By drawing a parallel between metadynamics and self interacting models for polymers, we study the longtime convergence of the original metadynamics algorithm in the adiabatic setting, namely when the dynamics along the collective variables decouples from the dynamics along the other degrees of freedom. We also discuss the bias which is introduced when the adiabatic assumption does not hold.
This work is supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement number 614492.
We would like to thank the anonymous referees for their careful reading of our manuscript and their many comments and suggestions.
"Convergence of metadynamics: Discussion of the adiabatic hypothesis." Ann. Appl. Probab. 31 (5) 2441 - 2477, October 2021. https://doi.org/10.1214/20-AAP1652