Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods

Modified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case, the bulk of the computational cost of MHMC algorithms lies in the numerical integration of a Hamiltonian system of diff...

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Detalles Bibliográficos
Autores: Radivojevic, T., Fernández-Pendás, M., Sanz-Serna, J.M., Akhmatskaya, E.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/835
Acceso en línea:http://hdl.handle.net/20.500.11824/835
Access Level:acceso abierto
Palabra clave:Hamiltonian Monte Carlo
Modified Hamiltonian
Multi-stage integrators
Enhanced sampling
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spelling Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methodsRadivojevic, T.Fernández-Pendás, M.Sanz-Serna, J.M.Akhmatskaya, E.Hamiltonian Monte CarloModified HamiltonianMulti-stage integratorsEnhanced samplingModified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case, the bulk of the computational cost of MHMC algorithms lies in the numerical integration of a Hamiltonian system of differential equations. We suggest novel integrators designed to enhance accuracy and sampling performance of MHMC methods. The novel integrators belong to families of splitting algorithms and are therefore easily implemented. We identify optimal integrators within the families by minimizing the energy error or the average energy error. We derive and discuss in detail the modified Hamiltonians of the new integrators, as the evaluation of those Hamiltonians is key to the efficiency of the overall algorithms. Numerical experiments show that the use of the new integrators may improve very significantly the sampling performance of MHMC methods, in both statistical and molecular dynamics problems.MTM2013-46553-C3-1-P, MTM2016-77660-P, VA024P17, BES-2014-068640201820182018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/835reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.sciencedirect.com/science/article/pii/S0021999118304844info:eu-repo/grantAgreement/MINECO//SEV-2013-0323info:eu-repo/grantAgreement/MINECO//MTM2016-76329-Rinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2014-2017info:eu-repo/grantAgreement/Gobierno Vasco/ELKARTEK/Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/8352026-06-19T12:47:47Z
dc.title.none.fl_str_mv Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods
title Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods
spellingShingle Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods
Radivojevic, T.
Hamiltonian Monte Carlo
Modified Hamiltonian
Multi-stage integrators
Enhanced sampling
title_short Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods
title_full Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods
title_fullStr Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods
title_full_unstemmed Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods
title_sort Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods
dc.creator.none.fl_str_mv Radivojevic, T.
Fernández-Pendás, M.
Sanz-Serna, J.M.
Akhmatskaya, E.
author Radivojevic, T.
author_facet Radivojevic, T.
Fernández-Pendás, M.
Sanz-Serna, J.M.
Akhmatskaya, E.
author_role author
author2 Fernández-Pendás, M.
Sanz-Serna, J.M.
Akhmatskaya, E.
author2_role author
author
author
dc.subject.none.fl_str_mv Hamiltonian Monte Carlo
Modified Hamiltonian
Multi-stage integrators
Enhanced sampling
topic Hamiltonian Monte Carlo
Modified Hamiltonian
Multi-stage integrators
Enhanced sampling
description Modified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case, the bulk of the computational cost of MHMC algorithms lies in the numerical integration of a Hamiltonian system of differential equations. We suggest novel integrators designed to enhance accuracy and sampling performance of MHMC methods. The novel integrators belong to families of splitting algorithms and are therefore easily implemented. We identify optimal integrators within the families by minimizing the energy error or the average energy error. We derive and discuss in detail the modified Hamiltonians of the new integrators, as the evaluation of those Hamiltonians is key to the efficiency of the overall algorithms. Numerical experiments show that the use of the new integrators may improve very significantly the sampling performance of MHMC methods, in both statistical and molecular dynamics problems.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018
2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/835
url http://hdl.handle.net/20.500.11824/835
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.sciencedirect.com/science/article/pii/S0021999118304844
info:eu-repo/grantAgreement/MINECO//SEV-2013-0323
info:eu-repo/grantAgreement/MINECO//MTM2016-76329-R
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2014-2017
info:eu-repo/grantAgreement/Gobierno Vasco/ELKARTEK/
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
repository.name.fl_str_mv
repository.mail.fl_str_mv
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