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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/5691
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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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1842268969681027072 |
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13.13397 |