5 papers
Convergence rates for an Adaptive Biasing Potential scheme from a Wasserstein optimization perspective
Tony Lelièvre, Xuyang Lin, Pierre Monmarché
Free-energy-based adaptive biasing methods, such as Metadynamics, the Adaptive Biasing Force (ABF) and their variants, are enhanced sampling algorithms widely used in molecular sim…
A spectral approach to the narrow escape problem in the disk
Tony Lelièvre, Mohamad Rachid, Gabriel Stoltz
We study the narrow escape problem in the disk, which consists in identifying the first exit time and first exit point distribution of a Brownian particle from the ball in dimensio…
Long-time convergence of an Adaptive Biasing Force method: the bi-channel case
Tony Lelievre, Kimiya Minoukadeh
We present convergence results for an adaptive algorithm to compute free energies, namely the adaptive biasing force (ABF) method. The free energy is the effective potential associ…
Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations
C. Le Bris, T. Lelievre, Y. Maday
We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial…
Long-time convergence of an Adaptive Biasing Force method
Tony Lelievre, Felix Otto, Mathias Rousset +1
We propose a proof of convergence of an adaptive method used in molecular dynamics to compute free energy profiles. Mathematically, it amounts to studying the long-time behavior of…