國立高雄大學圖資館 |

Language: English

Back to Search results for [ subject:"Sensitivity theory (Mathematics)" ]

The nth-order comprehensive adjoint sensitivity analysis methodology.Volume II,Overcoming the curse of dimensionality : large-scale application

Record Type:	Electronic resources : Monograph/item
Title/Author:	The nth-order comprehensive adjoint sensitivity analysis methodology.by Dan Gabriel Cacuci, Ruixian Fang.
remainder title:	Overcoming the curse of dimensionality :
Author:	Cacuci, Dan Gabriel.
other author:	Fang, Ruixian.
Published:	Cham :Springer International Publishing :2023.
Description:	xvi, 463 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Sensitivity theory (Mathematics)
Online resource:	https://doi.org/10.1007/978-3-031-19635-5
ISBN:	9783031196355$q(electronic bk.)

The nth-order comprehensive adjoint sensitivity analysis methodology.Volume II,Overcoming the curse of dimensionality : large-scale application
Cacuci, Dan Gabriel.

The nth-order comprehensive adjoint sensitivity analysis methodology.Volume II,Overcoming the curse of dimensionality : large-scale application[electronic resource] /Overcoming the curse of dimensionality :large-scale applicationby Dan Gabriel Cacuci, Ruixian Fang. - Cham :Springer International Publishing :2023. - xvi, 463 p. :ill., digital ;24 cm.

Chapter1. 1st-Order Sensitivity Analysis of the OECD/NEA PERP Reactor Physics Benchmark -- Chapter2. 2nd-Order Sensitivities of the PERP Benchmark to the Microscopic Total and Capture Cross Sections -- Chapter3. 2nd-Order Sensitivities of the PERP Benchmark to the Microscopic Scattering Cross Sections -- Chapter4. 2nd-Order Sensitivities of the PERP Benchmark to the Microscopic Fission Cross Sections -- Chapter5. 2nd-Order Sensitivities of the PERP Benchmark to the Average Number of Neutrons per Fission -- Chapter6. 2nd-Order Sensitivities of the PERP Benchmark to the Spontaneous Fission Source Parameters -- Chapter7. 2nd-Order Sensitivities of the PERP Benchmark to the Isotopic Number Densities -- Chapter8. 3rd-Order Sensitivities of the PERP Benchmark -- Chapter9. 4th-Order Sensitivities of the PERP Benchmark -- Chapter10. Overall Impact of 1st-, 2nd-, 3rd-, and 4th-Order Sensitivities on the PERP Benchmark's Response Uncertainties.

This text describes a comprehensive adjoint sensitivity analysis methodology (C-ASAM), developed by the author, enabling the efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The C-ASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby breaking the so-called "curse of dimensionality" in sensitivity and uncertainty analysis. The C-ASAM applies to any model; the larger the number of model parameters, the more efficient the C-ASAM becomes for computing arbitrarily high-order response sensitivities. The book will be helpful to those working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems and predictive modelling. This Volume Two, the second of three, presents the large-scale application of C-ASAM to compute exactly the first-, second-, third-, and fourth-order sensitivities of the Polyethylene-Reflected Plutonium (PERP) OECD/NEO international benchmark which is modeled mathematically by the Boltzmann particle transport equation. It follows from the description of the C-ASAM framework applied to linear systems in Volume One where the PERP benchmark's response of interest is the leakage of particles through its outer boundary. The benchmark represents the largest sensitivity analysis endeavor ever carried out in the field of reactor physics and the numerical results shown in this book prove, for the first time ever, that many of the second-order sensitivities are much larger than the corresponding first-order ones. Currently, the nth-CASAM is the only known methodology which enables such large-scale computations of the exact expressions and values of the nth-order response sensitivities.

ISBN: 9783031196355$q(electronic bk.)

Standard No.: 10.1007/978-3-031-19635-5doiSubjects--Topical Terms:

484885
Sensitivity theory (Mathematics)

LC Class. No.: QA402.3

Dewey Class. No.: 003.5

The nth-order comprehensive adjoint sensitivity analysis methodology.Volume II,Overcoming the curse of dimensionality : large-scale application
LDR:04077nmm a2200337 a 4500 001 643573
003 DE-He213
005 20230426165256.0
006 m d
007 cr nn 008maaau
008 231123s2023 sz s 0 eng d
020 $a 9783031196355$q(electronic bk.)
020 $a 9783031196348$q(paper)
024 7 $a 10.1007/978-3-031-19635-5 $2 doi
035 $a 978-3-031-19635-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA402.3
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
072 7 $a PHU $2 thema
082 0 4 $a 003.5 $2 23
090 $a QA402.3 $b .C119 2023
100 1 $a Cacuci, Dan Gabriel. $3 495560
245 1 4 $a The nth-order comprehensive adjoint sensitivity analysis methodology. $n Volume II, $p Overcoming the curse of dimensionality : large-scale application $h [electronic resource] / $c by Dan Gabriel Cacuci, Ruixian Fang.
246 3 0 $a Overcoming the curse of dimensionality : $b large-scale application
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xvi, 463 p. : $b ill., digital ; $c 24 cm.
505 0 $a Chapter1. 1st-Order Sensitivity Analysis of the OECD/NEA PERP Reactor Physics Benchmark -- Chapter2. 2nd-Order Sensitivities of the PERP Benchmark to the Microscopic Total and Capture Cross Sections -- Chapter3. 2nd-Order Sensitivities of the PERP Benchmark to the Microscopic Scattering Cross Sections -- Chapter4. 2nd-Order Sensitivities of the PERP Benchmark to the Microscopic Fission Cross Sections -- Chapter5. 2nd-Order Sensitivities of the PERP Benchmark to the Average Number of Neutrons per Fission -- Chapter6. 2nd-Order Sensitivities of the PERP Benchmark to the Spontaneous Fission Source Parameters -- Chapter7. 2nd-Order Sensitivities of the PERP Benchmark to the Isotopic Number Densities -- Chapter8. 3rd-Order Sensitivities of the PERP Benchmark -- Chapter9. 4th-Order Sensitivities of the PERP Benchmark -- Chapter10. Overall Impact of 1st-, 2nd-, 3rd-, and 4th-Order Sensitivities on the PERP Benchmark's Response Uncertainties.
520 $a This text describes a comprehensive adjoint sensitivity analysis methodology (C-ASAM), developed by the author, enabling the efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The C-ASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby breaking the so-called "curse of dimensionality" in sensitivity and uncertainty analysis. The C-ASAM applies to any model; the larger the number of model parameters, the more efficient the C-ASAM becomes for computing arbitrarily high-order response sensitivities. The book will be helpful to those working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems and predictive modelling. This Volume Two, the second of three, presents the large-scale application of C-ASAM to compute exactly the first-, second-, third-, and fourth-order sensitivities of the Polyethylene-Reflected Plutonium (PERP) OECD/NEO international benchmark which is modeled mathematically by the Boltzmann particle transport equation. It follows from the description of the C-ASAM framework applied to linear systems in Volume One where the PERP benchmark's response of interest is the leakage of particles through its outer boundary. The benchmark represents the largest sensitivity analysis endeavor ever carried out in the field of reactor physics and the numerical results shown in this book prove, for the first time ever, that many of the second-order sensitivities are much larger than the corresponding first-order ones. Currently, the nth-CASAM is the only known methodology which enables such large-scale computations of the exact expressions and values of the nth-order response sensitivities.
650 0 $a Sensitivity theory (Mathematics) $3 484885
650 0 $a Large scale systems. $3 247726
650 0 $a Linear systems. $3 182249
650 1 4 $a Computational Physics and Simulations. $3 913439
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 274070
650 2 4 $a Statistical Theory and Methods. $3 274054
650 2 4 $a Energy Policy, Economics and Management. $3 511210
650 2 4 $a Mathematical and Computational Engineering Applications. $3 915034
650 2 4 $a Nuclear Physics. $3 648560
700 1 $a Fang, Ruixian. $3 951370
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-19635-5
950 $a Physics and Astronomy (SpringerNature-11651)