.
Collège de France, 9 janvier 2015 : Processus stochastiques métastables et distributions quasi-stationnaires.
HIM, 29 janvier 2015 : Optimal scaling for the transient phase of Metropolis Hastings algorithms.
BIRS, 24 juillet 2015 : Accelerated dynamics.
Newton Institute, 3 décembre 2015 : The parallel replica algorithm: mathematical foundations and recent developments.
Université de Genève, 1er février 2017 : Accelerated dynamics and transition state theory.
ICTS, août 2017 : Algorithms for computational statistical physics: a mathematical viewpoint part 1, part 2.
IPAM, 16 octobre 2017: Metastability: a journey from stochastic processes to semiclassical analysis .
Newton Institute, 20 novembre 2019: Hybrid Monte Carlo methods for sampling probability measures on submanifolds .
BIRS, 24 novembre 2020 : Effective dynamics for stochastic differential equations .
CIRM 28 juillet 2021 : How to compute mean transition times?
KAUST 31 mai 2023 : Unbiased sampling using reversibility checks .

Evènements

Workshop "Numerical methods in molecular simulation", Bonn, April 7-11th 2008.
Workshop "Rheology of complex fluids: modeling and numerics", Ecole des Ponts, January 5-9th 2009.
Workshop "Hybrid simulations of dynamical systems and applications to molecular dynamics", Institut Henri Poincaré, 27 septembre - 30 septembre 2010.
Minisymposium "Numerical Methods for Molecular Dynamics", ENUMATH 2011 conference, September 5-9th 2011, slides.
Workshop "Metastability and stochastic processes", Ecole des Ponts, September 21st-23rd 2011.
CECAM workshop "Free energy calculations: From theory to applications", Ecole des Ponts, June 4th-8th 2012: CECAM webpage, local webpage.
CEMRACS 2013: Modelling and simulation of complex systems: stochastic and deterministic approaches. Co-organized with Nicolas Champagnat and Anthony Nouy. The proceedings are available here.
NASPDE 2013 : Numerical Analysis of Stochastic PDEs, 10 et 11 septembre 2013. Co-organisé avec Jocelyne Erhel et Erwan Faou.
Journées SMAI/INRIA EDP-Proba,2013-2018, Co-organisées avec Florent Malrieu.
Workshop "Numerical methods for high-dimensional problems". Ecole des Ponts, April 14-18th 2014. Co-organized with Virginie Ehrlacher, Yvon Maday and Anthony Nouy
Journées Inverse problems for multiscale and stochastic problems, Ecole des Ponts, October 2-3rd 2014. Co-organized with Virginie Ehrlacher, Frédéric Legoll and Karam Sab.
MoMaS'14 conference. CIRM, November 17-20th, 2014. Co-organized with Grégoire Allaire, Clément Cancès, Alexandre Ern and Raphaèle Herbin.
Free-energy calculations: A mathematical perspective, BIRS, Casa Matemática Oaxaca, Mexico, July 19-24th, 2015. Co-organized with Chris Chipot and Robert Skeel.
Workshop "COmputational Statistics and MOlecular Simulation", Paris, February 2-5th, 2016. Co-organized with Arnaud Guyader and Gabriel Stoltz.
IHP conference on "Recent developments in numerical methods for model reduction", November 7-10th 2016. Co-organized with Simona Perotto and Gianluigi Rozza.
Workshop "Piecewise Deterministic Markov Processes and sampling", January 25-27th, 2017. Co-organized with Florent Malrieu and Pierre-André Zitt.
Rencontre Math-Industrie "simulation moléculaire dans l’industrie pharmaceutique", 28 avril 2017. Co-organisé avec Chris Chipot et Gabriel Stoltz.
FoCM 2017, Stochastic Computation Workshop, July 10th-12th, 2017. Co-organized with Arnulf Jentzen.
IPAM Long Program on "Complex High-Dimensional Energy Landscapes", September 11th - December 15th 2017. Co-organized with Cecilia Clementi, Graeme Henkelman, Richard Hennig, Mitchell Luskin, Noa Marom, Petr Plechac and Christof Schuette.
ICTS program on "Large deviation theory in statistical physics: Recent advances and future challenges", August 14th - October 13th 2017. Co-organized with Arvind Ayyer, Frank den Hollander, Abhishek Dhar, Juan P. Garrahan, Christopher Jarzynski, Manjunath Krishnapur, Sanjib Sabhapandit and Hugo Touchette.
Workshop "Advances in Computational Statistical Physics", CIRM, September 17th-21st, 2018. Co-organized with Gabriel Stoltz and Greg Pavliotis. Link to videos.
CECAM discussion meeting "Coarse-graining with Machine Learning in molecular dynamics". Sanofi Campus Gentilly, December 4-8th, 2018. Co-organized with Paraskevi Gkeka, Pierre Monmarché and Gabriel Stoltz.
CECAM workshop "Learning the collective variables of biomolecular processes". INRIA Paris July 10-12th 2019. Co-organized with Lucie Delemotte, Jérôme Hénin and Gerhard Stock.
ICL/CNRS workshop on "Interacting Particle Systems and applications". Imperial College of London, December 9-10th 2019. Co-organized with Greg Pavliotis.
13th International Workshop on Rare-Event Simulation - RESIM 2021, Les Cordeliers Paris, 18th-21st May 2021. Co-organized with Gersende Fort, Emmanuel Gobet and Arnaud Guyader.
Machine Learning-Assisted Sampling for Scientific Computing - Applications in Physics, Collège de France - site Ulm, Paris, October 3-4th 2022. Co-organized with Marylou Gabrié and Valentin de Bortoli.
Analysis and simulation of metastable systems, CIRM, 3rd-7th April 2023. Co-organized with Alessandra Bianchi and Claudio Landim.
MCM 2023, 14th Monte Carlo Methods Conference, Paris, 26-30th June 2023. Co-organized with Stéphanie Allassonnière, Jean-François Chassagneux, Florence Forbes, Emmanuel Gobet, Benjamin Jourdain and Gilles Pagès.

Distinctions

Jean-Frédéric Gerbeau, Claude Le Bris et moi-même avons reçu le Prix CS 2002 décerné par la société Communications & Systèmes pour notre travail sur la modélisation magnétohydrodynamique des cuves d'électrolyse d'aluminium (pdf).
Prix de thèse (2004) de l''Ecole Nationale des Ponts et Chaussées, de ParisTech, et du groupe GAMNI.
Grand prix Alcan de l'Académie des Sciences 2010.
Prix de la recherche de la fondation iXCore 2011
Ordway visiting professor 2012-2013, University of Minnesota.
ERC consolidator grant 2013-2019. Pour plus d'information, cf. projet ERC MSMath.
Bourse de professeur invité de the Leverhulme Trust, 2019.

Activité éditoriale

Co-éditeur en chef de ESAIM: Proceedings and Surveys, avec Djalil Chafai, Cyril Imbert et Pauline Lafitte, 2012-2020.
Membre du comité éditorial de SIAM/ASA Journal of Uncertainty Quantification (JUQ) (depuis 2017), IMA Journal of Numerical Analysis (depuis 2018), Communications in Mathematical Sciences (depuis 2019), Journal of Computational Physics (depuis 2019), ESAIM:M2AN (depuis 2020), Foundations of Computational Mathematics (depuis 2022).

Livres

(avec J-F. Gerbeau et C. Le Bris) Mathematical methods for the Magnetohydrodynamics of liquid metals, 324 pp., Numerical Mathematics and Scientific Computation, Oxford University Press, 2006.
(avec M. Rousset et G. Stoltz) Free energy computations: A mathematical perspective, 472 pp., Imperial College Press, 2010.

Mathematical methods for the magnetohydrodynamics of
liquid metals

Free Energy Computations: A
mathematical perspective

Publications dans des revues à comité de lecture

(avec B. Jourdain et C. Le Bris) Numerical analysis of micro-macro simulations of polymeric fluid flows: a simple case, Mathematical Models and Methods in Applied Sciences, 12(9), 1205-1243, (2002).
(avec J-F. Gerbeau et C. Le Bris) Simulations of MHD flows with moving interfaces, Journal of Computational Physics, 184, 163-191, (2003).
(avec J-F. Gerbeau et C. Le Bris) Modelling and simulation of the industrial production of aluminium: the nonlinear approach, Computers and Fluids, 33, 801-814, (2004).
Optimal error estimate for the CONNFFESSIT approach in a simple case, Computers and Fluids, 33, 815-820, (2004).
(avec B. Jourdain et C. Le Bris) Existence of solution for a micro-macro model of polymeric fluid : the FENE model, Journal of Functional Analysis, 209, 162-193, (2004).
(avec B. Jourdain et C. Le Bris) On a variance reduction technique for micro-macro simulations of polymeric fluids, Journal of Non-Newtonian Fluid Mechanics, 122, 91-106, (2004).
(avec F. Dubois) Efficient pricing of Asian options by the PDE approach, Journal of Computational Finance, 8(2), 55-64, (2005). Voir aussi le programme en C, implémenté dans Premia, ainsi qu'une première version de cet article.
(avec J.P. Croisille, A. Ern et J. Proft) Analysis and simulation of a coupled hyperbolic/parabolic model problem, Journal of Numerical Mathematics, 13(2), 81-156, (2005). Voir aussi les fichiers de résultat pour les solutions de référence
(avec B. Jourdain et C. Le Bris) An elementary argument regarding the long-time behaviour of the solution to a stochastic differential equation, Annals of Craiova University, Mathematics and Computer Science series, 32, 39-47, (2005).
(avec B. Jourdain, C. Le Bris et F. Otto) Long-time asymptotics of a multiscale model for polymeric fluid flows, Archive for Rational Mechanics and Analysis, 181(1), 97-148, (2006).
(avec E. Cancès et B. Jourdain) Quantum Monte Carlo simulations of fermions. A mathematical analysis of the fixed-node approximation, Mathematical Models and Methods in Applied Sciences, 16(9), 1403-1440, (2006).
(avec M. Rousset et G. Stoltz) Computation of free energy differences through nonequilibrium stochastic dynamics: the reaction coordinate case, Journal of Computational Physics, 222(2), 624-643, (2007).
(avec M. Caffarel, E. Cancès, A. Scemama et G. Stoltz) An efficient sampling algorithm for Variational Monte Carlo, Journal of Chemical Physics, 125, 114105 (2006).
(avec G. Ciccotti et E. Vanden-Eijnden) Projection of diffusions on submanifolds: Application to mean force computation, Communications on Pure and Applied Mathematics, 61(3), 371-408, (2008).
(avec M. El Makrini et B. Jourdain) Diffusion Monte Carlo method: numerical analysis in a simple case, ESAIM: Mathematical Modelling and Numerical Analysis, 41(2), 189-213, (2007).
(avec M. Rousset et G. Stoltz) Computation of free energy profiles with parallel adaptive dynamics, Journal of Chemical Physics 126, 134111 (2007).
(avec A. Ern) Adaptive models for polymeric fluid flow simulation, C. R. Acad. Sci. Paris, Ser. I, 344(7), 473-476 (2007).
(avec D. Hu) New entropy estimates for the Oldroyd-B model, and related models, Communications in Mathematical Sciences 5(4), 909-916 (2007).
(avec C. Le Bris et E. Vanden-Eijnden) Analysis of some discretization schemes for constrained Stochastic Differential Equations, C. R. Acad. Sci. Paris, Ser. I, 346(7-8), 471-476 (2008).
(avec M. Rousset et G. Stoltz) Long-time convergence of an Adaptive Biasing Force method, Nonlinearity, 21, 1155-1181 (2008).
(avec E. Faou) Conservative stochastic differential equations: Mathematical and numerical analysis, Mathematics of Computation, 78, 2047-2074 (2009).
(avec J-F. Gerbeau) Generalized Navier Boundary Condition and Geometric Conservation Law for surface tension, Computer Methods in Applied Mechanics and Engineering, 198(5-8), 644-656, (2009).
A general two-scale criteria for logarithmic Sobolev inequalities, Journal of Functional Analysis, 256(7), 2211-2221 (2009).
(avec S. Boyaval et C. Mangoubi) Free-energy-dissipative schemes for the Oldroyd-B model, ESAIM: Mathematical Modelling and Numerical Analysis, 43, 523-561, (2009).
(avec C. Le Bris et Y. Maday) Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations, Constructive Approximation, 30(3), 621-651, (2009).
(avec S. Boyaval) A variance reduction method for parametrized stochastic differential equations using the reduced basis paradigm, Communications in Mathematical Sciences, 8(3), 735-762, (2010).
(avec B. Jourdain et R. Roux) Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process, ESAIM: Mathematical Modelling and Numerical Analysis, 44, 831-865, (2010).
(avec C. Chipot et K. Minoukadeh) Potential of mean force calculations: a multiple-walker adaptive biasing force approach, Journal of Chemical Theory and Computation, 6(4), 1008-1017, (2010).
(avec S. Boyaval, C. Le Bris, Y. Maday, N.C. Nguyen et A.T. Patera) Reduced basis techniques for stochastic problems, Archives of Computational Methods in Engineering, 17(4), 435-454, (2010).
(avec B. Dickson, F. Legoll, G. Stoltz et P. Fleurat-Lessard) Free energy calculations: An efficient adaptive biasing potential method, Journal of Physical Chemistry B, 114, 5823-5830, (2010).
(avec X. Blanc, F. Legoll et C. Le Bris) Beyond multiscale and multiphysics: Multimaths for model coupling, Networks and Heterogeneous Media, 5(3), 423-460, (2010).
(avec V. Legat et G. Samaey) A numerical closure approach for kinetic models of polymeric fluids: exploring closure relations for FENE dumbbells, Computers and Fluids, 43, 119-133, (2011).
(avec F. Legoll) Effective dynamics using conditional expectations, Nonlinearity, 23, 2131-2163, (2010).
(avec F. Cérou, A. Guyader et D. Pommier) A multiple replica approach to simulate reactive trajectories, Journal of Chemical Physics, 134, 054108, (2011).
(avec K. Minoukadeh) Long-time convergence of an Adaptive Biasing Force method : the bi-channel case, Archive for Rational Mechanics and Analysis, 202(1), 1-34, (2011).
(avec E. Cancès et V. Ehrlacher) Convergence of a greedy algorithm for high-dimensional convex nonlinear problems, Mathematical Models and Methods in Applied Sciences, 21(12), 2433-2467, (2011).
(avec N. Chopin et G. Stoltz) Free energy methods for Bayesian inference: efficient exploration of univariate Gaussian mixture posteriors, Statistics and Computing, 22(4), 897-916, (2012).
(avec C. Chipot) Enhanced sampling of multidimensional free-energy landscapes using adaptive biasing forces, SIAM Journal of Applied Mathematics, 71(5), 1673-1695, (2011).
(avec A. Ern et R. Joubaud) Numerical study of a thin liquid film flowing down an inclined wavy plane, Physica D, 240(21), 1714-1723, (2011).
(avec M. Rousset et G. Stoltz) Langevin dynamics with constraints and computation of free energy differences, Mathematics of Computation, 81(280), 2071-2125, (2012).
(avec L. He et C. Le Bris) Periodic long-time behaviour for an approximate model of nematic polymers, Kinetic and Related Models, 5(2), 357-382, (2012).
(avec A. Ern et R. Joubaud) Mathematical study of non-ideal electrostatic correlations in equilibrium electrolytes, Nonlinearity 25, 1635-1652, (2012).
(avec C. Le Bris, M. Luskin et D. Perez) A mathematical formalization of the parallel replica dynamics, Monte Carlo Methods and Applications, 18(2), 119–146, (2012).
(avec D. Benoit, L. He et C. Le Bris) Mathematical analysis of a one-dimensional model for an aging fluid, Mathematical Models and Methods in Applied Sciences, 23(9), 1561-1602, (2013).
(avec M. Dobson, F. Legoll et G. Stoltz) Derivation of Langevin Dynamics in a nonzero Background Flow Field, ESAIM: Mathematical Modelling and Numerical Analysis, 47(6), 1583-1626, (2013).
(avec F. Legoll et G. Samaey) A micro-macro parareal algorithm: application to singularly perturbed ordinary differential equations, SIAM Journal on Scientific Computing, 35(4), A1951–A1986, (2013).
(avec F. Cérou, A. Guyader et F. Malrieu) On the length of one-dimensional reactive paths, ALEA Latin American Journal of Probability and Mathematical Statistics, 10(2), 359-389, (2013).
(avec F. Nier et G. Pavliotis) Optimal non-reversible linear drift for the convergence to equilibrium of a diffusion, Journal of Statistical Physics, 152(2), 237-274, (2013).
(avec F. Casenave et A. Ern) Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method, ESAIM: Mathematical Modelling and Numerical Analysis, 48(1), 207-229, (2014).
(avec B. Jourdain et B. Miasojedow) Optimal scaling for the transient phase of Metropolis Hastings algorithms: the longtime behavior, Bernoulli, 20(4), 1930-1978, (2014).
(avec G. Fort, B. Jourdain, E. Kuhn et G. Stoltz) Convergence of the Wang-Landau algorithm, Mathematics of Computation, 84(295), 2297–2327, (2015).
(avec G. Fort, B. Jourdain, E. Kuhn et G. Stoltz) Efficiency of the Wang-Landau algorithm: a simple test case, AMRX, 2, 275-311, (2014).
(avec M. Athènes, L. Cao, M.-C. Marinica et G. Stoltz) Free energy calculations from adaptive molecular dynamics simulations with adiabatic reweighting, Journal of Chemical Physics, 140, 104108, (2014).
(avec D. Aristoff) Mathematical analysis of Temperature Accelerated Dynamics, SIAM Multiscale Modeling and Simulation, 12(1), 290–317, (2014).
(avec B. Jourdain et B. Miasojedow) Optimal scaling for the transient phase of the random walk Metropolis algorithm: the mean-field limit, Annals of Applied Probability, 25(4), 2263-2300, (2015).
(avec D. Benoit et C. Le Bris) Macroscopic limit of a one-dimensional model for aging fluids, SIAM Multiscale Modeling and Simulation, 12(3), 1335–1378, (2014).
(avec E. Cancès et V. Ehrlacher) Greedy algorithms for high-dimensional eigenvalue problems, Constructive Approximation, 40(3), 387-423, (2014).
(avec F. Casenave et A. Ern) A nonintrusive Reduced Basis Method applied to aeroacoustic simulations, Advances in Computational Mathematics, 1-26, (2015).
(avec D. Aristoff et G. Simpson) The parallel replica method for simulating long trajectories of Markov chains, AMRX, 2, 332-352, (2014).
(avec J. Comer, J.C. Gumbart, J. Hénin, A. Pohorille et C. Chipot), The adaptive biasing force method: everything you always wanted to know, but were afraid to ask, The Journal of Physical Chemistry B, 119(3), 1129-1151, (2015).
(avec C.-E. Bréhier et M. Rousset) Analysis of Adaptive Multilevel Splitting algorithms in an idealized case, ESAIM P&S, 19, 361 - 394, (2015).
(avec F. Nier) Low temperature asymptotics for Quasi-Stationary Distributions in a bounded domain, Analysis & PDE, 8(3), 561-628, (2015).
(avec A. Binder et G. Simpson) A Generalized Parallel Replica Dynamics, Journal of Computational Physics, 284, 595-616, (2015).
(avec H. Alrachid) Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection, SMAI Journal of Computational Mathematics, 1, 55-82, (2015).
(avec F. Casenave et A. Ern) Variants of the Empirical Interpolation Method: symmetric formulation, choice of norms and rectangular extension, Advances in Computational Mathematics, 41(5), 961-986, (2015).
(avec H. Alrachid et R. Talhouk) Local and global solution for a nonlocal Fokker-Planck equation related to the adaptive biasing force process, Journal of Differential Equations, 260, 7032-7058, (2016).
(avec G. Fort, B. Jourdain et G. Stoltz) Self-Healing Umbrella Sampling: Convergence and efficiency, Statistics and computing, 27(1), 147-168, (2017).
(avec A.B. Duncan et G.A. Pavliotis) Variance reduction using nonreversible Langevin samplers, Journal of Statistical Physics, 163(3), 457-491, (2016).
(avec C.-E. Bréhier, M. Gazeau, L. Goudenège et M. Rousset) Unbiasedness of some generalized Adaptive Multilevel Splitting algorithms, Annals of Applied Probability, 26(6), 3559-3601, (2016). Cf. [arXiv:1505.02674] pour une version étendue de ce travail.
(avec C. Mayne, K. Schulten et I. Teo) Adaptive multilevel splitting method for molecular dynamics calculation of benzamidine-trypsin dissociation time, Journal of Chemical Theory and Computation, 12(6), 2983–2989, (2016).
(avec L. Brochard, E. Cancès, F. Legoll, G. Stoltz and I.G. Tejada) Coupling a reactive potential with a harmonic approximation for atomistic simulations of material failure, Computer Methods in Applied Mechanics and Engineering, 305, 422-440, (2016).
(avec J. Infante Acevedo) A non linear approximation method for solving high dimensional partial differential equations: Application in Finance, Mathematics and Computers in Simulation, 143, 14-34, (2018).
(avec G. Stoltz) Partial differential equations and stochastic methods in molecular dynamics, Acta Numerica, 25, 681-880, (2016).
(avec G. Di Gesù, D. Le Peutrec et B. Nectoux) Jump Markov models and transition state theory: the Quasi-Stationary Distribution approach, Faraday Discussion, 195, 469-495, (2016).
(avec J. Hénin, A. Lesage et G. Stoltz) Smoothed biasing forces yield unbiased free energies with the extended-system adaptive biasing force method, Journal of Physical Chemistry B, 121(15), 3676-3685, (2017).
(avec F. Legoll et S. Olla) Pathwise estimates for an effective dynamics, Stochastic Processes and their Applications, 127, 2841-2863, (2017).
(avec T. Zhao, H. Fu, X. Shao, C. Chipot et W. Cai) The Extended Generalized Adaptive Biasing Force Algorithm for Multidimensional Free-Energy Calculations, Journal of Chemical Theory and Computation, 13(4), 1566-1576, (2017).
(avec R. Assaraf, B. Jourdain et R. Roux) Computation of sensitivities for the invariant measure of a parameter dependent diffusion, Stochastics and Partial Differential Equations: Analysis and Computations 6(2), 125-183, (2018).
(avec G. Fort, B. Jourdain et G. Stoltz) Convergence and efficiency of adaptive importance sampling techniques with partial biasing, Journal of Statistical Physics, 171(2), 220-268 (2018).
(avec L.Pillaud-Vivien et J. Reygner) Central Limit Theorem for stationary Fleming-Viot particle systems in finite spaces, ALEA Latin American Journal of Probability and Mathematical Statistics, 15, 1163-1182 (2018).
(avec F. Hédin) gen.parRep: a first implementation of the Generalized Parallel Replica dynamics for the long time simulation of metastable biochemical systems, Computer Physics Communications, 239, 311-324, (2019). Le code est disponible sur github.
(avec L.J.S. Lopes) Analysis of the Adaptive Multilevel Splitting method with the alanine di-peptide's isomerization, Journal of Computational Chemistry, 40(11), 1198-1208, (2019).
(avec G. Di Gesù, D. Le Peutrec et B. Nectoux) Sharp asymptotics of the first exit point density, Annals of PDE, 5(1), (2019).
(avec C.-E. Bréhier) On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting, Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(3), 033126, (2019).
(avec G. Di Gesù, D. Le Peutrec et B. Nectoux) The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points, part 1, Journal de Mathématiques Pures et Appliquées, 138, 242-306, (2020).
(avec M. Rousset et G. Stoltz) Hybrid Monte Carlo methods for sampling probability measures on submanifolds, Numerische Mathematik, 143(2), 379-421, (2019). Une correction se trouve ici.
(avec W. Zhang) Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates, SIAM Multiscale Modeling and Simulation, 17(3), 1019-1051, (2019).
(avec G. Samaey et P. Zielinski) Analysis of a micro-macro acceleration method with minimum relative entropy moment matching, Stochastic Processes and their Applications, 130, 3753-3801, (2020).
(avec T. Hudson et F. Legoll) Stochastic homogenization of a scalar viscoelastic model exhibiting stress-strain hysteresis, ESAIM: Mathematical Modelling and Numerical Analysis, 54, 879-928, (2020).
(avec F. Legoll et U. Sharma) Effective dynamics for non-reversible stochastic differential equations: a quantitative study, Nonlinearity, 32(12), 4779, (2019).
(avec B. Leimkuhler et Z. Trstanova) Local and global perspectives on diffusion maps in the analysis of molecular systems, Proceedings of the Royal Society A, 476, 20190036, (2020).
(avec F. Legoll, K. Myerscough et G. Samaey) Parareal computation of stochastic differential equations with time-scale separation: a numerical study, Computing and Visualization in Science, 23(9), (2020) .
(avec P. Gkeka, G. Stoltz, A. Barati Farimani, Z. Belkacemi, M. Ceriotti, J. Chodera, A.R. Dinner, A. Ferguson, J.-B. Maillet, H. Minoux, C. Peter, F. Pietrucci, A. Silveira, A. Tkatchenko, Z. Trstanova et R. Wiewiora) Machine learning force fields and coarse-grained variables in molecular dynamics: application to materials and biological systems, Journal of Chemical Theory and Computation, 16(8), 4757-4775, (2020).
(avec B. Jourdain et P.A. Zitt) Convergence of metadynamics: discussion of the adiabatic hypothesis, Annals of Applied Probability, 31(5), 2441-2477, (2021).
(avec D. Le Peutrec et B. Nectoux) The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points, part 2, Stochastics and Partial Differential Equations: Analysis and Computations, 10, 317-357, (2022).
(avec F. Legoll et U. Sharma) An adaptive parareal algorithm: application to the simulation of molecular dynamics trajectories, SIAM Journal on Scientific Computing, 44(1), B146–B176, (2022).
(avec V. Ehrlacher et P. Monmarché) Adaptive force biasing algorithms: new convergence results and tensor approximations of the bias, Annals of Applied Probability, 32(5), 3850-3888, (2022).
(avec Z. Belkacemi, P. Gkeka et G. Stoltz) Chasing collective variables using autoencoders and biased trajectories, Journal of Chemical Theory and Computation, 18(1), 59–78, (2022).
(avec G. Stoltz et W. Zhang) Multiple projection MCMC algorithms on submanifolds, IMA Journal of Numerical Analysis, 43(2), 737-788, (2023). Les codes sont disponibles ici: https://github.com/zwpku/Constrained-HMC .
(avec M. Ramil et J. Reygner) Quasi-stationary distribution for the Langevin process in cylindrical domains, part I: existence, uniqueness and long-time convergence, Stochastic Processes and their Applications, 144, 176-201, (2022).
(avec L. Maurin et P. Monmarché) The Adaptive Biasing Force algorithm with non-conservative forces and related topics, ESAIM: Mathematical Modelling and Numerical Analysis, 56(2), 529-564, (2022).
(avec M. Ramil et J. Reygner) A probabilistic study of the kinetic Fokker-Planck equation in cylindrical domains, Journal of Evolution Equations, 22(38), (2022).
(avec M. Baudel et A. Guyader) On the Hill relation and the mean reaction time for metastable processes, Stochastic Processes and their Applications, 155, 393-436, (2023). Cf. [arXiv:2008.09790] pour une version étendue de ce travail.
(avec L. Delemotte, J. Hénin, M.R. Shirts et O. Valsson) Enhanced sampling methods for molecular dynamics simulations, Living Journal of Computational Molecular Science (LiveCoMS), 4(1), (2022).
(avec M. Ramil et J. Reygner) Estimation of statistics of transitions and Hill relation for Langevin dynamics, à paraître dans Annales de l’Institut Henri Poincaré, https://hal-enpc.archives-ouvertes.fr/hal-03659510 .
(avec A. Anciaux-Sekadrian, M. Corral-Valero, M. Moreaud, T. Pigeon, P. Raybaud et G. Stoltz) Computing surface reaction rates by Adaptive Multilevel Splitting combined with Machine Learning and Ab Initio Molecular Dynamics, Journal of Chemical Theory and Computation, 19(12), 3538–3550, (2023).
(avec O. Gorynina, F. Legoll et D. Perez) Combining machine-learned and empirical force fields with the parareal algorithm: application to the diffusion of atomistic defects, à paraître dans Comptes Rendus Mécanique, https://hal.archives-ouvertes.fr/hal-03909092 .
(avec Z. Belkacemi, M. Bianciotto, P. Gkeka, H. Minoux et G. Stoltz) Autoencoders for dimensionality reduction in molecular dynamics: collective variable dimension, biasing and transition states, Journal of Chemical Physics, 159, 024122 (2023).
(avec P. Parpas) Using Witten Laplacians to locate index-1 saddle points, à paraître dans SIAM Journal on Scientific Computing, https://hal.archives-ouvertes.fr/hal-03909090v1.

Actes de conférences / Chapitres de livres

(avec J-F. Gerbeau, C. Le Bris et N. Ligonesche) Metal pad roll instabilities, proceeding of the 2002 TMS Annual Meeting and Exhibition, Light Metals, 483-487, (2002).
(avec B. Jourdain) Mathematical analysis of a stochastic differential equation arising in the micro-macro modelling of polymeric fluids, Rapport CERMICS 2002-225, Probabilistic Methods in Fluids Proceedings of the Swansea 2002 Workshop, Eds: I M Davies, N Jacob, A Truman, O Hassan, K Morgan & N P Weatherill, 205-223, (2002).
(avec J-F. Gerbeau et C. Le Bris) Numerical simulations of two-fluids MHD flows, Fundamental and Applied MHD. Proceedings of the Fifth international PAMIR Conference, I.101-I.105, (2002).
(avec J-F. Gerbeau et C. Le Bris) Modeling and simulation of MHD phenomena in aluminium reduction cells, Proceedings of the fourth International Conference on Electromagnetic Processing of Materials, EPM 2003, C3-10.4, 57-62, (2003).
(avec B. Jourdain) Convergence of a stochastic particle approximation of the stress tensor for the FENE-P model, Rapport CERMICS 2004-263 .
(avec B. Jourdain et C. Le Bris) Coupling PDEs and SDEs: the illustrative example of the multiscale simulation of viscoelastic flows, in Multiscale Methods in Science and Engineering, B. Engquist, P. Lötstedt, O. Runborg, eds., Lect. Notes Comput. Sci. Eng. 44, Springer, 151-170, (2005).
(avec T. Tomasino, M. Le Hervet et O. Martin) Stability analysis of simplified electrolysis cells with Mistral, proceeding of the 2006 TMS Annual Meeting and Exhibition, Light Metals, 335-340, (2006).
(avec J.-F. Gerbeau, C. Le Bris, A. Orriols et T. Tomasino) Linear versus nonlinear approaches for the stability analysis of aluminium production cells, Proceedings de la conférence ECCOMAS 2006.
(avec J.-F. Gerbeau) Variational formulation of the Generalized Navier Boundary Condition, http://hal.inria.fr/inria-00081751, in Recent Progress in Scientific computing, SCPDE05 conference proceeding, Eds: W Liu, M Ng and Z-C Shi, Science Press, Beijing, 2007.
(avec Y. Achdou et O. Bokanowski) Partial differential equations in finance, Rapport CERMICS 2007-363, in Encyclopedia of Financial Models, Ed: F.J. Fabozzi, John Wiley and Sons Inc, 2012.
(avec F. Legoll et G. Stoltz) Some remarks on sampling methods in molecular dynamics, ESAIM Proceedings, 22, 217-233, (2008) pdf.
(avec C. Le Bris) Multiscale modelling of complex fluids: A mathematical initiation, in Multiscale Modeling and Simulation in Science Series, B. Engquist, P. Lötstedt, O. Runborg, eds., Lect. Notes Comput. Sci. Eng. 66, Springer, p. 49-138, (2009). Pour obtenir les programmes Matlab, me contacter.
(avec F. Legoll) Some remarks on free energy and coarse-graining, in Numerical Analysis and Multiscale Computations, B. Engquist, P. Lötstedt, O. Runborg, eds., Lect. Notes Comput. Sci. Eng., 82, Springer, p. 279-329, (2012).
(avec C. Le Bris) Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics, http://hal.archives-ouvertes.fr/hal-00562325/fr/, Science China Mathematics, 55(2), p. 353-384, (2012).
Two mathematical tools to analyze metastable stochastic processes, in Numerical Mathematics and Advanced Applications 2011, A. Cangiani, R.L. Davidchack, E. Georgoulis, A.N. Gorban, J. Levesley, M.V. Tretyakov, eds., Springer, p. 791-810, (2013).
(avec E. Cancès et V. Ehrlacher) Greedy algorithms for high-dimensional non-symmetric linear problems, ESAIM Proceedings, 41, 95-131, (2013) pdf.
(avec F. Casenave, A. Ern et G. Sylvand) A nonintrusive method to approximate linear systems with nonlinear parameter dependence, http://hal.archives-ouvertes.fr/hal-00845822 .
(avec D. Aristoff, C.G. Mayne et I. Teo) Adaptive multilevel splitting in molecular dynamics simulations, ESAIM Proceedings and Surveys, 48, 215-225, (2015) pdf.
(avec I. G. Tejada, L. Brochard, G. Stoltz, F. Legoll et E. Cancès). Combining a reactive potential with a harmonic approximation for molecular dynamics simulation of failure. J. Phys. : Conf. Ser. 574 012041, (2015).
Accelerated dynamics: Mathematical foundations and algorithmic improvements, Eur. Phys. J. Special Topics 224, 2429-2444, (2015).
(avec C.M. Diop, E. Dumonteil, H. Louvin and M. Rousset) Adaptive Multilevel Splitting for Monte Carlo particle transport, Eur. Phys. J. N 153, 06006, (2017).
Mathematical foundations of Accelerated Molecular Dynamics methods, In: W. Andreoni and S. Yip (Eds) Handbook of Materials Modeling. Springer, Cham, (2018). cf. aussi Long-Timescale Simulations: Challenges, Pitfalls, Best Practices, for Development and Applications dans ce même ouvrage.
(avec D. Le Peutrec et B. Nectoux) Exit event from a metastable state and Eyring-Kramers law for the overdamped Langevin dynamics, In: Stochastic Dynamics out of Equilibrium, G. Giacomin, S. Olla, E. Saada, H. Spohn and G. Stoltz (Eds), Springer Proceedings in Mathematics and Statistics (2019).
(avec F. Bach, L. Pillaud-Vivien, A. Rudi et G. Stoltz) Statistical Estimation of the Poincaré constant and Application to Sampling Multimodal Distributions, Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108, 2753-2763 (2020).
(avec M. Ramil et J. Reygner) Mathematical foundations for the Parallel Replica algorithm applied to the underdamped Langevin dynamics, MRS Communications, 12, 454-459 (2022).
(avec G. Robin, I. Sekkat, G. Stoltz et G. Victorino Cardoso) Generative methods for sampling transition paths in molecular dynamics, ESAIM Proceedings and Surveys, 73, 238-256, (2023) pdf.

Prépublications

(avec M.R. Blel et V. Ehrlacher) Influence of sampling on the convergence rates of greedy algorithms for parameter-dependent random variables, https://hal.archives-ouvertes.fr/hal-03238244 .
(avec M. Chak, N. Kantas et G. Pavliotis) Optimal friction matrix for underdamped Langevin sampling, https://hal.archives-ouvertes.fr/hal-03455809 .
(avec D. Le Peutrec et B. Nectoux) Eyring-Kramers exit rates for the overdamped Langevin dynamics: the case with saddle points on the boundary, https://hal.archives-ouvertes.fr/hal-03728053.
(avec R. Santet et G. Stoltz) Unbiasing Hamiltonian Monte Carlo algorithms for a general Hamiltonian function, https://hal.science/hal-04050146.
(avec Y. Conjungo Taumhas, G. Dusson, V. Ehrlacher et F. Madiot) Reduced basis method for non-symmetric eigenvalue problems: application to the multigroup neutron diffusion equations, https://cea.hal.science/cea-04156959 .
(avec M. Chak, G. Stoltz, et U. Vaes) Optimal importance sampling for overdamped Langevin dynamics, https://hal.science/hal-04169540v1 .

Dernière mise à jour le 31 août 2023.