Session A7 - Stochastic Computation
July 11, 15:00 ~ 15:25 - Room B2
Self-repelling processes and metadynamics
Université Paris Est Marne la Vallée, France - Pierre-Andre.Zitt@u-pem.fr
A usual drawback of Markov Chain Monte Carlo algorithms is their inherent difficulty to overcome potential barriers, which may lead to a poor exploration of the sampling space, and large sampling errors. The "metadynamics" algorithm introduced by Bussi, Laio and Parrinello in the 00s exemplifies one of the ideas to tackle this difficulty: by keeping track of the past trajectory of the sampling process, one can use it to bias the process so that it avoids the regions it has already visited, leading to a better sampling. The processes describing the evolution of the algorithm turn out to be quite difficult to analyze rigorously. We present two toy models that are amenable to such an analysis, using results from the self-interacting processes literature.
Joint work with Benjamin Jourdain (École des Ponts ParisTech) and Tony Lelièvre (École des Ponts ParisTech).