Publications – CERMICS

Books and book chapters

Free Energy Computations: A mathematical Perspective [link]
Together with Tony Lelièvre (CERMICS) and Mathias Rousset (INRIA Lille), we published a book on the mathematical study of free energy computations. You can also find here the codes advertised in the preface to the book.
Stochastic Dynamics out of Equilibrium, Springer Proceedings in Mathematics & Statistics, volume 282 [link]
Edited by G. Giacomin, S. Olla, E. Saada, H. Spohn and G. Stoltz, following up on the trimester we organized at Institut Henri Poincare.
C. Chipot, P. Gkeka, T. Lelièvre and G. Stoltz, Equilibrium and nonequilibrium methods for free-energy calculations with molecular dynamics, Reference Module in Chemistry, Molecular Sciences and Chemical Engineering, Elsevier (2023) [link]

Molecular dynamics & related fields

G. Pavliotis, R. Spacek, G. Stoltz and U. Vaes, Neural network approaches for variance reduction in fluctuation formulas, arXiv preprint 2410.00278 (2024) pdf
P. Monmarché, R. Spacek and G. Stoltz, Transient subtraction: A control variate method for computing transport coefficients, arXiv preprint 2410.00212 (2024) pdf
S. Darshan, A. Eberle and G. Stoltz, Sticky coupling as a control variate for sensitivity analysis, arXiv preprint 2409.15500 (2024) pdf
C. Schönle, M. Gabrié, T. Lelièvre and G. Stoltz, Sampling metastable systems using collective variables and Jarzynski-Crooks paths, arXiv preprint 2405.18160 (2024) pdf
T. Lelièvre, G. A. Pavliotis, G. Robin, R. Santet and G. Stoltz, Optimizing the diffusion coefficient of overdamped Langevin dynamics, arXiv preprint 2404.12087 (2024) pdf
T. Lelièvre, M. Rachid and G. Stoltz, A spectral approach to the narrow escape problem in the disk, arXiv preprint 2401.06903 (2024) pdf
E. Camrud, A. O. Durmus, P. Monmarché and G. Stoltz, Second order quantitative bounds for unadjusted generalized Hamiltonian Monte Carlo, arXiv preprint 2306.09513 (2023) pdf
G. Brigati and G. Stoltz, How to construct decay rates for kinetic Fokker–Planck equations?, arXiv preprint 2302.14506 (2023) pdf
K. Karoni, B. Leimkuhler and G. Stoltz, Friction-adaptive descent: A family of dynamics-based optimization methods, J. Comput. Dyn. 10(4), 450-484 (2023) pdf
M. Chak, T. Lelièvre, G. Stoltz and U. Vaes, Optimal importance sampling for overdamped Langevin dynamics, arXiv preprint 2307.11744 (2023) pdf
N. Blassel and G. Stoltz, Fixing the flux: A dual approach to computing transport coefficients, J. Stat. Phys. 191:17 (2024) pdf
T. Lelièvre, R. Santet and G. Stoltz, Unbiasing Hamiltonian Monte Carlo algorithms for a general Hamiltonian function, arXiv preprint 2303.15918 (2023) pdf
T. Pigeon, G. Stoltz, M. Corral-Valero, A. Anciaux-Sedrakian, M. Moreaud, T. Lelièvre, P. Raybaud, Computing surface reaction rates by Adaptive Multilevel Splitting combined with machine learning and ab initio molecular dynamics, J. Chem. Theory Comput. 19(12), 3538–3550 (2023) pdf
R. Spacek and G. Stoltz, Extending the regime of linear response with synthetic forcings, Multiscale Model. Sim. 21(4), 1602-1643 (2023) pdf
T. Hoang Ngoc Minh, G. Stoltz, and B. Rotenberg, Frequency and field-dependent response of confined electrolytes from Brownian dynamics simulations, J. Chem. Phys. 158, 104103 (2023) pdf
G. Stoltz, Error estimates and variance reduction for nonequilibrium stochastic dynamics. In A. Hinrichs, P. Kritzer and F. Pillichshammer (eds) Monte Carlo and Quasi-Monte Carlo Methods. MCQMC 2022. Springer Proceedings in Mathematics & Statistics, vol 460, pages 163-187 (2024) pdf
G. A. Pavliotis, G. Stoltz, U. Vaes, Mobility estimation for Langevin dynamics using control variates, Multiscale Model. Sim. 21(2), 680-715 (2023) pdf
T. Lelièvre, G. Robin, I. Sekkat, G. Stoltz, and G. Victorino Cardoso, Generative methods for sampling transition paths in molecular dynamics, ESAIM Proc. 73, 238-256 (2023) pdf
G. Stoltz, Computational statistical physics and hypocoercivity, arXiv preprint 2112.08221 (2021) pdf
P. Plechac, G. Stoltz and T. Wang, Martingale product estimators for sensitivity analysis in computational statistical physics, IMA J. Numer. Anal. 43(6), 3430-3477 (2023) pdf
I. Sekkat and G. Stoltz, Removing the mini-batching error in Bayesian inference using Adaptive Langevin dynamics, J. Machin. Learn. Res. 24(329), 1-58 (2023) pdf
A. Durmus, A. Enfroy, E. Moulines and G. Stoltz, Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics, arXiv preprint 2107.14542 (2021) pdf
E. Camrud, D. P. Herzog, G. Stoltz and M. Gordina, Weighted L2-contractivity of Langevin dynamics with singular potentials, Nonlinearity 35(2), 998-1035 (2022) pdf
G. A. Pavliotis, G. Stoltz and U. Vaes, Scaling limits for the generalized Langevin equation, Journal of Nonlinear Science 31, no.8 (2021) pdf
E. Bernard, M. Fathi, A. Levitt, G. Stoltz, Hypocoercivity with Schur complements, Annales Henri Lebesgue 5, 523-557 (2022) pdf
A. Iacobucci, S. Olla and G. Stoltz, Thermo-mechanical transport in rotor chains, J. Stat. Phys. 183, 26 (2020) pdf
T. Lelièvre, G. Stoltz and W. Zhang, Multiple projection MCMC algorithms on submanifolds, arXiv preprint 2003.09402 (2020) pdf
P. Plechac, G. Stoltz and T. Wang, Convergence of the likelihood ratio method for linear response of non-equilibrium stationary states, M2AN 55, S593-S623 (2021) pdf
L. Pillaud-Vivien, F. Bach, T. Lelièvre, A. Rudi and 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) pdf
B. Leimkuhler, M. Sachs and G. Stoltz, Hypocoercivity properties of adaptive Langevin dynamics, SIAM J. Appl. Math., 80(3), 1197–1222 (2020) pdf
D. Chafaï, G. Ferré and G. Stoltz, Coulomb gases under constraint: some theoretical and numerical results, SIAM J. Math. Anal. 53(1), 181–220 (2021) pdf
G. Ferré and G. Stoltz, Large deviations of the empirical measure of diffusions in weighted topologies, Electronic Journal of Probability 25, 121 (2020) pdf
G. Ferré, M. Rousset and G. Stoltz, More on the long time stability of Feynman-Kac semigroups, Stoch. PDE 9(3), 630-673 (2021) pdf
T. Lelièvre, M. Rousset and G. Stoltz, Hybrid Monte Carlo methods for sampling probability measures on submanifolds, Numer. Math. 143(2), 379-421 (2019) preprint, erratum
J. Roussel and G. Stoltz, A perturbative approach to control variates in molecular dynamics, Multiscale Model. Simul. 17(1), 552–591 (2019) pdf
G. Ferré and G. Stoltz, Error estimates on ergodic properties of discretized Feynman-Kac semigroups, Numer. Math. 143(2), 261–313 (2019) preprint
G. Stoltz and E. Vanden-Eijnden, Longtime convergence of the Temperature-Accelerated Molecular Dynamics Method, Nonlinearity 31(8), 3748-3769 (2018) pdf
J. Roussel and G. Stoltz, Spectral methods for Langevin dynamics and associated error estimates, M2AN 52(3), 1051-1083 (2018) preprint
A. Iacobucci, S. Olla and G. Stoltz, Convergence rates for nonequilibrium Langevin dynamics, Ann. Math. Quebec 43(1), 73-98 (2019) pdf
G. Fort, B. Jourdain, T. Lelievre and G. Stoltz, Convergence and efficiency of adaptive importance sampling techniques with partial biasing, J. Stat. Phys. 171(2), 220-268 (2018) link
A. Lesage, T. Lelièvre, G. Stoltz and J. Hénin, Smoothed biasing forces yield unbiased free energies with the extended-system adaptive biasing force method, J. Phys. Chem. B 121(15), 3676–3685 (2017)
G. Stoltz and Z. Trstanova, Langevin dynamics with general kinetic energies, Multiscale Model. Simul., 16(2), 777-806 (2018) preprint
T. Lelièvre and G. Stoltz, Partial differential equations and stochastic methods in molecular dynamics, Acta Numerica 25, 681-880 (2016) link
S. Redon, G. Stoltz and Z. Trstanova, Error Analysis of Modified Langevin Dynamics, J. Stat. Phys. 164(4), 735-771 (2016) preprint
I. G. Tejada, L. Brochard, T. Lelièvre, G. Stoltz, F. Legoll and E. Cancès, 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) preprint
M. Fathi and G. Stoltz, Improving dynamical properties of stabilized discretizations of overdamped Langevin dynamics, Numer. Mathematik 136(2), 545–602 (2017) preprint
H. Spohn and G. Stoltz, Nonlinear fluctuating hydrodynamics in one dimension: the case of two conserved fields, J. Stat. Phys. 160(4), 861-884 (2015) preprint
G. Fort, B. Jourdain, T. Lelievre and G. Stoltz, Self-Healing Umbrella Sampling: Convergence and efficiency, Stat. Comput. 27(1) 147-168 (2017) preprint
R. Joubaud, G. Pavliotis and G. Stoltz, Langevin dynamics with space-time periodic nonequilibrium forcing, J. Stat. Phys. 158(1), 1-36 (2015) preprint
M. Fathi, A.-A. Homman and G. Stoltz, Error analysis of the transport properties of Metropolized schemes, ESAIM Proc. 48, 341-363 (2015) preprint
G. Fort, B. Jourdain, E. Kuhn, T. Lelièvre and G. Stoltz, Efficiency of the Wang-Landau algorithm: a simple test case, Appl. Math. Res. Express 2014(2), 275-311 (2014) preprint
L. Cao, M.-C. Marinica, G. Stoltz, T. Lelièvre and M. Athènes, Using Bayes formula to average the biasing forces and recover free energies in adaptive Monte Carlo simulations, J. Chem. Phys. 140, 104108 (2014) pdf
B. Leimkuhler, Ch. Matthews and G. Stoltz, The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics, IMA J. Numer. Anal. 36(1), 13-79 (2016) preprint
G. Fort, B. Jourdain, E. Kuhn, T. Lelièvre and G. Stoltz, Convergence of the Wang-Landau algorithm, Math. Comput. 84(295), 2297-2327 (2015) preprint
M. Dobson, F. Legoll, T. Lelièvre and G. Stoltz, Derivation of Langevin dynamics in a nonzero background flow field, M2AN 47, 1583–1626 (2013) preprint
A. Iacobucci, F. Legoll, S. Olla and G.Stoltz, Negative thermal conductivity of chains of rotors with mechanical forcing, Phys. Rev. E 84 061108 (2011) preprint
R. Joubaud and G. Stoltz, Nonequilibrium shear viscosity computations with Langevin dynamics, Multiscale Model. Sim. 10, 191-216 (2012) (preprint, erratum of the published version)
C. Bernardin and G. Stoltz, Anomalous diffusion for a class of systems with two conserved quantities, Nonlinearity 25, 1099- 1133 (2012) preprint
T. Lelièvre, M. Rousset and G. Stoltz, Langevin dynamics with constraints and computation of free energy differences, Math. Comput. 81, 2071-2125 (2012) preprint
N. Chopin, T. Lelièvre and G. Stoltz, Free energy methods for efficient exploration of mixture posterior densities, Statist. Comput. 22(4), 897-916 (2012) preprint
A. Iacobucci, F. Legoll, S. Olla, G. Stoltz, Thermal conductivity of the Toda lattice with conservative noise, J. Stat. Phys. 140(2), 336-348 (2010) preprint
B. Dickson, F. Legoll, T. Lelièvre, G. Stoltz, P. Fleurat-Lessard, Free energy calculations: An efficient adaptive biasing potential method, J. Phys. Chem. B 114(17), 5823–5830 (2010) preprint
J.B. Maillet and G. Stoltz, Sampling constraints in average: The example of Hugoniot curves, Appl. Math. Res. Express 2008, abn:004 (2009) preprint
T. Lelièvre, M. Rousset and G. Stoltz, Long-time convergence of an Adaptive Biasing Force method, Nonlinearity 21, 1155-1181 (2008) preprint
T. Lelièvre, M. Rousset and G. Stoltz, Computation of free energy profiles with parallel adaptive dynamics, J. Chem. Phys. 126, 134111 (2007) preprint
G. Stoltz, Path sampling with stochastic dynamics: some new algorithms, J. Comput. Phys. 225, 491-508 (2007) preprint
T. Lelièvre, M. Rousset and G. Stoltz, Computation of free energy differences through nonequilibrium stochastic dynamics: the reaction coordinate case, J. Comput. Phys. 222(2), 624-643 (2007) preprint
M. Rousset and G. Stoltz, An interacting particle system approach for molecular dynamics, J. Stat. Phys. 123(6), 1251-1272 (2006) preprint
E. Cancès, F. Legoll, and G. Stoltz, Theoretical and numerical comparison of some sampling methods, M2AN 41(2) 351-390(2007) preprint

Coarse-graining and machine learning

T. Lelièvre, T. Pigeon, G. Stoltz and W. Zhang, Analyzing multimodal probability measures with autoencoders, J. Phys. Chem. B 128(11) 2607-2631 (2024) pdf
Z. Belkacemi, M. Bianciotto, H. Minoux, T. Lelièvre, G. Stoltz and P. Gkeka, Autoencoders for dimensionality reduction in molecular dynamics: collective variable dimension, biasing and transition states, J. Chem. Phys 159, 024122 (2023) pdf
A. Castellano, F. Bottin, J. Bouchet, A. Levitt, and G. Stoltz, Ab initio canonical sampling based on variational inference, Phys. Rev. B 106, L161110 (2022) pdf
Z. Belkacemi, P. Gkeka, T. Lelièvre, G. Stoltz, Chasing collective variables using autoencoders and biased trajectories, J. Chem. Theory Comput. 18(1), 59-78 (2022) pdf
P. Gkeka, G. Stoltz, A. Barati Farimani, Z. Belkacemi, M. Ceriotti, J. Chodera, A. Dinner, A. Ferguson, J.-B. Maillet, H. Minoux, C. Peter, F. Pietrucci, A. Silveira, A. Tkatchenko, Z. Trstanova, R. Wiewiora, T. Lelièvre, Machine learning force fields and coarse-grained variables in molecular dynamics: application to materials and biological systems, J. Chem. Theory Comput. 16(8), 4757–4775 (2020) pdf
P. Terrier and G. Stoltz, A mathematical justification of the finite time approximation of Becker-Döring equations by a Fokker–Planck dynamics, arXiv preprint 1810.01462 (2018) pdf
G. Faure and G. Stoltz, Stable and accurate schemes for smoothed dissipative particle dynamics, Appl. Math. Mech.-Engl. 39(1), 83-102 (2018) preprint
G. Stoltz, Stable schemes for dissipative particle dynamics with conserved energy, J. Comput. Phys. 340, 451–469 (2017) preprint
P. Terrier, M. Athènes, T. Jourdan, G. Adjanor, G. Stoltz, Cluster dynamics modelling of materials: a new hybrid deterministic/stochastic coupling approach, J. Comput. Phys. 350, 280-295 (2017) pdf
G. Faure, J. Roussel, J.-B. Maillet and G. Stoltz, Size consistency in Smoothed Dissipative Particle Dynamics, Phys. Rev. E 94 043305 (2016) preprint
T. Jourdan, G. Stoltz, F. Legoll and L. Monasse, An accurate scheme to solve cluster dynamics equations using a Fokker-Planck approach, Comput. Phys. Commun. 207 170-178 (2016) preprint
A.-A. Homman, J.-B. Maillet, J. Roussel and G. Stoltz, New parallelizable schemes for integrating the Dissipative Particle Dynamics with Energy Conservation, J. Chem. Phys. 144 024112 (2016) preprint
G. Ferre, J.-B. Maillet and G. Stoltz, Permutation-invariant distance between atomic configurations, J. Chem. Phys. 143 104114 (2015) preprint
A.-A. Homman, E. Bourasseau, G. Stoltz, P. Malfreyt, L. Strafella and A. Ghoufi, Surface tension of spherical drops from surface of tension, J. Chem. Phys. 140 034110 (2014) link
G. Faure, J.-B. Maillet and G. Stoltz, Local density dependent potential for compressible mesoparticles, J. Chem. Phys. 140 114105 (2014) preprint
J.-B. Maillet, G. Vallverdu, N.Desbiens and G. Stoltz, Molecular Simulations of Shock to Detonation Transition in Nitromethane, Europhys. Lett. 96 68007 (2011) preprint
E. Bourasseau, J.-B. Maillet, N.Desbiens and G. Stoltz, Microscopic calculations of Hugoniot curves of neat TATB and of its detonation products, J. Phys. Chem. A 115(39) 10729-10737 (2011) preprint
J.-B. Maillet, E. Bourasseau, L. Soulard, J. Clerouin and G. Stoltz, Constant entropy sampling and release waves of shock compressions, Phys. Rev. E 80, 021135 (2009) preprint
J.-B. Maillet, L. Soulard and G. Stoltz, A reduced model for shock and detonation waves. 2. The reactive case, Europhys. Lett. 78(6), 68001(2007) preprint
G. Stoltz, A reduced model for shock and detonation waves. 1. The inert case, Europhys. Lett. 76(5), 849-855 (2006) preprint (Erratum: Europhys. Lett., 77(3), 39901 (2007))
G. Stoltz, Shock waves in an augmented one-dimensional chain, Nonlinearity 18, 1967-1985 (2005) preprint

Quantum chemistry and quantum physics

É. Cancès, L. Cao and G. Stoltz, Removing a slab from the Fermi sea: the reduced Hartree-Fock model, Nonlinearity 33(1), 156-195 (2020) preprint
É. Cancès, A. Levitt, G. Panati and G. Stoltz, Robust determination of maximally-localized Wannier functions, Phys. Rev. B 95, 075114 (2017) preprint
E. Cancès, D. Gontier and G. Stoltz, A mathematical analysis of the GW0 method for computing electronic excited state energies of molecules, Rev. Math. Phys. 28(4) 1650008 (2016) preprint
E. Cancès and G. Stoltz, A mathematical formulation of the random phase approximation for crystals, Ann. I. H. Poincare-An. 29(6) 887-925 (2012) pdf
Christian Brouder, Gianluca Panati and Gabriel Stoltz, Gell-Mann and Low formula for degenerate unperturbed states, Ann. I. H. Poincare-Phy 10(7) 1285-1309 (2010) preprint
Christian Brouder, Gianluca Panati and Gabriel Stoltz, The Green function of degenerate systems, Phys. Rev. Lett. 103, 230401 (2009) preprint
Gabriel Stoltz, Natalio Mingo and Francesco Mauri, Reducing the thermal conductivity of carbon nanotubes below the random isotope limit, Phys. Rev. B 80, 113408 (2009) preprint
Gabriel Stoltz, Michele Lazzeri and Francesco Mauri,Thermal transport in isotopically disordered carbon nanotubes: a comparison between Green’s functions and Boltzmann approaches, J. Phys. Cond. Matter 21, 245302 (2009) pdf
Christian Brouder, Gabriel Stoltz and Gianluca Panati, Adiabatic approximation, Gell-Mann and Low theorem and degeneracies: A pedagogical example, Phys. Rev. A 78, 042102 (2008) pdf
E. Cancès, G. Stoltz, G. Scuseria, V. Staroverov and E. Davidson, Local exchange potentials for electronic structure calculations, MathS In Action 2, 1-42 (2009) link, preprint
A.F. Izmaylov, V.N. Staroverov, G. Scuseria, E.R. Davidson, G. Stoltz, and E. Cancès, The effective local potential method: Implementation for molecules and relation to approximate optimized effective potential techniques, J. Chem. Phys. 126, 084107 (2007)
A. Scemama, T. Lelièvre, G. Stoltz, E. Cancès, M. Caffarel, An efficient sampling algorithm for Variational Monte Carlo, J. Chem. Phys. 125, 114105 (2006) preprint
E. Cancès, M. Lewin and G. Stoltz, The Electronic Ground State Energy Problem: a New Reduced Density Matrix Approach, J. Chem. Phys. 125, 064101 (2006) preprint

PhD & Habilitation thesis

You will find here an electronic version of the manuscript of my habilitation thesis (abstract, english except for the first pages…), as well as an electronic version of my PhD thesis (abstract, english, french).