Adaptive multilevel splitting: Historical perspective and recent results.

This article first presents a short historical perpective of the importance splitting approach to simulate and estimate rare events, with a detailed description of several variants. We then give an account of recent theoretical results on these algorithms, including a central limit theorem for Adaptive Multilevel Splitting (AMS). Considering the asymptotic variance in the latter, the choice of the importance function, called the reaction coordinate in molecular dynamics, is also discussed. Finally, we briefly mention some worthwhile applications of AMS in various domains.

Computation of free energy profiles with parallel adaptive dynamics.

We propose a formulation of an adaptive computation of free energy differences, in the adaptive biasing force or nonequilibrium metadynamics spirit, using conditional distributions of samples of configurations which evolve in time. This allows us to present a truly unifying framework for these methods, and to prove convergence results for certain classes of algorithms. From a numerical viewpoint, a parallel implementation of these methods is very natural, the replicas interacting through the reconstructed free energy. We demonstrate how to improve this parallel implementation by resorting to some selection mechanism on the replicas. This is illustrated by computations on a model system of conformational changes.