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Accuracy and Performance Analysis of the 1/t wang-landau algorithm in the Joint Density of States Estimation

OPTICAL MEMORY AND NEURAL NETWORKS 2024年第3期33卷 302-307页

作者： Egorov, V. I. Kryzhanovsky, B. V. Russian Acad Sci Sci Res Inst Syst Anal Moscow 117312 Russia

The 1/t wang-landau algorithm is analyzed from the viewpoint of execution time and accuracy when it is used in computations of the density of states of a two-dimensional Ising model. We find that the simulation results have a systematic error, the magnitude of which decreases with increasing the lattice size. The relative error has two maxima: the first one is located near the energy of the ground state, and the second maximum corresponds to the value of the internal energy at the critical point. We demonstrate that it is impossible to estimate the execution time of the 1/t wang-landau algorithm in advance when simulating large lattices. The reason is that when the final value of the modification factor was reached, the criterion for transition to mode 1/t was not met. The simultaneous calculations of the density of states for energy and magnetization are shown to lead to higher accuracy in estimating statistical moments of internal energy.

关键词： wang-landau algorithm the density of states algorithm execution speed critical transition

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Influence of Initial Guess on the Convergence Rate and the Accuracy of wang-landau algorithm

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OPTICAL MEMORY AND NEURAL NETWORKS 2021年第4期30卷 284-290页

作者： Egorov, V Kryzhanovsky, B. Russian Acad Sci Ctr Opt & Neural Technol Sci Res Inst Syst Anal Moscow 117312 Russia

The influence of the initial guess for the density of states on the convergence rate of the wang-landau algorithm was studied. The simulation was carried out for the two-dimensional Ising model. We used two different initial guesses (by the m-vicinity method and by the exact solution). It was found that the stability of the initial guess depends on the value of the initial modification factor. The improvement in the accuracy of the final simulation results is observed only when the exact solution is used as the initial guess with the small initial modification factor. We find that the simulation with the m-vicinity estimation as the initial guess gives more accurate spectral density estimations until the final stages of the simulation process where it becomes identical to the results of the standard algorithm.

关键词： wang-landau algorithm initial guess convergence rate accuracy spectral density Ising model

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Folding-unfolding transition in the mini-protein villin headpiece (HP35): An equilibrium study using the wang-landau algorithm

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CHEMICAL PHYSICS 2016年 468卷 1-8页

作者： Singh, Priya Sarkar, Subir K. Bandyopadhyay, Pradipta Jawaharlal Nehru Univ Sch Phys Sci New Delhi 110067 India Jawaharlal Nehru Univ Sch Computat & Integrat Sci New Delhi 110067 India

A computational study, using the wang-landau algorithm, is carried out for the 35 residue mini-protein villin headpiece (HP35) to investigate some equilibrium aspects of its folding-unfolding transition in water. The force field used is ECEPP/3 and a solvent-accessible surface area method is used to describe the interaction with water. The density of states and the conditional probabilities of some physically interesting geometrical descriptors of the molecule at various energies are calculated by analyzing the high-statistics data generated by the simulations. All canonical ensemble averages are subsequently calculated by using these data. The computed quantities include specific heat, radius of gyration, number of native contacts, number of helical residues and the potential of mean force for three pairs of geometric descriptors. High precision and a systematic check on the convergence of the computation are the two key points of our methodology. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Protein folding wang-landau algorithm Villin head-piece (HP-35)

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Joint Density of States Calculation Employing wang-landau algorithm

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JOURNAL OF STATISTICAL PHYSICS 2016年第1期163卷 197-209页

作者： Kalyan, M. Suman Bharath, R. Sastry, V. S. S. Murthy, K. P. N. Manipal Univ MCNS Manipal 576104 Karnataka India Indian Inst Technol Dept Chem Engn Bombay 400076 Maharashtra India Univ Hyderabad Sch Phys Hyderabad 500046 Andhra Pradesh India

Joint density of states (JDoS), which depends both on energy and another variable like order parameter provides more information than the conventional density of states (DoS) which depend only on energy. Calculation of JDoS requires huge computational time. In this paper we employ two level method to calculate JDoS which requires relatively much less computational time. We demonstrate this method on a two dimensional Ising spin system, lattice spin model of double strand DNA (dsDNA) and Heisenberg ferromagnet.

关键词： Monte Carlo methods wang-landau algorithm Joint density of states Ising model DNA Heisenberg ferromagnet

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Efficiency of the wang-landau algorithm: A Simple Test Case

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APPLIED MATHEMATICS RESEARCH EXPRESS 2014年第2期2014卷 275-311页

作者： Fort, Gersende Jourdain, Benjamin Kuhn, Estelle Lelievre, Tony Stoltz, Gabriel CNRS LTCI 46 Rue Barrault F-75634 Paris 13 France Telecom ParisTech F-75634 Paris 13 France Univ Paris Est CERMICS ENPC INRIA F-77455 Marne La Vallee France INRA Unite MIA F-78352 Jouy En Josas France

We analyze the efficiency of the wang-landau algorithm to sample a multimodal distribution on a prototypical simple test case. We show that the exit time from a metastable state is much smaller for the wang-landau dynamics than for the original standard Metropolis-Hastings algorithm, in some asymptotic regime. Our results are confirmed by numerical experiments on a more realistic test case.

关键词： wang-landau algorithm METASTABLE states DENSITY of states MONTE Carlo method WEIGHT (Physics) PROBABILITY density function DISTRIBUTION (Probability theory) FREE energy (Thermodynamics)

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Dynamical large deviations of the fractional Ornstein-Uhlenbeck process

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2025年第9期58卷 095002-095002页

作者： Valov, Alexander Meerson, Baruch Hebrew Univ Jerusalem Racah Inst Phys IL-91904 Jerusalem Israel

The fractional Ornstein-Uhleneck (fOU) process is described by the overdamped Langevin equation x(t)+gamma x = 2D xi(t), where xi(t) is the fractional Gaussian noise with the Hurst exponent 01/2) spectral density at zero frequency. For H>1/2, the fOU is long-correlated. Here we study dynamical large deviations of the fOU process and focus on the area A(n)= integral(T)(-T)x(n)(t)dt, n = 1,2,... over a long time window 2T. Employing the optimal fluctuation method, we determine the optimal path of the conditioned process, which dominates the large-A(n) tail of the probability distribution of the area, P(A(n),T)similar to exp[-S(A(n),T)]. We uncover a nontrivial phase diagram of scaling behaviors of the optimal paths and of the action S(A(n) equivalent to 2a(n)T,T)similar to T(alpha(H,n))a(n)(2/n) on the (H, n) plane. The phase diagram includes three distinct regions: (i) H > 1-1/n, where alpha(H,n) = 2-2H, and the optimal paths are delocalized in time, (ii) n = 2 and H <= 1/2, where alpha(H,n)=1, and the optimal paths oscillate with an H-dependent frequency, and (iii) H <= 1-1/n and n > 2, where alpha(H,n)=2/n, and the optimal paths are strongly localized. We verify our theoretical predictions in large-deviation simulations of the fOU process. By combining the wang-landau Monte-Carlo algorithm with the circulant embedding method of generation of stationary Gaussian fields, we were able to measure probability densities as small as 10(-170). We also generalize our findings to other stationary Gaussian processes with either divergent, or vanishing spectral density at zero frequency.

关键词： fractional Ornstein-Uhlenbeck process fractional Gaussian noise dynamical large deviations optimal fluctuation method wang-landau algorithm circulant embedding method

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THE wang-landau algorithm REACHES THE FLAT HISTOGRAM CRITERION IN FINITE TIME

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ANNALS OF APPLIED PROBABILITY 2014年第1期24卷 34-53页

作者： Jacob, Pierre E. Ryder, Robin J. Natl Univ Singapore Dept Stat & Appl Probabil Singapore 117548 Singapore Univ Paris 09 Ctr Rech Econ & Stat F-75016 Paris France Univ Paris 09 CEREMADE F-75016 Paris France

The wang-landau algorithm aims at sampling from a probability distribution, while penalizing some regions of the state space and favoring others. It is widely used, but its convergence properties are still unknown. We show that for some variations of the algorithm, the wang-landau algorithm reaches the so-called flat histogram criterion in finite time, and that this criterion can be never reached for other variations. The arguments are shown in a simple context-compact spaces, density functions bounded from both sides-for the sake of clarity, and could be extended to more general contexts.

关键词： Markov chain Monte Carlo wang-landau algorithm flat histogram

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Monte Carlo Approximation of Bayes Factors via Mixing With Surrogate Distributions

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2022年第538期117卷 765-780页

作者： Dai, Chenguang Liu, Jun S. Harvard Univ Dept Stat Cambridge MA 02138 USA

By mixing the target posterior distribution with a surrogate distribution, of which the normalizing constant is tractable, we propose a method for estimating the marginal likelihood using the wang-landau algorithm. We show that a faster convergence of the proposed method can be achieved via the momentum acceleration. Two implementation strategies are detailed: (i) facilitating global jumps between the posterior and surrogate distributions via the multiple-try Metropolis (MTM);(ii) constructing the surrogate via the variational approximation. When a surrogate is difficult to come by, we describe a new jumping mechanism for general reversible jump Markov chain Monte Carlo algorithms, which combines the MTM and a directional sampling algorithm. We illustrate the proposed methods on several statistical models, including the log-Gaussian Cox process, the Bayesian Lasso, the logistic regression, and the g-prior Bayesian variable *** this article are available online.

关键词： Marginal likelihood Mixture distribution Multiple-try Metropolis Reversible jump MCMC wang-landau algorithm

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Warp Bridge Sampling: The Next Generation

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2022年第538期117卷 835-851页

作者： wang, Lazhi Jones, David E. Meng, Xiao-Li Two Sigma Investments LP New York NY USA Texas A&M Univ Dept Stat College Stn TX 77843 USA Harvard Univ Dept Stat Cambridge MA 02138 USA

Bridge sampling is an effective Monte Carlo (MC) method for estimating the ratio of normalizing constants of two probability densities, a routine computational problem in statistics, physics, chemistry, and other fields. The MC error of the bridge sampling estimator is determined by the amount of overlap between the two densities. In the case of unimodal densities, Warp-I, II, and III transformations are effective for increasing the initial overlap, but they are less so for multimodal densities. This article introduces WarpU transformations that aim to transform multimodal densities into unimodal ones (hence "U") without altering their normalizing constants. The construction of a Warp-U transformation starts with a normal (or other convenient) mixture distribution fmix that has reasonable overlap with the target density p, whose normalizing constant is unknown. The stochastic transformation that maps fmix back to its generating distribution N(0, 1) is then applied to p yielding its Warp-U version, which we denote phi. Typically, phi is unimodal and has substantially increased overlap with f. Furthermore, we prove that the overlap between phi and N(0, 1) is guaranteed to be no less than the overlap between p and fmix, in terms of any phi-divergence. We propose a computationally efficient method to find an appropriate fmix, and a simple but effective approach to remove the bias which results from estimating the normalizing constant and fitting fmix with the same data. We illustrate our findings using 10 and 50 dimensional highly irregular multimodal densities, and demonstrate howWarp-U sampling can be used to improve the final estimation step of the Generalized wang-landau algorithm, a powerful sampling and estimation approach. Supplementary materials for this article are available online.

关键词： Bridge sampling Monte Carlo integration Normalizing constants Gaussian mixture Stochastic transformation wang-landau algorithm

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Berezinskii-Kosterlitz-Thouless transition in the XY model on the honeycomb lattice: a comprehensive Monte Carlo analysis

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PHYSICA SCRIPTA 2025年第6期100卷

作者： de Andrade, Felipe E. F. Jorge, L. N. Dasilva, Claudio J. Inst Fed Goias Rua 76Ctr Goiania GO Brazil Inst Fed Mato Grosso Campus CaceresAve Ramires s-n BR-78201380 Caceres MT Brazil

In this paper, we thoroughly examined the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the two-dimensional XY model on the honeycomb lattice. To address its thermodynamical behavior, we combined standard numerical Monte Carlo simulations with the simulated annealing (SA) protocol and entropic simulations based on the wang-landau (WL) algorithm. The transition temperature was determined using the second (& upsih;) and fourth-order (& upsih;4) helicity modulus as the order parameter. Our best finite-size scaling analysis suggests TBKT = 0.575(8) from SA and TBKT = 0.576(3) from WL. These values deviate significantly from the expected theoretical value of 1/2 . We believe that this discrepancy suggests that the theoretical assumptions regarding the analytical calculation may need to be revisited. Additionally, we calculated the vortex density and the formation energy of the vortex-antivortex pairs, where the obtained vortex formation energy is 2 mu = 5.80(12). Upon comparison with the square lattice, our results support the notion of instability of the honeycomb lattice to support the spin long-range order and give additional backing to the critical behavior we found.

关键词： BKT transition XY model Monte Carlo method wang-landau algorithm

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