Nonconvergence of the Wang-Landau algorithms with multiple random walkers

Autores
Belardinelli, Rolando Elio; Pereyra, Victor Daniel
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and 1/t algorithms. The classical algorithms are modified by the use of m-independent random walkers in the energy landscape to calculate the density of states (DOS). The Ising model is used to show the convergence properties in the calculation of the DOS, as well as the critical temperature, while the calculation of the number π by multiple dimensional integration is used in the continuum approximation. In each case, the error is obtained separately for each walker at a fixed time, t; then, the average over m walkers is performed. It is observed that the error goes as 1/m. However, if the number of walkers increases above a certain critical value m>mx, the error reaches a constant value (i.e., it saturates). This occurs for both algorithms; however, it is shown that for a given system, the 1/t algorithm is more efficient and accurate than the similar version of the WL algorithm. It follows that it makes no sense to increase the number of walkers above a critical value mx, since it does not reduce the error in the calculation. Therefore, the number of walkers does not guarantee convergence.
Fil: Belardinelli, Rolando Elio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada ; Argentina
Fil: Pereyra, Victor Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada ; Argentina
Materia
Monte Carlo
Entropic Sampling
Simulation
Algorithm
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/60420
Acceder
id CONICETDig_11b790f6e8b832ee020abdc4bc054bbf
oai_identifier_str oai:ri.conicet.gov.ar:11336/60420
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Nonconvergence of the Wang-Landau algorithms with multiple random walkersBelardinelli, Rolando ElioPereyra, Victor DanielMonte CarloEntropic SamplingSimulationAlgorithmhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and 1/t algorithms. The classical algorithms are modified by the use of m-independent random walkers in the energy landscape to calculate the density of states (DOS). The Ising model is used to show the convergence properties in the calculation of the DOS, as well as the critical temperature, while the calculation of the number π by multiple dimensional integration is used in the continuum approximation. In each case, the error is obtained separately for each walker at a fixed time, t; then, the average over m walkers is performed. It is observed that the error goes as 1/m. However, if the number of walkers increases above a certain critical value m>mx, the error reaches a constant value (i.e., it saturates). This occurs for both algorithms; however, it is shown that for a given system, the 1/t algorithm is more efficient and accurate than the similar version of the WL algorithm. It follows that it makes no sense to increase the number of walkers above a critical value mx, since it does not reduce the error in the calculation. Therefore, the number of walkers does not guarantee convergence.Fil: Belardinelli, Rolando Elio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada ; ArgentinaFil: Pereyra, Victor Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada ; ArgentinaAmerican Physical Society2016-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60420Belardinelli, Rolando Elio; Pereyra, Victor Daniel; Nonconvergence of the Wang-Landau algorithms with multiple random walkers; American Physical Society; Physical Review E; 93; 5; 5-2016; 1-9; 0533062470-0053CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.93.053306info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.053306info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:06:16Zoai:ri.conicet.gov.ar:11336/60420instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:06:17.044CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nonconvergence of the Wang-Landau algorithms with multiple random walkers
title Nonconvergence of the Wang-Landau algorithms with multiple random walkers
spellingShingle Nonconvergence of the Wang-Landau algorithms with multiple random walkers
Belardinelli, Rolando Elio
Monte Carlo
Entropic Sampling
Simulation
Algorithm
title_short Nonconvergence of the Wang-Landau algorithms with multiple random walkers
title_full Nonconvergence of the Wang-Landau algorithms with multiple random walkers
title_fullStr Nonconvergence of the Wang-Landau algorithms with multiple random walkers
title_full_unstemmed Nonconvergence of the Wang-Landau algorithms with multiple random walkers
title_sort Nonconvergence of the Wang-Landau algorithms with multiple random walkers
dc.creator.none.fl_str_mv Belardinelli, Rolando Elio
Pereyra, Victor Daniel
author Belardinelli, Rolando Elio
author_facet Belardinelli, Rolando Elio
Pereyra, Victor Daniel
author_role author
author2 Pereyra, Victor Daniel
author2_role author
dc.subject.none.fl_str_mv Monte Carlo
Entropic Sampling
Simulation
Algorithm
topic Monte Carlo
Entropic Sampling
Simulation
Algorithm
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and 1/t algorithms. The classical algorithms are modified by the use of m-independent random walkers in the energy landscape to calculate the density of states (DOS). The Ising model is used to show the convergence properties in the calculation of the DOS, as well as the critical temperature, while the calculation of the number π by multiple dimensional integration is used in the continuum approximation. In each case, the error is obtained separately for each walker at a fixed time, t; then, the average over m walkers is performed. It is observed that the error goes as 1/m. However, if the number of walkers increases above a certain critical value m>mx, the error reaches a constant value (i.e., it saturates). This occurs for both algorithms; however, it is shown that for a given system, the 1/t algorithm is more efficient and accurate than the similar version of the WL algorithm. It follows that it makes no sense to increase the number of walkers above a critical value mx, since it does not reduce the error in the calculation. Therefore, the number of walkers does not guarantee convergence.
Fil: Belardinelli, Rolando Elio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada ; Argentina
Fil: Pereyra, Victor Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada ; Argentina
description This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and 1/t algorithms. The classical algorithms are modified by the use of m-independent random walkers in the energy landscape to calculate the density of states (DOS). The Ising model is used to show the convergence properties in the calculation of the DOS, as well as the critical temperature, while the calculation of the number π by multiple dimensional integration is used in the continuum approximation. In each case, the error is obtained separately for each walker at a fixed time, t; then, the average over m walkers is performed. It is observed that the error goes as 1/m. However, if the number of walkers increases above a certain critical value m>mx, the error reaches a constant value (i.e., it saturates). This occurs for both algorithms; however, it is shown that for a given system, the 1/t algorithm is more efficient and accurate than the similar version of the WL algorithm. It follows that it makes no sense to increase the number of walkers above a critical value mx, since it does not reduce the error in the calculation. Therefore, the number of walkers does not guarantee convergence.
publishDate 2016
dc.date.none.fl_str_mv 2016-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/60420
Belardinelli, Rolando Elio; Pereyra, Victor Daniel; Nonconvergence of the Wang-Landau algorithms with multiple random walkers; American Physical Society; Physical Review E; 93; 5; 5-2016; 1-9; 053306
2470-0053
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60420
identifier_str_mv Belardinelli, Rolando Elio; Pereyra, Victor Daniel; Nonconvergence of the Wang-Landau algorithms with multiple random walkers; American Physical Society; Physical Review E; 93; 5; 5-2016; 1-9; 053306
2470-0053
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.93.053306
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.053306
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842269951078957056
score 13.13397

Publicaciones similares