30 citations · 36 across the 12 of their papers we have counts for
15 papers
A spectral approach to the narrow escape problem in two-dimensional domains
Louis Carillo, Tony Lelièvre, Thomas Normand +1
We study the law of the exit time and exit point of a Brownian motion in a two-dimensional domain with reflecting boundary conditions, except on small disjoint exit windows through…
The narrow escape problem in arbitrary dimension
Louis Carillo, Tony Lelièvre, Thomas Normand +2
The narrow escape problem is a prototypical example for studying entropic metastability, motivated by the analysis of biological and chemical systems. The problem concerns the dete…
Approximating committor functions: Objective functions and training data sampling
Thomas Pigeon, Gabriel Stoltz, Tony Lelièvre
Many molecular dynamics simulations aim at studying transitions between two states (from reactants to products). In this context, the committor function (which gives for a given mo…
Efficient Monte Carlo sampling of metastable systems using non-local collective variable updates
Christoph Schönle, Davide Carbone, Marylou Gabrié +2
Monte Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a…
Shape optimization of metastable states
Noé Blassel, Tony Lelièvre, Gabriel Stoltz
The definition of metastable states is an ubiquitous task in the design and analysis of molecular simulations, and is a crucial input in a variety of acceleration methods for the s…
Quantitative low-temperature spectral asymptotics for reversible diffusions in temperature-dependent domains
Noé Blassel, Tony Lelièvre, Gabriel Stoltz
We derive novel low-temperature asymptotics for the spectrum of the infinitesimal generator of the overdamped Langevin dynamics. The novelty is that this operator is endowed with h…
Improving sampling by modifying the effective diffusion
Tony Lelièvre, Régis Santet, Gabriel Stoltz
Markov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics liter…
Sampling metastable systems using collective variables and Jarzynski-Crooks paths
Christoph Schönle, Marylou Gabrié, Tony Lelièvre +1
We consider the problem of sampling a high dimensional multimodal target probability measure. We assume that a good proposal kernel to move only a subset of the degrees of freedoms…
Optimizing the diffusion coefficient of overdamped Langevin dynamics
Tony Lelièvre, Grigorios A. Pavliotis, Geneviève Robin +2
Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones ap…
An Application of Reduced Basis Methods to Core Computation in APOLLO3
Yonah Conjungo Taumhas, Geneviève Dusson, Virginie Ehrlacher +2
In the aim of reducing the computational cost of the resolution of parameter-dependent eigenvalue problems, a model order reduction (MOR) procedure is proposed. We focus on the cas…
Analyzing multimodal probability measures with autoencoders
Tony Lelièvre, Thomas Pigeon, Gabriel Stoltz +1
Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics.…
Statistical Estimation of the Poincar{é} constant and Application to Sampling Multimodal Distributions
Loucas Pillaud-Vivien, Francis Bach, Tony Lelièvre +2
Poincar{é} inequalities are ubiquitous in probability and analysis and have various applications in statistics (concentration of measure, rate of convergence of Markov chains). The…
Local and Global Perspectives on Diffusion Maps in the Analysis of Molecular Systems
Zofia Trstanova, Ben Leimkuhler, Tony Lelièvre
Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molec…
Local and global solution for a nonlocal Fokker-Planck equation related to the adaptive biaising force processes
Houssam Alrachid, Tony Lelièvre, Raafat Talhouk
We prove global existence, uniqueness and regularity of the mild, Lp and classical solution of a non-linear Fokker-Planck equation arising in an adaptive importance sampling method…
Efficiency of the Wang-Landau algorithm: a simple test case
G. Fort, B. Jourdain, E. Kuhn +2
We analyze the efficiency of the Wang-Landau algorithm to sample a multimodal distribution on a prototypical simple test case. We show that the exit time from a metastable state is…