Mathias Rousset
Civil Status:
Born: February 8, 1980. Nationality: French.
Academic Position:
Junior Scientist (CR1) at INRIA Paris Rocquencourt in the Matherials Project.
Address: CERMICS, Ecole des Ponts ParisTech, Batiment Coriolis, 6 et 8 avenue Blaise Pascal,
Cité Descartes  Champs sur Marne, 77455 Marne la Vallée Cedex 2, FRANCE.
Phone: +331.64.15.33.49
Detailed C.V.
Background:
PostDoc: CERMICS, ENPC (MarnelaVallée, France), with the MICMAC Project, CERMICS/INRIA.
PhD: Université Paul Sabatier, 2006.
M.S.: Ecole Polytechnique (X99) and DEA Université Paul Sabatier, 2003.
Email: mathias.rousset_at_inria.fr
HdR (Habilitation à Diriger des Recherches):
Title of dissertation: "Probability in Computational Physics and Biology: some mathematical contributions".
HdR dissertation.
HdR defense slides.
PhD:
Title of dissertation: "Continuous time "Population Monte Carlo" and Computational Physics".
PhD advisors: Pierre Del Moral and Laurent Miclo.
PhD dissertation.
Teaching (in french)
 Cours analyse, ENPC, 1A: Web page.
 Cours Outils Probabilistes pour la Finance, ENPC, 2A: Web page
Research topics
Probability and Analysis, Computational and Mathematical Physics, Statistical Mechanics. I focus on stochastic models arising in mathematical or computational physics and biology; it includes: mathematical analysis as well as development and improvement of numerical methods.
My HdR (Habilitation à Diriger des Recherches) manuscript can be used as a summary of my research: "Probability in Computational Physics and Biology: some mathematical contributions", together with the HdR defense slides.

Timescale Problem in Molecular Simulation, Free Energy Computations.

Articles: (m1), (10), (8), (6), (5), (4), and (3).

The main issue:
Simulating molecular systems with multiple time scales: fast timescales (e.g. rapid oscillations of atoms) are coupled to slow ones (e.g. conformation of molecules).

Numerical illustrations:
(i)In this simulation with periodic boundary conditions, a dimer (in red) is coupled to a solvant (in green). The slow degree of freedom (reaction coordinate) is the distance between the two atoms of the dimer, and has two different stable configurations (blue or red). The fast degrees of freedom comes from the motion of the atoms of the solvant (in green). In a second simulation, an adaptive biasing technique is used to accelerate the transition between configurations (between blue and red) of the dimer (references: (11), (7), and (6)).
(ii)In this simulation, we simulate a large polymeric chain of atoms attached at one hand and coupled to a thermostat. Bonds, and bond angles between atoms are rigid, and the time step is limited by the fast oscillation of the torsion angles. In a second simulation, the oscillation of torsion angles are correlated, using an implicit massmatrix penalty which does not modify the probability distribution of the different configurations of the system. It results in larger time steps, and in an accelerated simulation (references: (9)).

Splitting (birth\death of replicas) methods for rare event simulation.

Articles: (14) and (13)

The main issue:
Generalize and study some numerical methods simulating rare random events using replicas selection.

Particle methods for kinetic equations and PDEs (here, chemotaxis).

Articles: (12), (11) and (7)

The main issue:
Simulating/analyzing a multiscale phenomenon described by a hierarchy of PDEs (e.g. a kinetic equation at the microscopic level, and an advectiondiffusion equation at the macroscopic level). The idea is to use a particle (MonteCarlo) method at the micro level, coupled with a classical grid method at the macro one.

Particle methods for Schrödinger Groundstates, Quantum MonteCarlo methods.

Articles: (9) and (2)

The main issue:
Solving eigenvalue problems associated to an elliptic differential operator in high dimension (the Schrödinger operator) using stochastic particle methods (MonteCarlo). This includes the hard problem of Fermionic (skewsymmetric) solutions and excited states (the sign problem).

Large time and the coupling method for (conservative) particle systems.

Articles: (15)

The main issue:
Use the probabilistic coupling method to study the convergence to equilibrium of interacting particle systems with conservation laws (see Kac's particle system in kinetic theory); compare the latter with the large literature about other methods (entropic, spectral, etc...)
Support
ERC MsMaths
Publications

In revision
(15)M.Rousset (2014): A Nuniform quantitative Tanaka's theorem for the conservative Kac's Nparticle system with Maxwell molecules. Submitted pdf

Monographs
(m1)T.Lelièvre, M.Rousset and G.Stoltz (2010): Free energy computation: a mathematical perspective. Imperial College Press

Published articles
(14)C.E. Brehier, M Gazeau, L. Goudenège and M.Rousset (2014): Unbiasedness of some generalized Adaptive Multilevel Splitting algorithms Ann. Appl. Prob. pdf
(13)C.E. Brehier, T. Lelièvre and M.Rousset (2014): Analysis of Adaptive Multilevel Splitting algorithms in an idealized case. ESAIM P&S, to appear pdf
(p2)C.E. Brehier, M Gazeau, L. Goudenège and M.Rousset (2014): Analysis and simulation of rare events for SPDE. CEMRACS 2014 pdf
(12)M.Rousset and G.Samaey (2013): Simulating individualbased models of bacterial chemotaxis with asymptotic variance reduction. M3AS, 23:21552191. pdf
(11)M.Rousset and G.Samaey (2013): Individualbased models for bacterial chemotaxis in the diffusion asymptotics. M3AS, 23:20052037. pdf
(10)T. Lelièvre, M. Rousset and G. Stoltz (2012): Langevin dynamics with constraints and computation of free energy differences. Maths of Comp. 81, p 20712125: (Preprint pdf)
(9)M.Rousset (2010): On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes. M2AN, Vol. 44, Issue 5, p 977995. (Preprint version: pdf)
(8)P. Plechac and M. Rousset (2009): Implicit MassMatrix Penalization of Hamiltonian dynamics with application to exact sampling of stiff systems. SIAM MMS, 8, No 2, arXiv:0805.1092.
(7)T. Goudon and M. Rousset (2009): Stochastic Acceleration in an Inhomogeneous Time Random Force Field. Appl Math Res Express. 2009: 146 (Preprint version: pdf )
(6)T. Lelièvre, M. Rousset and G. Stoltz (2008): Long time convergence of the Adaptive Biaising Force method. Nonlinearity, 21, 11551181 (Preprint version: pdf)
(5)T.Lelièvre, M.Rousset and G.Stoltz (2007): Computation of free energy differences with parallel adaptive dynamics . J. Chem. Phys, Vol.126, No.13. (Preprint version: pdf)
(4)T.Lelièvre, M.Rousset and G.Stoltz (2007): Computation of free energy differences through nonequilibrium stochastic dynamics: the reaction coordinate case. J. Comp. Phys. 222(2), 624643. (Preprint version: pdf)
(3)M.Rousset and G.Stoltz (2006): Equilibrium sampling from nonequilibrium dynamics. J. Stat. Phys., 123 (6), 12511272. (Preprint version: pdf)
(p1)A.Doucet and M.Rousset (2006): Discussion of "Exact and computationnally efficient likelihood estimation of discretely observed diffusions" (by Beskos and co.). J. Roy. Stat. Soc. B. 68, 333. (Preprint version: pdf)
(2)M.Rousset (2006): On the control of an interacting particle approximation of Schrödinger ground states. SIAM J. Math. Anal., 38 (3), 824844.(Preprint version: pdf)
(1)M.Rousset (2004): Sur la rigidité de polyèdres hyperboliques en dimension 3: cas de volume fini, cas hyperidéal, cas fuchsien. Bull. SMF 132, 233261. (Preprint version: pdf)