Search this site

Personal webpage of Grégoire Ferré

Researcher in applied mathematics

Contact : gregoire[dot]ferre[at]ponts[dot]org

I am currently a Vice President at Capital Fund Management (CFM). My research interests lie at the intersection of probability theory, statistical physics, computational statistics and analysis. I am particularly interested in fluctuations of random systems, random matrix theory, ergodic theory, systems at low temperature, and the interaction between finance, statistical physics and machine learning. I obtained my PhD at Ecole des Ponts ParisTech under the supervision of Gabriel Stoltz. Before this, I have been involved in a machine learning project for statistical physics at the Los Alamos National Laboratory and Commissariat à l'Energie Atomique.

Research interests

Numerical analysis for stochastic differential equations and their discretizations;
Stochastic numerical methods (MCMC, filtering...);
Ergodic theory for Markov chains;
Feynman-Kac dynamics, nonlinear dynamics;
Large deviations theory and its application to physics (phase transition...);
Systems at low temperature, variance reduction;
Optimal control, Hamilton-Jacobi-Bellman equations;
Large random matrices, Coulomb gases;
Interaction between statistical physics and machine learning;
PDE theory, functional inequalities, spectral theory of operators.

Publications

Stochastic analysis

Ferré, G. (2022). A subexponential version of Cramér's theorem. Preprint
Ferré, G. (2021). Stochastic viscosity solutions of Hamilton-Jacobi equations and variance reduction. ESAIM: Mathematical Modelling and Numerical Analysis, 57(4), 2301-2318. Preprint
Ferré, G. and Grafke, T. (2020). Approximate optimal controls via instanton expansion for low temperature free energy computation. SIAM Multiscale Model. Simul., 19(3), 1310–1332 Preprint .
Ferré, G. and Stoltz, G. (2020). Large deviations of empirical measures of diffusions in weighted topologies. Electronic Journal of Probability, 121(25), 1-52. Preprint.
Chafaï, D., Ferré, G. and Stoltz, G. (2019). Coulomb gases under constraint: some theoretical and numerical results. SIAM Journal on Mathematical Analysis, 53(1), 181-220 . Preprint.
Ferré, G. , Rousset, M. and Stoltz, G. (2018). More on the long time stability of Feynman- Kac semigroups. Stochastics and Partial Differential Equations: Analysis and Computations, 9(3), 630-673. Preprint.
Chafaï, D. and Ferré, G. (2018). Simulating Coulomb and Log-Gases with Hybrid Monte Carlo Algorithms. The Journal of Statistical Physics, 174(3), 692-714. Preprint.
Ferré, G. and Touchette, H. (2018). Adaptive sampling of large deviations. The Journal of Statistical Physics, 172(6), 1525-1544. Preprint.
Ferré, G. and Stoltz, G. (2019). Error estimates on ergodic properties of Feynman-Kac semigroups. Numerische Mathematik, 143(2), 261-313. Preprint.

Machine learning and model reduction

Ferré, G., Haut, T. and Barros, K. (2017). Learning molecular energies using localized graph kernels. The Journal of Chemical Physics, 146(11), 114107. Preprint.
Zentner, I., Ferré, G., Poirion, F. and Benoit, M. (2016). A biorthogonal decomposition for the identification and simulation of non-stationary and non-Gaussian random fields. Journal of Computational Physics, 314, 1-13.
Ferré, G., Maillet, J.-B. and Stoltz, G. (2015). Permutation-invariant distance between atomic configurations. The Journal of Chemical Physics, 143(10), 104114. Preprint.

Talks given in conferences

GAMM Meeting, Munich, Conditioned random matrices and Coulomb gases: some numerical and theoretical aspects, 2019.
International Conference on Scientific Computation and Differential Equations (SciCADE), Innsbruck, Error estimates on ergodic properties of Feynman–Kac semigroups, 2019.
International Congress on Industrial and Applied Mathematics (ICIAM), Valencia, Conditioned random matrices and Coulomb gases: some numerical and theoretical aspects, 2019.
Journées de Probabilités 2019, Dourdan, Large deviations for the empirical measure of diffusion: revisiting Cramer’s condition with Lyapunov functions, 2019.
Franco-German Meeting Workshop on Mathematical Aspects in Computational Chemistry, Aachen, Feynman-Kac models: stability and further issues, 2018.
SIAM meeting on Mathematical Aspects of Material Science, Portland (Oregon), An Adaptive Algorithm for Sampling Large Deviation Functions, 2018.
SIAM meeting on Mathematical Aspects of Material Science, Portland (Oregon), Error Estimates and Stability for Diffusion Monte Carlo Algorithms, 2018.
International Conference in Monte Carlo and Quasi-Monte Carlo Methods in Scientific computing, Rennes, Long time stability of Feynman-Kac dynamics, 2018.
Congrès National d’Analyse Numérique, Cap d’Agde, Error estimates and ergodic properties of Markov chains and Feynman-Kac models, 2018.
IHP, Paris, Young Probabilists’ Day (Les probabilités de demain), Long time stability of Feynman-Kac models, 2018.
ICTS, Bengalore, Large deviations theory in statistical physics, recent advances and future challenges, Error estimates for Feynman-Kac semi-groups, 2017.
IHP, Paris, Stochastic Dynamics Out of Equilibrium, Young Researchers’ Talks, Error estimates for Feynman-Kac semi-groups, 2017.
Institute for Pure and Applied Mathematics, UCLA, Los Angeles, Understanding Many-Particle Systems with Machine Learning, Learning potential energy landscapes with localized graph kernels, 2016.

Talks given in seminars

Université de Versailles Saint-Quentin en Yvelines, A subexponential version of Cramer's theorem, 2023.
Delaware University, Probability seminar, Low temperature asymptotics and importance sampling, 2021.
Université de Versailles Saint-Quentin en Yvelines, Conditioned random matrices and Coulomb gases: some numerical and theoretical aspects, 2019.
Université de Marseille, Séminaire de probabilité, Large deviations of diffusion processes for unbounded observables, 2019.
Université de Lille, Séminaire, Long time behaviour of linear and nonlinear semigroups in probability, 2019.
Université Paris-Dauphine, Young researchers’ seminar, A gentle introduction to ergodic theory for Markov chains and Feynman-Kac dynamics, 2019.
CERMICS, ENPC, Paris, MsMath working group, presentation of the paper Scaling limit of the Stein variational gradient descent: the mean field regime, by J. Lu, Y Lu and J. Nolen, 2018.
Courant Institute of Mathematical Science, New York, Student Probability seminar, Ergodicity for Markov chains, coupling probabilities and analysis, 2018.
CERMICS, ENPC, Paris, PhD seminar, Crash course on ergodicity for Markov chains: doing probabilities like an analyst, 2018.

Research visits

Stellenbosch University, Division of Applied Mathematics, fall 2019, two weeks;
New York, Courant Institute of Mathematical Sciences (CIMS), fall 2018, two months;
Bangalore, International Center for Theoretical Sciences (ICTS), summer 2017, two weeks;
Los Angeles, Institute for Pure and Applied Mathematics (IPAM), fall 2016, two months;
Los Alamos, Los Alamos National Laboratory (LANL), summer 2016, three months.

Posters

CIB-CECAM, Lausanne, Computational Mathematics for model reduction and predictive modelling in molecular and complex systems, 2019.
CIRM, Marseille, Advances in Computational Statistical Physics, 2018.
INRIA Rennes, Simulation aléatoire : problèmes actuels, 2018.
Alan Turing Institute, London, Data-Driven Modelling of Complex Systems, 2018.
Duke University, Durham, Quasi Monte-Carlo and High-Dimensional Sampling Methods for Applied Mathematics, 2017.
IPAM, Los Angeles, Complex High-Dimensional Energy Landscapes, 2017.
IHP, Paris, Stochastic Dynamics Out of Equilibrium, 2017.
IPAM, Los Angeles, Understanding Many-Particle Systems with Machine Learning, 2016.

Teaching

Project with 4 students over a trimester (genealogical algorithms for rare events simulation) at Ecole des Ponts, 15h, 2018 and 2019.
Co-mentoring a 6 months graduate intern at Ecole des Ponts with Gabriel Stoltz, 2018.
First year course in analysis and optimization at Université Paris-Dauphine, 36h, 2017.
Tutoring in analysis (distributions, Sobolev spaces...) at Ecole des Ponts, 20h, 2017.

Distinctions

Prix Perronet (for engineering degree at Ecole des Ponts).
PhD prize of Université Paris-Est (for PhDs defended in 2019).
PhD prize of Fondation des Ponts (for PhDs defended in 2019 at Ecole des Ponts).

PhD material

these.pdf