Tony LELIEVRE
- Organization: Ecole
des Ponts ParisTech
- Research Unit: CERMICS
- Project: Molecular
and
Multiscale Simulation
- Phone: 33 (0)1 64 15 35 28
- Fax: 33 (0)1 64 15 35 86
- E-mail :
- Office : B304,
Coriolis building
- Mail:
CERMICS - Ecole des Ponts ParisTech
6 et 8 avenue Blaise Pascal
Cité Descartes - Champs sur Marne
77455 Marne la Vallée Cedex 2 (FRANCE)
Version
française
I am researcher and professor at the Ecole des
Ponts ParisTech, and the head of the applied mathematics
department CERMICS.
I am a member of the Molecular and
Multiscale Modelling group at CERMICS and of the Matherials
project-team at INRIA.
Here is my cv (pdf).
I spent the 2019-2020 academic year in the mathematics
department of Imperial College of London, in the Abraham de
Moivre International Researche Laboratory.
I defended my habilitation thesis on 3rd June 2009 (abstract, manuscript). Title: Mathematical and numerical analysis of
some models for materials, from the microscopic scale to the
macroscopic scale.
During year 2004-2005, I had a post-doc position at the Centre de Recherches
Mathématiques at the University of Montreal, in the context of
a special year about the
Mathematics of Stochastic and Multiscale Modeling.
I defended my PhD thesis on 21st June 2004 (abstract, manuscript). Title: Multiscale
models for viscoelastic fluids. PhD supervisors: Benjamin Jourdain
and Claude
Le Bris.
Research
interests
- Micro-macro models for viscoelastic fluids (dumbbell model,
CONNFFESSIT method, variance reduction methods, entropy
estimates).
- Free surface flow and magnetohydrodynamics. Application to
the simulation of aluminium electrolysis cells (Arbitrary
Lagrangian Eulerian method, moving contact line problem).
- Molecular simulation (molecular dynamics, constrained
dynamics, adaptive methods, Quantum Monte Carlo methods, Adaptive Multilevel
Splitting, Accelerated Molecular Dynamics).
Teaching activities
- Associate
professor at the Ecole Polytechnique
- Professor at the
Ecole des Ponts ParisTech
- In charge of the
projects "Modéliser, Programmer, Simuler"
Lectures and introductory seminars
- Lectures:
- CEMRACS
2008: Multiscale
modelling of complex fluids: a mathematical initiation slides, lecture notes.
- Ecole
doctorale ECODOQUI 2008: Monte Carlo methods in molecular dynamics slides, lecture notes (in French).
- Workshop Stress
tensor effects on fluid mechanics, China, 2010: Multiscale modelling of complex
fluids: a mathematical initiation, slides, lecture notes.
- Cornell University: Free energy calculations, slides.
- 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.
- Introductory seminars (videos):
- Horizons Maths 2012, 19th December 2012 : Méthodes
numériques en dynamique moléculaire (in French).
- Collège de France, 9th January 2015 : Processus
stochastiques métastables et distributions
quasi-stationnaires (in French).
- HIM, 29th January 2015 : Optimal
scaling for the transient phase of Metropolis Hastings
algorithms.
- BIRS, 24th July 2015 : Accelerated
dynamics.
- Newton Institute, 3rd December 2015: The parallel
replica algorithm: mathematical foundations and recent
developments.
- Université de Genève, 1st February 2017: Accelerated
dynamics and transition state theory.
- ICTS, August 2017 : Algorithms for computational statistical
physics: a mathematical viewpoint part 1,
part 2.
- IPAM, 16th October 2017: Metastability:
a journey from stochastic processes to semiclassical
analysis .
- Newton Institute, 20th November 2019: Hybrid
Monte Carlo methods for sampling probability measures on
submanifolds .
- BIRS, 24th November 2020: Effective
dynamics for stochastic differential equations .
- CIRM 28th July 2021: How to
compute mean transition times?
- KAUST 31st May 2023: Unbiased
sampling using reversibility checks .
Events
- 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-organized with Jocelyne Erhel
and Erwan Faou.
- Journées
SMAI/INRIA EDP-Proba,2013-2018, Co-organized with 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. 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.
- Maths/industry
workshop on molecular simulation for pharmaceutical industry,
April 28th 2017. Co-organized with Chris Chipot and
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.
Scientific awards
Editorial activity
- Co-editor in chief of ESAIM:
Proceedings and Surveys, with Djalil Chafai, Cyril Imbert and Pauline Lafitte,
2012-2020.
- Member of the editorial board of SIAM/ASA Journal
of Uncertainty Quantification (JUQ) (since 2017), IMA Journal of
Numerical Analysis (since 2018), Communications
in Mathematical Sciences (since 2019), Journal
of Computational Physics (since 2019), ESAIM:M2AN (since
2020), Foundations of
Computational Mathematics (since 2022).
- Co-editor of the third
volume of Transitions, Les Nouvelles annales des Ponts et
Chaussées, on "Models and data for the environment”,
with David Picard, 2023.
Books
- (with J-F. Gerbeau and C. Le Bris) Mathematical
methods for the Magnetohydrodynamics of liquid metals, 324
pp., Numerical Mathematics and Scientific Computation, Oxford
University Press, 2006.
- (with M. Rousset and G. Stoltz) Free energy computations: A
mathematical perspective, 472 pp., Imperial College
Press, 2010.
Journal articles
- (with B. Jourdain and 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).
- (with J-F. Gerbeau and C. Le Bris) Simulations of MHD
flows with moving interfaces, Journal of
Computational Physics, 184,
163-191, (2003).
- (with J-F. Gerbeau and 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).
- (with B. Jourdain and 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).
- (with B. Jourdain and 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).
- (with F. Dubois) Efficient pricing of Asian options by the
PDE approach, Journal of Computational Finance, 8(2), 55-64, (2005). See
also the program in C,
implemented in Premia,
and some first attempts on the subject (ps in French).
- (with 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). See also the reference
solutions files.
- (with B. Jourdain and 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).
- (with B. Jourdain, C. Le Bris and F. Otto) Long-time asymptotics of a
multiscale model for polymeric fluid flows, Archive for
Rational Mechanics and Analysis, 181(1), 97-148, (2006).
- (with E. Cancès and 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).
- (with M. Rousset and G. Stoltz) Computation of free energy differences through
nonequilibrium stochastic dynamics: the reaction coordinate
case, Journal of Computational Physics, 222(2), 624-643, (2007).
- (with M. Caffarel, E. Cancès, A. Scemama and G. Stoltz) An efficient sampling algorithm
for Variational Monte Carlo, Journal of Chemical
Physics, 125, 114105 (2006).
- (with G. Ciccotti and E. Vanden-Eijnden) Projection of diffusions on
submanifolds: Application to mean force computation,
Communications on Pure and Applied Mathematics, 61(3), 371-408, (2008).
- (with M. El Makrini and B. Jourdain) Diffusion Monte Carlo method: numerical analysis in a
simple case, ESAIM: Mathematical Modelling and
Numerical Analysis, 41(2),
189-213, (2007).
- (with M. Rousset and G. Stoltz) Computation of free energy profiles with parallel
adaptive dynamics, Journal of Chemical Physics 126, 134111 (2007).
- (with A. Ern) Adaptive
models for polymeric fluid flow simulation, C. R. Acad. Sci. Paris, Ser. I, 344(7), 473-476 (2007).
- (with D. Hu) New entropy
estimates for the Oldroyd-B model, and related models,
Communications in Mathematical Sciences 5(4), 909-916
(2007).
- (with C. Le Bris and 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).
- (with M. Rousset and G. Stoltz) Long-time convergence of an Adaptive Biasing Force
method, Nonlinearity, 21,
1155-1181 (2008).
- (with E. Faou) Conservative stochastic
differential equations: Mathematical and numerical analysis, Mathematics
of Computation, 78,
2047-2074 (2009).
- (with 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).
- (with S. Boyaval and C. Mangoubi) Free-energy-dissipative schemes for the Oldroyd-B
model, ESAIM: Mathematical Modelling and Numerical
Analysis, 43, 523-561,
(2009).
- (with C. Le Bris and Y. Maday) Results and questions on a nonlinear approximation
approach for solving high-dimensional partial differential
equations, Constructive Approximation, 30(3), 621-651, (2009).
- (with 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).
- (with B. Jourdain and 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).
- (with C. Chipot and 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).
- (with S. Boyaval, C. Le Bris, Y. Maday, N.C. Nguyen and A.T.
Patera) Reduced basis
techniques for stochastic problems, Archives of
Computational Methods in Engineering, 17(4), 435-454, (2010).
- (with B. Dickson, F. Legoll, G. Stoltz and P. Fleurat-Lessard)
Free energy calculations: An
efficient adaptive biasing potential method, Journal of
Physical Chemistry B, 114,
5823-5830, (2010).
- (with X. Blanc, F. Legoll and C. Le Bris) Beyond multiscale and
multiphysics: Multimaths for model coupling, Networks
and Heterogeneous Media, 5(3),
423-460, (2010).
- (with V. Legat and 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).
- (with F. Legoll) Effective
dynamics using conditional expectations, Nonlinearity,
23, 2131-2163, (2010).
- (with F. Cérou, A. Guyader and D. Pommier) A multiple replica approach to
simulate reactive trajectories, Journal of Chemical
Physics 134, 054108,
(2011).
- (with 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).
- (with E. Cancès and 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).
- (with N. Chopin and G. Stoltz) Free energy methods for Bayesian inference: efficient
exploration of univariate Gaussian mixture posteriors, Statistics
and Computing, 22(4),
897-916, (2012).
- (with C. Chipot) Enhanced
sampling of multidimensional free-energy landscapes using
adaptive biasing forces, SIAM Journal of
Applied Mathematics, 71(5),
1673-1695, (2011).
- (with A. Ern and R. Joubaud) Numerical study of a thin liquid film flowing down an
inclined wavy plane, Physica D, 240(21), 1714-1723,
(2011).
- (with M. Rousset and G. Stoltz) Langevin dynamics with constraints and computation of
free energy differences, Mathematics of Computation, 81(280), 2071-2125, (2012).
- (with L. He and C. Le Bris) Periodic
long-time behaviour for an approximate model of nematic
polymers, Kinetic and Related Models, 5(2), 357-382, (2012).
- (with A. Ern and R. Joubaud) Mathematical study of non-ideal electrostatic
correlations in equilibrium electrolytes, Nonlinearity
25, 1635-1652, (2012).
- (with C. Le Bris, M. Luskin and D. Perez) A mathematical formalization of
the parallel replica dynamics, Monte Carlo Methods and
Applications, 18(2),
119–146, (2012).
- (with D. Benoit, L. He and 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).
- (with M. Dobson, F. Legoll and G. Stoltz) Derivation of Langevin Dynamics in
a nonzero Background Flow Field, ESAIM: Mathematical
Modelling and Numerical Analysis, 47(6), 1583-1626, (2013).
- (with F. Legoll and G. Samaey) A micro-macro parareal algorithm: application to
singularly perturbed ordinary differential equations,
SIAM Journal on Scientific Computing, 35(4), A1951–A1986, (2013).
- (with F. Cérou, A. Guyader and F. Malrieu) On the length of one-dimensional
reactive paths, ALEA Latin American Journal of
Probability and Mathematical Statistics, 10(2), 359-389, (2013).
- (with F. Nier and G. Pavliotis) Optimal non-reversible linear drift for the
convergence to equilibrium of a diffusion, Journal of
Statistical Physics, 152(2),
237-274, (2013).
- (with F. Casenave and 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).
- (with B. Jourdain and B. Miasojedow) Optimal scaling for the transient phase of Metropolis
Hastings algorithms: the longtime behavior, Bernoulli,
20(4), 1930-1978,
(2014).
- (with G. Fort, B. Jourdain, E. Kuhn and 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).
- (with M. Athènes, L. Cao, M.-C. Marinica and G. Stoltz) Free energy calculations from
adaptive molecular dynamics simulations with adiabatic
reweighting, Journal of Chemical Physics, 140, 104108, (2014).
- (with D. Aristoff) Mathematical
analysis of Temperature Accelerated Dynamics, SIAM
Multiscale Modeling and Simulation, 12(1), 290–317, (2014).
- (with B. Jourdain and 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).
- (with D. Benoit and C. Le Bris) Macroscopic limit of a one-dimensional model for
aging fluids, SIAM Multiscale Modeling and Simulation,
12(3), 1335–1378,
(2014).
- (with E. Cancès and V. Ehrlacher) Greedy algorithms for high-dimensional eigenvalue
problems, Constructive Approximation, 40(3), 387-423,
(2014).
- (with F. Casenave and A. Ern) A nonintrusive Reduced Basis Method applied to
aeroacoustic simulations, Advances in Computational
Mathematics, 1-26, (2015).
- (with D. Aristoff and G. Simpson) The parallel replica method for simulating long
trajectories of Markov chains, AMRX, 2, 332-352, (2014).
- (with J. Comer, J.C. Gumbart, J. Hénin, A. Pohorille and 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).
- (with C.E. Bréhier and M. Rousset) Analysis of Adaptive Multilevel Splitting algorithms
in an idealized case, ESAIM P&S, 19, 361 - 394, (2015).
- (with F. Nier) Low
temperature asymptotics for Quasi-Stationary Distributions in
a bounded domain, Analysis & PDE, 8(3), 561-628, (2015).
- (with A. Binder and G. Simpson) A Generalized Parallel Replica Dynamics,
Journal of Computational Physics, 284, 595–616, (2015).
- (with 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).
- (with F. Casenave and 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).
- (with H. Alrachid and 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).
- (with G. Fort, B. Jourdain and G. Stoltz) Self-Healing Umbrella Sampling:
Convergence and efficiency, Statistics and computing, 27(1), 147-168, (2016).
- (with A.B. Duncan and G.A. Pavliotis) Variance reduction using
nonreversible Langevin samplers, Journal of Statistical
Physics, 163(3),
457-491 (2016).
- (with C.-E. Bréhier, M. Gazeau, L. Goudenège and M. Rousset) Unbiasedness of some generalized
Adaptive Multilevel Splitting algorithms, Annals of
Applied Probability, 26(6),
3559-3601, (2016). See [arXiv:1505.02674]
for a longer version of this work.
- (with C. Mayne, K. Schulten and 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).
- (with 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).
- (with 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).
- (with G. Stoltz) Partial
differential equations and stochastic methods in molecular
dynamics, Acta Numerica, 25, 681-880, (2016).
- (with G. Di Gesù, D. Le Peutrec and B. Nectoux) Jump Markov models and transition
state theory: the Quasi-Stationary Distribution approach,
Faraday Discussion, 195,
469-495, (2016).
- (with J. Hénin, A. Lesage and 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).
- (with F. Legoll and S. Olla) Pathwise estimates for an effective dynamics,
Stochastic Processes and their Applications, 127, 2841-2863, (2017).
- (with T. Zhao, H. Fu, X. Shao, C. Chipot and 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).
- (with R. Assaraf, B. Jourdain and 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).
- (with G. Fort, B. Jourdain and 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).
- (with 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). The code is available on github.
- (with 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).
- (with G. Di Gesù, D. Le Peutrec and B. Nectoux) Sharp asymptotics of the first
exit point density, Annals of PDE, 5(1), (2019).
- (with 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).
- (with G. Di Gesù, D. Le Peutrec and 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).
- (with M. Rousset and G. Stoltz) Hybrid Monte Carlo methods for sampling probability
measures on submanifolds, Numerische Mathematik, 143(2), 379-421, (2019). A
correction is here.
- (with W. Zhang) Pathwise
estimates for effective dynamics: the case of nonlinear
vectorial reaction coordinates, SIAM Multiscale
Modeling and Simulation, 17(3),
1019-1051, (2019).
- (with G. Samaey and P. Zielinski) Analysis of a micro-macro acceleration method with
minimum relative entropy moment matching, to appear in
Stochastic Processes and their Applications, (2019).
- (with T. Hudson and F. Legoll) Stochastic homogenization of a scalar viscoelastic
model exhibiting stress-strain hysteresis, ESAIM:
Mathematical Modelling and Numerical Analysis, 54, 879-928, (2020).
- (with F. Legoll and U. Sharma) Effective dynamics for non-reversible stochastic
differential equations: a quantitative study,
Nonlinearity, 32(12),
4779, (2019).
- (with B. Leimkuhler and Z. Trstanova) Local and global perspectives on
diffusion maps in the analysis of molecular systems,
Proceedings of the Royal Society A, 476, 20190036, (2020).
- (with F. Legoll, K. Myerscough and G. Samaey) Parareal computation of stochastic
differential equations with time-scale separation: a numerical
study, Computing and Visualization in Science, 23(9), (2020) .
- (with 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 and 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).
- (with B. Jourdain and P.A. Zitt) Convergence of metadynamics: discussion of the
adiabatic hypothesis, Annals of Applied Probability, 31(5),
2441-2477, (2021).
- (with D. Le Peutrec and 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).
- (with F. Legoll and U. Sharma) An adaptive parareal algorithm: application to the
simulation of molecular dynamics trajectories, SIAM
Journal on Scientific Computing, 44(1),
B146–B176, (2022).
- (with V. Ehrlacher and P. Monmarché) Adaptive force biasing algorithms: new convergence
results and tensor approximations of the bias, Annals
of Applied Probability, 32(5), 3850-3888, (2022).
- (with Z. Belkacemi, P. Gkeka and G. Stoltz) Chasing collective variables using
autoencoders and biased trajectories, Journal of
Chemical Theory and Computation, 18(1
- (with G. Stoltz and W. Zhang) Multiple projection MCMC
algorithms on submanifolds, IMA Journal of Numerical
Analysis, 43(2), 737-788, (2023). Codes are available
here: https://github.com/zwpku/Constrained-HMC
.
- (with M. Ramil and 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).
- (with L. Maurin and 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).
- (with M. Ramil and J. Reygner) A probabilistic study of the kinetic Fokker-Planck
equation in cylindrical domains, Journal of Evolution
Equations, 22(38), (2022).
- (with M. Baudel and A. Guyader) On the Hill relation and the mean reaction time for
metastable processes, Stochastic Processes and their
Applications, 155, 393-436, (2023). See [arXiv:2008.09790]
for a longer version of this work.
- (with L. Delemotte, J. Hénin, M.R. Shirts and O. Valsson) Enhanced
sampling methods for molecular dynamics simulations,
Living Journal of Computational Molecular Science (LiveCoMS), 4(1),
(2022).
- (with M. Ramil and J. Reygner) Estimation of statistics of
transitions and Hill relation for Langevin dynamics, to
appear in
Annales de l’Institut Henri Poincaré https://arxiv.org/abs/2206.13264
.
- (with A. Anciaux-Sekadrian, M. Corral-Valero, M. Moreaud, T.
Pigeon, P. Raybaud, and 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),
- (with O. Gorynina, F. Legoll and D. Perez) Combining
machine-learned and empirical force fields with the parareal
algorithm: application to the diffusion of atomistic defects,
to appear in Comptes Rendus Mécanique, https://arxiv.org/abs/2212.10508
.
- (with Z. Belkacemi, M. Bianciotto, P. Gkeka, H. Minoux and G.
Stoltz) Autoencoders for dimensionality reduction in
molecular dynamics: collective variable dimension, biasing and
transition states, Journal of Chemical
Physics, 159, 024122 (2023).
- (with P. Parpas) Using Witten Laplacians to locate index-1
saddle points, to appear in SIAM Journal on Scientific
Computing, https://arxiv.org/abs/2212.10135.
- (with M. Chak, N. Kantas and G. Pavliotis) Optimal
friction matrix for underdamped Langevin sampling, to
appear in ESAIM: Mathematical Modelling and Numerical Analysis,
https://arxiv.org/abs/2112.06844
.
Proceedings papers / Book chapters
- (with J-F. Gerbeau, C. Le Bris and N. Ligonesche) Metal
pad
roll instabilities, proceeding of the 2002 TMS
Annual Meeting and Exhibition, Light Metals, p. 483-487, 2002.
- (with B. Jourdain) Mathematical analysis of a stochastic
differential equation arising in the micro-macro modelling of
polymeric fluids, CERMICS
2002-225
report, 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, p. 205-223.
- (with J-F. Gerbeau and C. Le Bris) Numerical simulations
of two-fluids MHD flows, Fundamental and Applied MHD.
Proceedings of the Fifth international PAMIR Conference, p.
I.101-I.105, 2002.
- (with J-F. Gerbeau and 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, p. 57-62, 2003.
- (with B. Jourdain) Convergence of a stochastic particle
approximation of the stress tensor for the FENE-P model, CERMICS
2004-263
report .
- (with B. Jourdain and 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).
- (with T. Tomasino, M. Le Hervet and O. Martin) Stability analysis of simplified
electrolysis cells with Mistral, proceeding of the 2006
TMS Annual Meeting and Exhibition, Light Metals, p. 335-340,
2006.
- (with J.-F. Gerbeau, C. Le Bris, A. Orriols and T. Tomasino) Linear versus nonlinear approaches
for the stability analysis of aluminium production cells,
Proceedings of the 2006 ECCOMAS conference.
- (with 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.
- (with Y. Achdou and O. Bokanowski) Partial differential equations in finance, CERMICS
2007-363
report, in Encyclopedia of Financial Models, Ed: F.J.
Fabozzi, John Wiley and Sons Inc, 2012.
- (with F. Legoll and G. Stoltz) Some remarks on sampling methods in molecular
dynamics,
ESAIM Proceedings, 22,
217-233, (2008) pdf.
- (with 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). To get the Matlab programs, contact me.
- (with 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).
- (with C. Le Bris) Micro-macro
models for viscoelastic fluids: modelling, mathematics and
numerics, http://arxiv.org/abs/1102.0325,
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).
- (with E. Cancès and V. Ehrlacher) Greedy algorithms for high-dimensional non-symmetric
linear problems, ESAIM Proceedings, 41, 95-131, (2013) pdf.
- (with F. Casenave, A. Ern and G. Sylvand) A nonintrusive method to
approximate linear systems with nonlinear parameter dependence,
http://arxiv.org/abs/1307.4330
.
- (with D. Aristoff, C.G. Mayne and I. Teo) Adaptive multilevel splitting in
molecular dynamics simulations, ESAIM Proceedings
and Surveys, 48,
215-225, (2015) pdf.
- (with I. G. Tejada, L. Brochard, G. Stoltz, F. Legoll and 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).
- (with 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). See also Long-Timescale
Simulations: Challenges, Pitfalls, Best Practices, for
Development and Applications in this book.
- (with D. Le Peutrec and 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).
- (with F. Bach, L. Pillaud-Vivien, A. Rudi and G. Stoltz)
Statistical Estimation of the Poincaré constant and Application
to Sampling Multimoda Distributions, Proceedings of the Twenty
Third International Conference on Artificial Intelligence and
Statistics, PMLR 108, 2753-2763 (2020).
- (with M. Ramil and J. Reygner) Mathematical foundations
for the Parallel Replica algorithm applied to the underdamped
Langevin dynamics, MRS
Communications,12, 454-459 (2022).
- (with G. Robin, I. Sekkat, G. Stoltz and G. Victorino Cardoso)
Generative methods for sampling transition paths in molecular
dynamics, ESAIM Proceedings and Surveys, 73, 238-256, (2023) pdf.
- (with C. Chipot, P. Gkeka, et G. Stoltz) Equilibrium and
Nonequilibrium Methods for Free-Energy Calculations With
Molecular Dynamics, In: Comprehensive Computational
Chemistry, Vol. 3, p.384-400, (2024).
- (with D. Perez) Recent advances in Accelerated Molecular
Dynamics Methods: Theory and Applications, In:
Comprehensive Computational Chemistry, Vol. 3, p.360-383,
(2024).
Preprints
- (with M.R. Blel and V. Ehrlacher) Influence of sampling on the convergence rates of
greedy algorithms for parameter-dependent random variables,
https://arxiv.org/abs/2105.14091
.
- (with D. Le Peutrec and B. Nectoux) Eyring-Kramers exit
rates for the overdamped Langevin dynamics: the case with
saddle points on the boundary, https://arxiv.org/abs/2207.09284.
- (with R. Santet and G. Stoltz) Unbiasing Hamiltonian Monte
Carlo algorithms for a general Hamiltonian function, https://arxiv.org/abs/2303.15918.
- (with Y. Conjungo Taumhas, G. Dusson, V. Ehrlacher, and F.
Madiot)
Reduced basis method for non-symmetric eigenvalue problems:
application to the multigroup neutron diffusion equations,
https://arxiv.org/abs/2307.05978
.
- (with Y. Conjungo Taumhas, G. Dusson, V. Ehrlacher, and F.
Madiot) An Application of Reduced Basis Methods to Core
Computation in APOLLO3, https://arxiv.org/abs/2311.13902.
- (with M. Chak, G. Stoltz, and U. Vaes) Optimal importance
sampling for overdamped Langevin dynamics, https://arxiv.org/abs/2307.11744
.
- (with T. Pigeon, G. Stoltz, and W. Zhang) Analyzing
multimodal probability measures with autoencoders, https://arxiv.org/abs/2310.03492
.
- (with M. Rachid, and G. Stoltz) A spectral approach to the
narrow escape problem in the disk https://arxiv.org/abs/2401.06903
.
Last update: January 17th, 2024.