Adjoint-based constant-mass partial derivatives

Favorite, Jeffrey A.

doi:10.1016/j.anucene.2017.08.015

Title: Adjoint-based constant-mass partial derivatives

Abstract

In transport theory, adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to surface locations (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. This study derives the constant-mass partial derivative of a response with respect to an internal interface location or the outer system boundary and the constant-mass partial derivative of a response with respect to the mass density of a region. Numerical results are given for a multiregion two-dimensional (r-z) cylinder for three very different responses: the uncollided gamma-ray flux at an external detector point, k_eff of the system, and the total neutron leakage. Finally, results from the derived formulas compare extremely well with direct perturbation calculations.

Authors:

Favorite, Jeffrey A. ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Fri Sep 01 00:00:00 EDT 2017

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA), Office of Defense Nuclear Nonproliferation

OSTI Identifier:: 1402629

Report Number(s):: LA-UR-17-22871
Journal ID: ISSN 0306-4549; TRN: US1702884

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Annals of Nuclear Energy (Oxford)

Additional Journal Information:: Journal Name: Annals of Nuclear Energy (Oxford); Journal Volume: 110; Journal ID: ISSN 0306-4549

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; perturbation theory; surface perturbation theory; partial derivative

Citation Formats


                    Favorite, Jeffrey A. Adjoint-based constant-mass partial derivatives.  United States: N. p., 2017. 
Web.  doi:10.1016/j.anucene.2017.08.015.

Copy to clipboard


                    Favorite, Jeffrey A. Adjoint-based constant-mass partial derivatives.  United States.  https://doi.org/10.1016/j.anucene.2017.08.015

Copy to clipboard


                    Favorite, Jeffrey A. Fri .  
"Adjoint-based constant-mass partial derivatives".  United States.  https://doi.org/10.1016/j.anucene.2017.08.015.  https://www.osti.gov/servlets/purl/1402629.

Copy to clipboard


                    
@article{osti_1402629,

  title        = {Adjoint-based constant-mass partial derivatives},

  author       = {Favorite, Jeffrey A.},

  abstractNote = {In transport theory, adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to surface locations (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. This study derives the constant-mass partial derivative of a response with respect to an internal interface location or the outer system boundary and the constant-mass partial derivative of a response with respect to the mass density of a region. Numerical results are given for a multiregion two-dimensional (r-z) cylinder for three very different responses: the uncollided gamma-ray flux at an external detector point, keff of the system, and the total neutron leakage. Finally, results from the derived formulas compare extremely well with direct perturbation calculations.},

  doi          = {10.1016/j.anucene.2017.08.015},

  journal      = {Annals of Nuclear Energy (Oxford)},

  number       = ,

  volume       = 110,

  place        = {United States},

  year         = {Fri Sep 01 00:00:00 EDT 2017},

  month        = {Fri Sep 01 00:00:00 EDT 2017}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.anucene.2017.08.015

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 4 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Using the Levenberg-Marquardt Method for Solutions of Inverse Transport Problems in One- and Two-Dimensional Geometries
journal, October 2011

Bledsoe, Keith C.; Favorite, Jeffrey A.; Aldemir, Tunc
Nuclear Technology, Vol. 176, Issue 1
DOI: 10.13182/NT176-106

Maximum polar angle subtended by a right circular cylinder
journal, December 2008

Favorite, Jeffrey A.
Annals of Nuclear Energy, Vol. 35, Issue 12
DOI: 10.1016/j.anucene.2008.09.009

Adjoint-Based Sensitivity and Uncertainty Analysis for Density and Composition: A User’s Guide
journal, March 2017

Favorite, Jeffrey A.; Perkó, Zoltán; Kiedrowski, Brian C.
Nuclear Science and Engineering, Vol. 185, Issue 3
DOI: 10.1080/00295639.2016.1272990

Eigenvalue sensitivity to system dimensions
journal, April 2010

Favorite, Jeffrey A.; Bledsoe, Keith C.
Annals of Nuclear Energy, Vol. 37, Issue 4
DOI: 10.1016/j.anucene.2010.01.004

Surface and Volume Integrals of Uncollided Adjoint Fluxes and Forward-Adjoint Flux Products
journal, September 2009

Favorite, Jeffrey A.; Bledsoe, Keith C.; Ketcheson, David I.
Nuclear Science and Engineering, Vol. 163, Issue 1
DOI: 10.13182/NSE163-73

Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems
journal, March 2017

Favorite, Jeffrey A.; Gonzalez, Esteban
Nuclear Science and Engineering, Vol. 185, Issue 3
DOI: 10.1080/00295639.2016.1277108

Works referencing / citing this record:

SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k _eff , and α Using PARTISN
journal, July 2018

Favorite, Jeffrey A.
Nuclear Science and Engineering, Vol. 192, Issue 1
DOI: 10.1080/00295639.2018.1471296

Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses
journal, March 2018

Cacuci, Dan G.; Favorite, Jeffrey A.
Nuclear Science and Engineering, Vol. 190, Issue 2
DOI: 10.1080/00295639.2018.1426899

Similar Records in DOE PAGES and OSTI.GOV collections:

Adjoint-Based Constant-Mass Partial Derivatives

Journal Article Favorite, Jeffrey A. - Transactions of the American Nuclear Society

It is well known that the adjoint equation in transport theory provides an economical means of computing derivatives of a system response to system parameters. It is also well known, though not often remarked on, that adjoint-based partial derivatives with respect to mass density are constant-volume derivatives. Likewise, adjoint-based partial derivatives with respect to dimensions (i.e., internal interface locations and the outer system boundary) are constant-density derivatives. In this paper, we derive a formula for the constant-mass partial derivative of a response with respect to internal interface locations and the outer system boundary. The formula uses the partial derivatives formore »« less
(U) Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses Using Ray-Tracing

Technical Report Favorite, Jeffrey A.

The Second-Level Adjoint Sensitivity System (2nd-LASS) that yields the second-order sensitivities of a response of uncollided particles with respect to isotope densities, cross sections, and source emission rates is derived in Refs. 1 and 2. In Ref. 2, we solved problems for the uncollided leakage from a homogeneous sphere and a multiregion cylinder using the PARTISN multigroup discrete-ordinates code. In this memo, we derive solutions of the 2nd-LASS for the particular case when the response is a flux or partial current density computed at a single point on the boundary, and the inner products are computed using ray-tracing. Both themore »« less
https://doi.org/10.2172/1411336

Full Text Available
Multidual Sensitivity Method in Ray-Tracing Transport Simulations

Journal Article Balcer, Matthew R. ; Millwater, Harry ; Favorite, Jeffrey A. - Nuclear Science and Engineering

The multidual differentiation method has been implemented in a ray-tracing transport simulation for the purpose of calculating arbitrary-order sensitivities of the uncollided particle leakage. This method extends dual number differentiation by perturbing variables along multiple nonreal axes to calculate arbitrary-order derivatives. Numerical results of first-through third-order multidual sensitivities of the uncollided particle leakage with respect to isotope densities, microscopic cross sections, source emission rates, and material interface locations (including the outer boundary) are shown for a two-region sphere. The relative error of first and second partial derivatives with respect to isotopic parameters and first partial derivatives of the leakage withmore »« less
https://doi.org/10.1080/00295639.2021.1883949
(U) SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k_eff, α, and Subcritical Multiplication Using PARTISN

Technical Report Favorite, Jeffrey A.

SENSMG is a tool for computing first-order sensitivities of neutron reaction rates, reaction-rate ratios, leakage, k_eff, α, and subcritical multiplication using the PARTISN multigroup discrete-ordinates code. SENSMG computes sensitivities to all of the transport cross sections and data (total, fission,^a nu, chi, and all scattering moments), two edit cross sections (absorption and capture), and the density for every nuclide and energy group. It also computes sensitivities to the mass density for every material and derivatives with respect to all interface locations and outer boundaries. It computes sensitivities to user specified reactions whose cross sections are available in a user-supplied NJOYmore »« less
https://doi.org/10.2172/1884735

Full Text Available
USING THE LEVENBERG-MARQUARDT METHOD FOR SOLUTIONS OF INVERSE TRANSPORT PROBLEMS IN ONE- AND TWO-DIMENSIONAL GEOMETRIES

Journal Article Aldemir, Tunc - Nuclear Technology

Determining the components of a radioactive source/shield system using the system's radiation signature, a type of inverse transport problem, is one of great importance in homeland security, material safeguards, and waste management. Here, the Levenberg-Marquardt (or simply 'Marquardt') method, a standard gradient-based optimization technique, is applied to the inverse transport problems of interface location identification, shield material identification, source composition identification, and material mass density identification (both separately and combined) in multilayered radioactive source/shield systems. One-dimensional spherical problems using leakage measurements of neutron-induced gamma-ray lines and two-dimensional cylindrical problems using flux measurements of uncollided passive gamma-ray lines are considered. Gradientsmore »« less

Similar Records

Title: Adjoint-based constant-mass partial derivatives

Abstract

Citation Formats

Using the Levenberg-Marquardt Method for Solutions of Inverse Transport Problems in One- and Two-Dimensional Geometries journal, October 2011

Maximum polar angle subtended by a right circular cylinder journal, December 2008

Adjoint-Based Sensitivity and Uncertainty Analysis for Density and Composition: A User’s Guide journal, March 2017

Eigenvalue sensitivity to system dimensions journal, April 2010

Surface and Volume Integrals of Uncollided Adjoint Fluxes and Forward-Adjoint Flux Products journal, September 2009

Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems journal, March 2017

SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k eff , and α Using PARTISN journal, July 2018

Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses journal, March 2018

Using the Levenberg-Marquardt Method for Solutions of Inverse Transport Problems in One- and Two-Dimensional Geometries
journal, October 2011

Maximum polar angle subtended by a right circular cylinder
journal, December 2008

Adjoint-Based Sensitivity and Uncertainty Analysis for Density and Composition: A User’s Guide
journal, March 2017

Eigenvalue sensitivity to system dimensions
journal, April 2010

Surface and Volume Integrals of Uncollided Adjoint Fluxes and Forward-Adjoint Flux Products
journal, September 2009

Revisiting Boundary Perturbation Theory for Inhomogeneous Transport Problems
journal, March 2017

SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k _eff , and α Using PARTISN
journal, July 2018

Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses
journal, March 2018