The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume II: Overcoming the Curse of Dimensionality: Large-Scale Application

ISBN-13: 9783031196348 / Angielski / Twarda / 2023 / 467 str.

Dan Gabriel Cacuci; Ruixian Fang

Opis

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.

Spis treści

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O autorze

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.

Blurb

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.