Intrinsic convergence properties of entropic sampling algorithms

Autores
Belardinelli, Rolando Elio; Pereyra, Victor Daniel; Dickman, Ronald; Lourenço, Bruno Jeferson
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the convergence of the density of states and thermodynamic properties in three flat-histogram simulation methods, the Wang–Landau (WL) algorithm, the 1/t algorithm, and tomographic sampling (TS). In the first case the refinement parameter f is rescaled (f → f/2) each time the flat-histogram condition is satisfied, in the second f ~ 1/t after a suitable initial phase, while in the third f is constant (t corresponds to Monte Carlo time). To examine the intrinsic convergence properties of these methods, free of any complications associated with a specific model, we study a featureless entropy landscape, such that for each allowed energy E = 1, ..., L, there is exactly one state, that is, g(E) = 1 for all E. Convergence of sampling corresponds to g(E, t) → const. as t → ∞, so that the standard deviation σg of g over energy values is a measure of the overall sampling error. Neither the WL algorithm nor TS converge: in both cases σg saturates at long times. In the 1/t algorithm, by contrast, σg decays $\propto 1/\sqrt{t}$ . Modified TS and 1/t procedures, in which f ∝ 1/tα, converge for α values between 0 < α ≤ 1. There are two essential facets to convergence of flat-histogram methods: elimination of initial errors in g(E) and correction of the sampling noise accumulated during the process. For a simple example, we demonstrate analytically, using a Langevin equation, that both kinds of errors can be eliminated, asymptotically, if f ~ 1/t α with 0 < α ≤ 1. Convergence is optimal for α = 1. For α ≤ 0 the sampling noise never decays, while for α > 1 the initial error is never completely eliminated.
Fil: Belardinelli, Rolando Elio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina
Fil: Pereyra, Victor Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina
Fil: Dickman, Ronald. Universidade Federal do Minas Gerais; Brasil
Fil: Lourenço, Bruno Jeferson. Universidade Federal do Minas Gerais; Brasil
Materia
STOCHASTIC PROCESSES
ANALYSIS OF ALGORITHM
MONTE CARLO SIMULATION
ENTROPIC SAMPLING
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:11336/5691

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network_name_str CONICET Digital (CONICET)
spelling Intrinsic convergence properties of entropic sampling algorithmsBelardinelli, Rolando ElioPereyra, Victor DanielDickman, RonaldLourenço, Bruno JefersonSTOCHASTIC PROCESSESANALYSIS OF ALGORITHMMONTE CARLO SIMULATIONENTROPIC SAMPLINGhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We study the convergence of the density of states and thermodynamic properties in three flat-histogram simulation methods, the Wang–Landau (WL) algorithm, the 1/t algorithm, and tomographic sampling (TS). In the first case the refinement parameter f is rescaled (f → f/2) each time the flat-histogram condition is satisfied, in the second f ~ 1/t after a suitable initial phase, while in the third f is constant (t corresponds to Monte Carlo time). To examine the intrinsic convergence properties of these methods, free of any complications associated with a specific model, we study a featureless entropy landscape, such that for each allowed energy E = 1, ..., L, there is exactly one state, that is, g(E) = 1 for all E. Convergence of sampling corresponds to g(E, t) → const. as t → ∞, so that the standard deviation σg of g over energy values is a measure of the overall sampling error. Neither the WL algorithm nor TS converge: in both cases σg saturates at long times. In the 1/t algorithm, by contrast, σg decays $\propto 1/\sqrt{t}$ . Modified TS and 1/t procedures, in which f ∝ 1/tα, converge for α values between 0 < α ≤ 1. There are two essential facets to convergence of flat-histogram methods: elimination of initial errors in g(E) and correction of the sampling noise accumulated during the process. For a simple example, we demonstrate analytically, using a Langevin equation, that both kinds of errors can be eliminated, asymptotically, if f ~ 1/t α with 0 < α ≤ 1. Convergence is optimal for α = 1. For α ≤ 0 the sampling noise never decays, while for α > 1 the initial error is never completely eliminated.Fil: Belardinelli, Rolando Elio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; ArgentinaFil: Pereyra, Victor Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; ArgentinaFil: Dickman, Ronald. Universidade Federal do Minas Gerais; BrasilFil: Lourenço, Bruno Jeferson. Universidade Federal do Minas Gerais; BrasilIop Publishing2014-06-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/5691Belardinelli, Rolando Elio; Pereyra, Victor Daniel; Dickman, Ronald; Lourenço, Bruno Jeferson; Intrinsic convergence properties of entropic sampling algorithms; Iop Publishing; Journal Of Statistical Mechanics: Theory And Experiment; 2014; 7; 2-6-2014; 1-131742-5468enginfo:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1742-5468/2014/07/P07007info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2014/00/000000info:eu-repo/semantics/altIdentifier/doi/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:49:21Zoai:ri.conicet.gov.ar:11336/5691instacron: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 09:49:21.463CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Intrinsic convergence properties of entropic sampling algorithms
title Intrinsic convergence properties of entropic sampling algorithms
spellingShingle Intrinsic convergence properties of entropic sampling algorithms
Belardinelli, Rolando Elio
STOCHASTIC PROCESSES
ANALYSIS OF ALGORITHM
MONTE CARLO SIMULATION
ENTROPIC SAMPLING
title_short Intrinsic convergence properties of entropic sampling algorithms
title_full Intrinsic convergence properties of entropic sampling algorithms
title_fullStr Intrinsic convergence properties of entropic sampling algorithms
title_full_unstemmed Intrinsic convergence properties of entropic sampling algorithms
title_sort Intrinsic convergence properties of entropic sampling algorithms
dc.creator.none.fl_str_mv Belardinelli, Rolando Elio
Pereyra, Victor Daniel
Dickman, Ronald
Lourenço, Bruno Jeferson
author Belardinelli, Rolando Elio
author_facet Belardinelli, Rolando Elio
Pereyra, Victor Daniel
Dickman, Ronald
Lourenço, Bruno Jeferson
author_role author
author2 Pereyra, Victor Daniel
Dickman, Ronald
Lourenço, Bruno Jeferson
author2_role author
author
author
dc.subject.none.fl_str_mv STOCHASTIC PROCESSES
ANALYSIS OF ALGORITHM
MONTE CARLO SIMULATION
ENTROPIC SAMPLING
topic STOCHASTIC PROCESSES
ANALYSIS OF ALGORITHM
MONTE CARLO SIMULATION
ENTROPIC SAMPLING
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the convergence of the density of states and thermodynamic properties in three flat-histogram simulation methods, the Wang–Landau (WL) algorithm, the 1/t algorithm, and tomographic sampling (TS). In the first case the refinement parameter f is rescaled (f → f/2) each time the flat-histogram condition is satisfied, in the second f ~ 1/t after a suitable initial phase, while in the third f is constant (t corresponds to Monte Carlo time). To examine the intrinsic convergence properties of these methods, free of any complications associated with a specific model, we study a featureless entropy landscape, such that for each allowed energy E = 1, ..., L, there is exactly one state, that is, g(E) = 1 for all E. Convergence of sampling corresponds to g(E, t) → const. as t → ∞, so that the standard deviation σg of g over energy values is a measure of the overall sampling error. Neither the WL algorithm nor TS converge: in both cases σg saturates at long times. In the 1/t algorithm, by contrast, σg decays $\propto 1/\sqrt{t}$ . Modified TS and 1/t procedures, in which f ∝ 1/tα, converge for α values between 0 < α ≤ 1. There are two essential facets to convergence of flat-histogram methods: elimination of initial errors in g(E) and correction of the sampling noise accumulated during the process. For a simple example, we demonstrate analytically, using a Langevin equation, that both kinds of errors can be eliminated, asymptotically, if f ~ 1/t α with 0 < α ≤ 1. Convergence is optimal for α = 1. For α ≤ 0 the sampling noise never decays, while for α > 1 the initial error is never completely eliminated.
Fil: Belardinelli, Rolando Elio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina
Fil: Pereyra, Victor Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico San Luis. Instituto de Física Aplicada; Argentina
Fil: Dickman, Ronald. Universidade Federal do Minas Gerais; Brasil
Fil: Lourenço, Bruno Jeferson. Universidade Federal do Minas Gerais; Brasil
description We study the convergence of the density of states and thermodynamic properties in three flat-histogram simulation methods, the Wang–Landau (WL) algorithm, the 1/t algorithm, and tomographic sampling (TS). In the first case the refinement parameter f is rescaled (f → f/2) each time the flat-histogram condition is satisfied, in the second f ~ 1/t after a suitable initial phase, while in the third f is constant (t corresponds to Monte Carlo time). To examine the intrinsic convergence properties of these methods, free of any complications associated with a specific model, we study a featureless entropy landscape, such that for each allowed energy E = 1, ..., L, there is exactly one state, that is, g(E) = 1 for all E. Convergence of sampling corresponds to g(E, t) → const. as t → ∞, so that the standard deviation σg of g over energy values is a measure of the overall sampling error. Neither the WL algorithm nor TS converge: in both cases σg saturates at long times. In the 1/t algorithm, by contrast, σg decays $\propto 1/\sqrt{t}$ . Modified TS and 1/t procedures, in which f ∝ 1/tα, converge for α values between 0 < α ≤ 1. There are two essential facets to convergence of flat-histogram methods: elimination of initial errors in g(E) and correction of the sampling noise accumulated during the process. For a simple example, we demonstrate analytically, using a Langevin equation, that both kinds of errors can be eliminated, asymptotically, if f ~ 1/t α with 0 < α ≤ 1. Convergence is optimal for α = 1. For α ≤ 0 the sampling noise never decays, while for α > 1 the initial error is never completely eliminated.
publishDate 2014
dc.date.none.fl_str_mv 2014-06-02
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/11336/5691
Belardinelli, Rolando Elio; Pereyra, Victor Daniel; Dickman, Ronald; Lourenço, Bruno Jeferson; Intrinsic convergence properties of entropic sampling algorithms; Iop Publishing; Journal Of Statistical Mechanics: Theory And Experiment; 2014; 7; 2-6-2014; 1-13
1742-5468
url http://hdl.handle.net/11336/5691
identifier_str_mv Belardinelli, Rolando Elio; Pereyra, Victor Daniel; Dickman, Ronald; Lourenço, Bruno Jeferson; Intrinsic convergence properties of entropic sampling algorithms; Iop Publishing; Journal Of Statistical Mechanics: Theory And Experiment; 2014; 7; 2-6-2014; 1-13
1742-5468
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1742-5468/2014/07/P07007
info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2014/00/000000
info:eu-repo/semantics/altIdentifier/doi/
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
application/pdf
dc.publisher.none.fl_str_mv Iop Publishing
publisher.none.fl_str_mv Iop Publishing
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
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