Fast adaptive flat-histogram ensemble to enhance the sampling in large systems

Shun XU; Xin ZHOU; Yi JIANG; YanTing WANG

doi:10.1007/s11433-015-5690-7

SCIENCE CHINA Physics, Mechanics & Astronomy

SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 58, Issue 9: 590501(2015) https://doi.org/10.1007/s11433-015-5690-7

Fast adaptive flat-histogram ensemble to enhance the sampling in large systems

Shun XU, Xin ZHOU, Yi JIANG, YanTing WANG

More info

ReceivedFeb 27, 2015
AcceptedApr 29, 2015
PublishedAug 4, 2015

PACS numbers

Previous Table of Contents Next

Rating

Abstract

An efficient novel algorithm was developed to estimate the Density of States (DOS) for large systems by calculating the ensemble means of an extensive physical variable, such as the potential energy, U, in generalized canonical ensembles to interpolate the interior reverse temperature curve βs (U) ≡? S(U) ?U , where S(U) is the logarithm of the DOS. This curve is computed with different accuracies in different energy regions to capture the dependence of the reverse temperature on U without setting prior grid in the U space. By combining with a U-compression transformation, we decrease the computational complexity from O(N^3/2) in the normal Wang Landau type method to O(N^1/2) in the current algorithm, as the degrees of freedom of system N. The efficiency of the algorithm is demonstrated by applying to Lennard Jones fluids with various N, along with its ability to find different macroscopic states, including metastable states.

Funded by

National Natural Science Foundation of China and by the Open Project Grant from the State Key Laboratory of Theoretical Physics. Zhou X thanks the financial support of the Hundred of Talents Program in Chinese Academy of Sciences(11175250)

References

[1] Fang Y. A Gibbs free energy formula for protein folding derived from quantum statistics. Sci China-Phys Mech Astron, 2014, 57: 1547-1551 CrossRef Google Scholar

[2] Luo L F. Quantum theory on protein folding. Sci China-Phys Mech Astron, 2014, 57: 458-468 CrossRef Google Scholar

[3] Gong P, Wang X, Shao Y, et al. Ti-Zr-Be-Fe quaternary bulk metallic glasses designed by Fe alloying. 2013, 56: 2090–2097. Google Scholar

[4] Berg B, Neuhaus T. Multicanonical –algorithms for first order phase transitions. Phys Lett B, 1991, 267: 249253 Google Scholar

[5] Wang F, Landau D. Efficient, multiple-range random walk algorithm to calculate the density of states. Phys Rev Lett, 2001, 86: 2050-2053 CrossRef Google Scholar

[6] Laio A, Parrinello M. Escaping free-energy minima. Proc Natl Acad Sci USA, 2002, 99: 12562-12566 CrossRef Google Scholar

[7] Yan Q, de Pablo J. Fast calculation of the density of states of a fluid by Monte Carlo simulations. Phys Rev Lett, 2003, 90: 035701 CrossRef Google Scholar

[8] Zhou C, Bhatt R N. Understanding and improving the Wang-Landau algorithm. Phys Rev E, 2005, 72: 025701 CrossRef Google Scholar

[9] Zhou X, Jiang Y, Kremer K, et al. Hyperdynamics for entropic systems: Time-space compression and pair correlation function approximation. Phys Rev E, 2006, 74: 035701 CrossRef Google Scholar

[10] Kim J, Straub J E, Keyes T. Statistical-temperature Monte Carlo and molecular dynamics algorithms. Phys Rev Lett, 2006, 97: 050601 CrossRef Google Scholar

[11] Zhou C, Schulthess T C, Torbrügge S, et al. Wang-landau algorithm for continuous models and joint density of states. Phys Rev Lett, 2006, 96: 120201 CrossRef Google Scholar

[12] Je?ewski W. Stationary and nonstationary properties of evolving networks with preferential linkage. Phys Rev E, 2002, 66: 067102 CrossRef Google Scholar

[13] Gao Y Q. An integrate-over-temperature approach for enhanced sampling. J Chem Phys, 2008, 128: 064105 CrossRef Google Scholar

[14] Zhang C, Ma J. Enhanced sampling in generalized ensemble with large gap of sampling parameter: Case study in temperature space random walk. J Chem Phys, 2009, 130: 194112 CrossRef Google Scholar

[15] Gong L, Zhou X. Structuring and sampling complex conformation space: Weighted ensemble dynamics simulations. Phys Rev E, 2009, 80: 026707 CrossRef Google Scholar

[16] Gong L, Zhou X. Kinetic transition network based on trajectory mapping. J Phys Chem B, 2010, 114: 10266-10276 CrossRef Google Scholar

[17] Xu S, Zhou X, OuYang Z C. Parallel tempering simulation on generalized canonical ensemble. Commun Comput Phys, 2012, 12: 1293-1306 Google Scholar

[18] Junghans C, Perez D, Vogel T. Molecular dynamics in the multicanonical ensemble: Equivalence of Wang-Landau sampling, statistical temperature molecular dynamics, and metadynamics. J Chem Theory Comput, 2014, 10: 1843-1847 CrossRef Google Scholar

[19] Mastny E A, de Pablo J J. Direct calculation of solid-liquid equilibria from density-of-states Monte Carlo simulations. J Chem Phys, 2005, 122: 124109 CrossRef Google Scholar

[20] Vogel T, Li Y W, Wüst T, et al. Generic, hierarchical framework for massively parallel Wang-Landau sampling. Phys Rev Lett, 2013, 110: 210603 CrossRef Google Scholar

[21] Earl D J, Deem M W. Parallel tempering: Theory, applications, and new perspectives. Phys Chem Chem Phys, 2005, 7: 3910-3916 CrossRef Google Scholar

Click to view Download high-quality image

Figure 1
(Color online) The obtained T_s, ${(\frac{d T_{s}}{d u})}^{? 1}$ , and S are shown as functions of U in the LJ systems with different size N. The number of requiring points {(U_i, b_i)} increases as N increases.
Click to view Download high-quality image

Figure 2
(Color online) The required MD steps for getting the same accuracy of b_s(U) with the size of system N. The accuracy is measured by the B factors in estimating ensemble averages of U (see the text). The red dash line is from t_MDμN^1/2.
Click to view Download high-quality image

Figure 3
(Color online) T_s(U) in the supersaturated liquid and the solid phases, respectively, of the LJ system with N=108. The transition can easily happen when U<U₁(from liquid to solid) and U> U₂ (from solid to liquid).
Click to view Download high-quality image

Figure 4
(Color online) The T_s(U) function in a LJ system with N=108 and r=0.8 at the low-temperature region. Each branch of the function corresponds to a particular macroscopic phase. The blue-filled squares cover the unstable liquid/solid coexistence region where $c_{v} \equiv {(\frac{d T_{s}}{d u})}^{? 1},$ which can be thought as the heat capacity in the iso-U ensemble, are negative, as shown in the bottom panel. The green down-triangles correspond to the complete FCC solid, which is a metastable state in the current system. Some phase transitions from metastable solids to the stable solid (the black circles) can be found at lower temperatures. When T_s→0, more complex phase behaviors are expected.

6

Citations
0

Altmetric
Article metrics

Email
Export


02.70.Ns	Molecular dynamics and particle methods
05.10.-a	Computational methods in statistical physics and nonlinear dynamics (see also 02.70.-c in mathematical methods in physics)
64.70.D-	Solid-liquid transition

Fast adaptive flat-histogram ensemble to enhance the sampling in large systems

Abstract

Funded by

References

6

0

Interesting search

Top 5Related Articles