Abstract.
It is common practice in molecular dynamics and Monte Carlo computer simulations to run multiple, separately-initialized simulations in order to improve the sampling of independent microstates. Here we examine the utility of an extreme case of this strategy, in which we run a large ensemble of M independent simulations (a “swarm”), each of which is relaxed to equilibrium. We show that if M is of order \(10^{3}\), we can monitor the swarm’s relaxation to equilibrium, and confirm its attainment, within \(\sim 10\bar{\tau}\), where \(\bar{\tau}\) is the equilibrium relaxation time. As soon as a swarm of this size attains equilibrium, the ensemble of M final microstates from each run is sufficient for the evaluation of most equilibrium properties without further sampling. This approach dramatically reduces the wall-clock time required, compared to a single long simulation, by a factor of several hundred, at the cost of an increase in the total computational effort by a small factor. It is also well suited to modern computing systems having thousands of processors, and is a viable strategy for simulation studies that need to produce high-precision results in a minimum of wall-clock time. We present results obtained by applying this approach to several test cases.
Graphical abstract
Similar content being viewed by others
References
D. Frenkel, B. Smit, Understanding Molecular Simulations: From Algorithms to Applications, 2nd edition (Academic Press, San Diego, 2002)
L. Berthier, G. Biroli, Rev. Mod. Phys. 83, 587 (2011)
L.S.D. Caves, J.D. Evanseck, M. Karplus, Protein Sci. 7, 649 (1998)
A. Elofsson, L. Nilsson, J. Mol. Biol. 233, 766 (1993)
P.V. Coveney, S. Wan, Phys. Chem. Chem. Phys. 18, 30236 (2016)
A.P. Bhati, S. Wan, D.W. Wright, P.V. Coveney, J. Chem. Theory Comput. 13, 210 (2017)
W. Kob, J.-L. Barrat, Phys. Rev. Lett. 78, 4581 (1997)
E. La Nave, S. Sastry, F. Sciortino, Phys. Rev. E 74, 050501 (2006)
F.H. Stillinger, A. Rahman, J. Chem. Phys. 60, 1545 (1974)
O. Steinhauser, Mol. Phys. 45, 335 (1982)
P.H. Poole, F. Sciortino, U. Essmann, H.E. Stanley, Nature 360, 324 (1992)
P.H. Poole, I. Saika-Voivod, F. Sciortino, J. Phys.: Condens. Matter 17, L431 (2005)
P.H. Poole, S.R. Becker, F. Sciortino, F.W. Starr, J. Phys. Chem. B 115, 14176 (2011)
V. Holten, J.C. Palmer, P.H. Poole, P.G. Debenedetti, M.A. Anisimov, J. Chem. Phys. 140, 104502 (2014)
J.C. Palmer, F. Martelli, Y. Liu, R. Car, A.Z. Panagiotopoulos, P.G. Debenedetti, Nature 510, 385 (2014)
S.K. Morris, O. Zavalov, R.K. Bowles, I. Saika-Voivod, F. Sciortino, P.H. Poole, unpublished (2017)
A.J. Kovacs, Fortschr. Hochpolym. Forsch. 3, 394 (1963)
S. Mossa, F. Sciortino, Phys. Rev. Lett. 92, 045504 (2004)
J.L.F. Abascal, C. Vega, J. Chem. Phys. 123, 234505 (2005)
S.M.A. Malek, P.H. Poole, I. Saika-Voivod, unpublished (2017)
S. Nose, Mol. Phys. 52, 255 (1984)
W.G. Hoover, Phys. Rev. A 31, 1695 (1985)
A. Widmer-Cooper, P. Harrowell, J. Chem. Phys. 126, 154503 (2007)
P.H. Poole, R.K. Bowles, I. Saika-Voivod, F. Sciortino, J. Chem. Phys. 138, 034505 (2013)
J.C. Dyre, J. Chem. Phys. 143, 114507 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Malek, S.M.A., Bowles, R.K., Saika-Voivod, I. et al. “Swarm relaxation”: Equilibrating a large ensemble of computer simulations⋆ . Eur. Phys. J. E 40, 98 (2017). https://doi.org/10.1140/epje/i2017-11588-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2017-11588-2