357 citations · 1.7k across the 74 of their papers we have counts for
10 papers · 1 filter
Exit event from a metastable state and Eyring-Kramers law for the overdamped Langevin dynamics
Tony Lelièvre, Dorian Le Peutrec, Boris Nectoux
In molecular dynamics, several algorithms have been designed over the past few years to accelerate the exit event from a metastable region of the configuration space. Some of them…
On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting
Charles-Edouard Bréhier, Tony Lelièvre
We investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated a…
Effective dynamics for non-reversible stochastic differential equations: a quantitative study
Frédéric Legoll, Tony Lelièvre, Upanshu Sharma
Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller cl…
gen.parRep: a first implementation of the Generalized Parallel Replica dynamics for the long time simulation of metastable biochemical systems
Florent Hédin, Tony Lelièvre
Metastability is one of the major encountered obstacle when performing long molecular dynamics simulations, and many methods were developed to address this challenge. The "Parallel…
Hybrid Monte Carlo methods for sampling probability measures on submanifolds
Tony Lelièvre, Mathias Rousset, Gabriel Stoltz
Probability measures supported on submanifolds can be sampled by adding an extra momentum variable to the state of the system, and discretizing the associated Hamiltonian dynamics…
Central Limit Theorem for stationary Fleming--Viot particle systems in finite spaces
Tony Lelievre, Loucas Pillaud-Vivien, Julien Reygner
We consider the Fleming--Viot particle system associated with a continuous-time Markov chain in a finite space. Assuming irreducibility, it is known that the particle system posses…
Pathwise estimates for effective dynamics: the case of nonlinear vectorial reaction coordinates
Tony Lelièvre, Wei Zhang
Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Lelièvre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion…
Stochastic homogenization of a scalar viscoelastic model exhibiting stress-strain hysteresis
Thomas Hudson, Frédéric Legoll, Tony Lelièvre
Motivated by rate-independent stress-strain hysteresis observed in filled rubber, this article considers a scalar viscoelastic model in which the constitutive law is random and var…
Mathematical foundations of Accelerated Molecular Dynamics methods
Tony Lelièvre
The objective of this review article is to present recent results on the mathematical analysis of the Accelerated Dynamics algorithms introduced by A.F. Voter in collaboration with…
Analysis of a micro-macro acceleration method with minimum relative entropy moment matching
Tony Lelièvre, Giovanni Samaey, Przemysław Zieliński
We analyse convergence of a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with time-scale separation between the (fast) evolut…