Feynman-Kac measures and Interacting Particle systems :

Selected applications on : Applied Probability & Physics

(see also : (presentation video at the Isaac Newton Institute for Mathematical Sciences 2010), Analysis and Probability in Nice ( lecture 2008, lecture 2010 ), IHP 2010, Bonn 2008 , 2011-Sino-French Summer Institute (lecture 1, lecture 2, and lecture 3) & other application areas)

This webpage presents an overview of resources concerned with stochastic particle methods in numerical physics and applied probability

Molecular dynamics,
Diffusion Monte Carlo, ground state energies
Multiscale dynamical systems
Optical tomography
Complex turbulent systems
Feynman-Kac-Schrodinger models
This list of topics is clearly far from being exhaustive, and it is partially biased towards my work on stochastic particle models. More references and links to this subject can be added on demand. This webpage also contains some articles on particle methods and their performance analysis. We also recommend to consult the related webpage on rare event particle simulation, and the one applications in biology and chemistry.

logo design Timothée Del Moral

The software BIIPS is a general software developed by the INRIA team ALEA for bayesian inference with interacting particle systems, a.k.a. Sequential Monte Carlo methods. A demonstration of the BiiPS software for estimating the stochastic volatility of financial data can be found in

BIIPS : Bayesian inference with interacting Particle Systems in Finance,

INRIA project manager :

F. Caron

Design and developement engineer :

A. Todeschini

Project contributors :

P. Del Moral

P. Legrand

Logo designer :

Timothée Del Moral

Some websites

Advanced Learning Evolutionary Algorithms (ALEA project, Centre INRIA Bordeaux Sud-Ouest)

Molecular and Multi-scale Modeling (MICMAC, joint project-team of INRIA and Ecole des Ponts ParisTech)

Monte Carlo methods (Wikipedia website)

Stochastic Filtering of Turbulent Fluids (Ch. Baehr website)

Computational Statistical Mechanics: (M. Rousset website)

Molecular dynamics, diffusion Monte Carlo, ground states

On the Control of an Interacting Particle Estimation of Schrodinger Ground States (M. Rousset, CERMICS)

Particle approximations of Lyapunov exponents connected to Schrodinger operators and Feynman-Kac semigroups.
(Del Moral P., Miclo L.) ESAIM: Probabilités et Statistiques. (2003).

Particle Motions in Absorbing Medium with Hard and Soft Obstacles. Del Moral P., Doucet A. (Nice-Sophia Antipolis Univ. and UBC Vancouver)

Equilibrium Sampling from Nonequilibrium Dynamics (M. Rousset, G. Stoltz; CERMICS)

Computing the first eigen-elements of some linear operators using branching Monte Carlo methods. (A. Lejay, S. Maire 2007)

Diffusion Monte Carlo method : Numerical analysis in a simple case (M. El Makrini, B. Jourdain and T. Lelievre, M2AN 2007)

Dynamique moleculaire et calcul d'energie libre (T. Lelievre, Ecole ECODOQUI: resume du cours 2008)

On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes. (M. Rousset, INRIA Lille 2010)

A multiple replica approach to simulate reactive trajectories (Frederic Cerou, Arnaud Guyader, Tony Lelievre, David Pommier, 2010)

Methodes deterministes et stochastiques pour la simulation moleculaire (Kimiya Minoukadeh, Ph.D. Paris Est Univ. 2010)

Free energy computations by minimization of Kullback-Leibler divergence: an efficient adaptive biasing potential method for sparse representations (I. Bilionis, P.S. Koutsourelakis, Cornell University, 2010)

Multiscale dynamical systems, optical tomography, complex turbulent systems

Scalable Bayesian reduced order models for simulated high-dimensional multiscale dynamical systems (P.S. Koutsourelakis, E. Bilionis, 2010)

Solutions for diffuse optical tomography using the Feynman-Kac formula and interacting particle method (Nannan Cao, Mathias Ortner, and Arye Nehorai, Department of Electrical and Systems Engineering, Washington University)

Filtering complex turbulent systems (Andrew J. Majda, John Harlim; Center for Atmosphere and Ocean Sciences, Courant Institute, and North Carolina University)

Stochastic modeling and filtering of discrete measurements for a turbulent field. Application to measurements of atmospheric wind. (Ch. Baehr, Meteo-France-CNRS; International Journal of Modern Physics B 2008)

Related studies on Feynman-Kac-Schrodinger semigroups

Particle Methods: An introduction with applications (Pierre Del Moral, Arnaud Doucet) HAL-INRIA RR-6991 [50p] (2009), 2008 Machine Learning Summer School, Springer LNCS/LNAI Tutorial book no. 6368 (2010-2011).

Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering (Del Moral P., Miclo L.)
Séminaire de Probabilités XXXIV, Ed. J. Azéma and M. Emery and M. Ledoux and M. Yor. Lecture Notes in Mathematics, Springer-Verlag Berlin, Vol. 1729, 1-145 (2000).

On the stability of interacting processes with applications to filtering and genetic algorithms (Del Moral P., Guionnet A. Annales de l'Institut Henri Poincaré, Vol. 37, No. 2, 155-194 (2001)).

Annealed Feynman-Kac Models. (Del Moral P., Miclo L.) Communications in Mathematical Physics, vol. 235, no. 2, pp.191--214 (2003).

Towards pathwise stochastic fast dynamo in magneto-hydrodynamics (S.B. Hasra, F. Viens)

Feynman-Kac Formulae, Genealogical and Interacting Particle Systems with Applications Del Moral P., Springer New York; Springer Heidelberg, Series: Probability and its Applications, [585 pages] (April 2004).

Pierre Del Moral, Peng Hu, Liming Wu
On the concentration properties of Interacting particle processes HAL-INRIA RR-7677 (2011),
Foundations and Trends in Machine Learning, Vol. 3, No. 3 - 4, 225-389 (2012). (online article, 167 pages)

On the Stability of Non Linear Semigroup of Feynman-Kac Type. Del Moral P. and Miclo L.
Annales de la Faculté des Sciences de Toulouse, vol.11,no.2, pp. (2002)

A Backward Particle Interpretation of Feynman-Kac Formulae
Pierre Del Moral, Arnaud Doucet and Sumeetpal S. Singh (HAL-INRIA RR-7019 (07-2009)) vol 44, no. 5, pp. 947--976 M2AN (sept. 2010)

Sequential Monte Carlo Samplers (Del Moral P., Doucet A., Jasra A) Journal of the Royal Society of Statistics, Series B. vol. 68, No. 3, pp. 411-436 (2006).

Stability of Sequential Markov Chain Monte Carlo Methods (A. Eberle, C. Marinelli, Bonn Univ.)

Numerical Solution of a Class of SPDEs with Applications to Filtering (T. Kurtz, J. Xiong; Wisconsin Univ.)

A Stochastic Evolution Equation Arising from The Fluctuation of a Class of Interacting Particle Systems (T. Kurtz, J. Xiong; Wisconsin Univ.)

Asymptotic Stability of Non Linear Semigroup of Feynman-Kac Type. (Del Moral P., Miclo L.) Publications du LSP-CNRS No 04-99 (1999).

On a class of genealogical and interacting Metropolis Models. Del Moral P., Doucet A. Séminaire de Probabilités XXXVII, Ed. J. Azéma and M. Emery and M. Ledoux and M. Yor, Lecture Notes in Mathematics 1832, Springer-Verlag Berlin, pp. 415--446 (2003).

A non asymptotic variance theorem for unnormalized Feynman-Kac particle models( Fr. Cerou, P. Del Moral, A. Guyader ) HAL-INRIA RR-6716 (Nov. 2008) Annales de l'Institut Henri Poincare Probab. Statist. Volume 47, Number 3, 629-649 (2011).

On Adaptive Resampling Procedures for Sequential Monte Carlo Methods (Pierre Del Moral, Arnaud Doucet, Ajay Jasra) HAL-INRIA RR-6700 [46p], (Oct. 2008).