Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang–Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics

2014/01/31 by Christoph Junghans, Danny Perez, Thomas Vogel · 2 citations
Materials Science · Physics and Astronomy · #Machine Learning in Materials Science #Material Dynamics and Properties #Statistical Mechanics and Entropy

paper · doi:10.1021/ct500077d

openalex publication_date 2014/04/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show a direct formal relationship between the Wang-Landau iteration [PRL 86, 2050 (2001)], metadynamics [PNAS 99, 12562 (2002)], and statistical temperature molecular dynamics (STMD) [PRL 97, 050601 (2006)] that are the major work-horses for sampling from generalized ensembles. We demonstrate that STMD, itself derived from the Wang-Landau method, can be made indistinguishable from metadynamics. We also show that Gaussian kernels significantly improve the performance of STMD, highlighting the practical benefits of this improved formal understanding.

Citations

• Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling
• Monte Carlo study of phase transitions in the bond-diluted 3D 4-state Potts model

Cited by

• Metadynamics [wikipedia]
• Wang and Landau algorithm [wikipedia]