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The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume II

Overcoming the Curse of Dimensionality: Large-Scale Application

  • Book
  • © 2023

Overview

Authors:
  1. Dan Gabriel Cacuci

    1. University of South Carolina, Columbia, USA

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  2. Ruixian Fang

    1. Department of Mechanical Engineering, University of South Carolina, Columbia, USA

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  • Describes the large-scale application of the innovative nth-CASAM framework
  • Presents detailed mathematical calculations of the sensitivity analysis of a reactor system
  • Proves how the nth-CASAM overcomes the "curse of dimensionality" in uncertainty analysis

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xvii
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  2. First-Order Adjoint Sensitivity and Uncertainty Analysis of the OECD/NEA PERP Reactor Physics Benchmark

    • Dan Gabriel Cacuci, Ruixian Fang
    Pages 1-44

  3. Second-Order Analysis: Effects of Total Cross Sections

    • Dan Gabriel Cacuci, Ruixian Fang
    Pages 45-86

  4. Second-Order Analysis: Effects of Scattering Cross Sections

    • Dan Gabriel Cacuci, Ruixian Fang
    Pages 87-137

  5. Second-Order Analysis: Effects of Fission Cross Sections

    • Dan Gabriel Cacuci, Ruixian Fang
    Pages 139-193

  6. Second-Order Analysis: Effects of Average Number of Neutrons Per Fission

    • Dan Gabriel Cacuci, Ruixian Fang
    Pages 195-234

  7. Second-Order Analysis: Effects of Source Parameters

    • Dan Gabriel Cacuci, Ruixian Fang
    Pages 235-292

  8. Second-Order Analysis: Effects of Isotopic Number Densities

    • Dan Gabriel Cacuci, Ruixian Fang
    Pages 293-361

  9. Third- and Fourth-Order Adjoint Sensitivity and Uncertainty Analysis of the PERP Benchmark

    • Dan Gabriel Cacuci, Ruixian Fang
    Pages 363-438

  10. Concluding Remarks

    • Dan Gabriel Cacuci, Ruixian Fang
    Pages 439-446

  11. Back Matter

    Pages 447-463
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Keywords

About this book

This text describes a comprehensive adjoint sensitivity analysis methodology (nth-CASAM), developed by the author, which enablesthe efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The nth-CASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby overcoming the so-called “curse of dimensionality” in sensitivity and uncertainty analysis. The nth-CASAM is applicable to any model; the larger the number of model parameters, the more efficient the nth-CASAM 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 the nth-CASAM to perform a representative fourth-order sensitivity analysis of the Polyethylene-Reflected Plutonium benchmark described in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. This benchmark is modeled mathematically by the Boltzmann particle transport equation, involving 21,976 imprecisely-known parameters, the numerical solution of which requires representative large-scale computations. The sensitivity analysis presented in this volume is the most comprehensive ever performed in the field of reactor physics and the results presented in this book prove, perhaps counter-intuitively, that many of the 4th-order sensitivities are much larger than the corresponding 3rd-order ones, which are, in turn, much larger than the 2nd-order ones, all of which are much larger than the 1st-order sensitivities. Currently, the nth-CASAM is the only known methodology which enables such large-scale computations of exactly obtained expressions of arbitrarily-high-order response sensitivities.


Authors and Affiliations

  • University of South Carolina, Columbia, USA

    Dan Gabriel Cacuci

  • Department of Mechanical Engineering, University of South Carolina, Columbia, USA

    Ruixian Fang

About the authors

Professor Cacuci’s career spans over 40 years in the field of nuclear science and energy, encompassing both academia and national multidisciplinary research centers. His scientific expertise includes predictive best-estimate analysis of large-scale physical and engineering systems, large scale scientific computations and, within nuclear science and engineering, reactor multi-physics,

dynamics, and safety. Prof. Cacuci served as the Chaired Professor and Director of the Institutes for Reactor Technology (Uni Karlsruhe/KIT) and Reactor Safety (KfK/FZK/KIT) and has also served as the Scientific Director of the Nuclear Energy Directorate of France’s Atomic Energy Commission. During 1984-2019, Prof. Cacuci was the Editor of Nuclear Science and Engineering; since 2019, he has been serving as the Founding Editor of the open-access Journal of Nuclear Engineering (MDPI). Prof. Cacuci has received many prestigious awards, including four titles of Doctor Honoris Causa, the E. O. Lawrence Award and Gold Medal from the US DOE, the Alexander von Humboldt Prize for Senior Scholars; from the American Nuclear Society (ANS), he has received the Arthur Holly Compton Award, the Eugene P. Wigner Award, the Glenn Seaborg Medal, Young Members Engineering Achievement Award, and was elected an ANS Fellow. He is a member of several international and national academies of arts and sciences, has made over 600 presentations worldwide, has authored 6 books, 6 book chapters, over 300 peer-reviewed articles, and has edited the comprehensive Handbook of Nuclear Engineering (Springer, 2010). He is currently the Director of the Center of Economic Excellence in Nuclear Science and Energy and SmartState Endowed Chair Professor of Nuclear Engineering at University of South Carolina.

Dr. Fang is a Research Associate Professor in the Department of Mechanical Engineering at the University of South Carolina, performing research on predictive modeling of large-scale physical and engineering systems with applications in the broad areas of thermal science, nuclear science and energy. He received his B.S. from the Thermal Power Engineering at Xi’an Jiaotong University, China; and M.E. and Ph.D. degrees from the Department of Mechanical Engineering at the University of South Carolina in 2011. Dr. Fang has authored over 50 peer-reviewed articles in thermal-hydraulic safety analysis for liquid-metal cooled advanced Small Modular Reactors, facility modeling for separation and safeguards, and thermal management of all-electric ship’s power electronic systems.

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