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Title: A Histogram-Free Multicanonical Monte Carlo Algorithm for the Basis Expansion of Density of States

Abstract

We report a new multicanonical Monte Carlo (MC) algorithm to obtain the density of states (DOS) for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain an analytical form for the DOS expressed in a chosen basis set, instead of a numerical array of finite resolution as in previous variants of this class of MC methods such as the multicanonical (MUCA) sampling and Wang-Landau (WL) sampling. This is enabled by storing the visited states directly in a data set and avoiding the explicit collection of a histogram. This practice also has the advantage of avoiding undesirable artificial errors caused by the discretization and binning of continuous state variables. Our results show that this scheme is capable of obtaining converged results with a much reduced number of Monte Carlo steps, leading to a significant speedup over existing algorithms.

Authors:
 [1];  [1]
  1. National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1567465
DOE Contract Number:  
AC05-00OR22725
Resource Type:
Conference
Resource Relation:
Conference: PASC '17 Proceedings of the Platform for Advanced Scientific Computing Conference
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Computer Science

Citation Formats

Li, Ying Wai, and Eisenbach, Markus. A Histogram-Free Multicanonical Monte Carlo Algorithm for the Basis Expansion of Density of States. United States: N. p., 2017. Web. doi:10.1145/3093172.3093235.
Li, Ying Wai, & Eisenbach, Markus. A Histogram-Free Multicanonical Monte Carlo Algorithm for the Basis Expansion of Density of States. United States. doi:10.1145/3093172.3093235.
Li, Ying Wai, and Eisenbach, Markus. Sun . "A Histogram-Free Multicanonical Monte Carlo Algorithm for the Basis Expansion of Density of States". United States. doi:10.1145/3093172.3093235.
@article{osti_1567465,
title = {A Histogram-Free Multicanonical Monte Carlo Algorithm for the Basis Expansion of Density of States},
author = {Li, Ying Wai and Eisenbach, Markus},
abstractNote = {We report a new multicanonical Monte Carlo (MC) algorithm to obtain the density of states (DOS) for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain an analytical form for the DOS expressed in a chosen basis set, instead of a numerical array of finite resolution as in previous variants of this class of MC methods such as the multicanonical (MUCA) sampling and Wang-Landau (WL) sampling. This is enabled by storing the visited states directly in a data set and avoiding the explicit collection of a histogram. This practice also has the advantage of avoiding undesirable artificial errors caused by the discretization and binning of continuous state variables. Our results show that this scheme is capable of obtaining converged results with a much reduced number of Monte Carlo steps, leading to a significant speedup over existing algorithms.},
doi = {10.1145/3093172.3093235},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2017},
month = {1}
}

Conference:
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