Description
I will present free-energy-based adaptive biasing techniques
and discuss convergence results for these methods, focusing in
particular on recent joint work with Xuyang Lin and Pierre Monmarché.
Free-energy-based adaptive biasing methods, such as metadynamics, the
Adaptive Biasing Force (ABF) method, and their variants, are
enhanced-sampling algorithms widely used in molecular simulations.
Although their efficiency has been empirically recognized for decades,
obtaining theoretical insight through a quantitative convergence
analysis remains challenging, particularly for kinetic Langevin
diffusion, which is nonreversible and hypocoercive. We establish the
first exponential convergence result for such a process in an idealized
setting, in which the dynamics can be associated with a nonlinear
mean-field flow on the space of probability measures. A key ingredient
of the analysis is the interpretation of the idealized algorithm as
gradient descent for a suitable functional defined on the space of
probability distributions.