Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation

This work addresses the problem of propagating uncertainty from group-wise neutron cross-sections to the results of neutronics diffusion calculations. Automatic differentiation based on dual number arithmetic was applied to uncertainty propagation in the framework of local sensitivity analy...

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Autores principales:	Bokov Pavel M., Botes Danniell, Groenewald Suzanne A.
Formato:	article
Lenguaje:	EN
Publicado:	VINCA Institute of Nuclear Sciences 2021
Materias:	automatic differentiation dual numbers sandwich formula sensitivity analysis uncertainty propagation power iteration Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/927026ac70e24cf4a29dc7f3fbe0bfe5
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spelling	oai:doaj.org-article:927026ac70e24cf4a29dc7f3fbe0bfe52021-11-22T11:03:07ZDual number automatic differentiation as applied to two-group cross-section uncertainty propagation1451-39941452-818510.2298/NTRP2102107Bhttps://doaj.org/article/927026ac70e24cf4a29dc7f3fbe0bfe52021-01-01T00:00:00Zhttp://www.doiserbia.nb.rs/img/doi/1451-3994/2021/1451-39942102107B.pdfhttps://doaj.org/toc/1451-3994https://doaj.org/toc/1452-8185This work addresses the problem of propagating uncertainty from group-wise neutron cross-sections to the results of neutronics diffusion calculations. Automatic differentiation based on dual number arithmetic was applied to uncertainty propagation in the framework of local sensitivity analysis. As an illustration, we consider a two-group diffusion problem in an infinite medium, which has a solution in a closed form. We employ automatic differentiation in conjunction with the sandwich formula for uncertainty propagation in three ways. Firstly, by evaluating the analytical expression for the multiplication factor using dual number arithmetic. Then, by solving the diffusion problem with the power iteration algorithm and the algebra of dual matrices. Finally, automatic differentiation is used to calculate the partial derivatives of the production and loss operators in the perturbation formula from the adjoint-weighted technique. The numerical solution of the diffusion problem is verified against the analytical formulas and the results of the uncertainty calculations are compared with those from the global sensitivity analysis approach. The uncertainty values obtained in this work differ from values given in the literature by less than 1•10–5.Bokov Pavel M.Botes DanniellGroenewald Suzanne A.VINCA Institute of Nuclear Sciencesarticleautomatic differentiationdual numberssandwich formulasensitivity analysisuncertainty propagationpower iterationNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENNuclear Technology and Radiation Protection, Vol 36, Iss 2, Pp 107-115 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	automatic differentiation dual numbers sandwich formula sensitivity analysis uncertainty propagation power iteration Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	automatic differentiation dual numbers sandwich formula sensitivity analysis uncertainty propagation power iteration Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Bokov Pavel M. Botes Danniell Groenewald Suzanne A. Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation
description	This work addresses the problem of propagating uncertainty from group-wise neutron cross-sections to the results of neutronics diffusion calculations. Automatic differentiation based on dual number arithmetic was applied to uncertainty propagation in the framework of local sensitivity analysis. As an illustration, we consider a two-group diffusion problem in an infinite medium, which has a solution in a closed form. We employ automatic differentiation in conjunction with the sandwich formula for uncertainty propagation in three ways. Firstly, by evaluating the analytical expression for the multiplication factor using dual number arithmetic. Then, by solving the diffusion problem with the power iteration algorithm and the algebra of dual matrices. Finally, automatic differentiation is used to calculate the partial derivatives of the production and loss operators in the perturbation formula from the adjoint-weighted technique. The numerical solution of the diffusion problem is verified against the analytical formulas and the results of the uncertainty calculations are compared with those from the global sensitivity analysis approach. The uncertainty values obtained in this work differ from values given in the literature by less than 1•10–5.
format	article
author	Bokov Pavel M. Botes Danniell Groenewald Suzanne A.
author_facet	Bokov Pavel M. Botes Danniell Groenewald Suzanne A.
author_sort	Bokov Pavel M.
title	Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation
title_short	Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation
title_full	Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation
title_fullStr	Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation
title_full_unstemmed	Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation
title_sort	dual number automatic differentiation as applied to two-group cross-section uncertainty propagation
publisher	VINCA Institute of Nuclear Sciences
publishDate	2021
url	https://doaj.org/article/927026ac70e24cf4a29dc7f3fbe0bfe5
work_keys_str_mv	AT bokovpavelm dualnumberautomaticdifferentiationasappliedtotwogroupcrosssectionuncertaintypropagation AT botesdanniell dualnumberautomaticdifferentiationasappliedtotwogroupcrosssectionuncertaintypropagation AT groenewaldsuzannea dualnumberautomaticdifferentiationasappliedtotwogroupcrosssectionuncertaintypropagation
_version_	1718417747698778112

Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation

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