Second Order Adjoint Sensitivity Analysis Methodology
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The Second Order Adjoint Sensitivity Analysis Methodology
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Author : Dan Gabriel Cacuci
language : en
Publisher: CRC Press
Release Date : 2018-02-19
The Second Order Adjoint Sensitivity Analysis Methodology written by Dan Gabriel Cacuci and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-19 with Mathematics categories.
The Second-Order Adjoint Sensitivity Analysis Methodology generalizes the First-Order Theory presented in the author’s previous books published by CRC Press. This breakthrough has many applications in sensitivity and uncertainty analysis, optimization, data assimilation, model calibration, and reducing uncertainties in model predictions. The book has many illustrative examples that will help readers understand the complexity of the subject and will enable them to apply this methodology to problems in their own fields. Highlights: • Covers a wide range of needs, from graduate students to advanced researchers • Provides a text positioned to be the primary reference for high-order sensitivity and uncertainty analysis • Applies to all fields involving numerical modeling, optimization, quantification of sensitivities in direct and inverse problems in the presence of uncertainties. About the Author: Dan Gabriel Cacuci is a South Carolina SmartState Endowed Chair Professor and the Director of the Center for Nuclear Science and Energy, Department of Mechanical Engineering at the University of South Carolina. He has a Ph.D. in Applied Physics, Mechanical and Nuclear Engineering from Columbia University. He is also the recipient of many awards including four honorary doctorates, the Ernest Orlando Lawrence Memorial award from the U.S. Dept. of Energy and the Arthur Holly Compton, Eugene P. Wigner and the Glenn Seaborg Awards from the American Nuclear Society.
Second Order Adjoint Sensitivity Analysis Methodology
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Author : DAN GABRIEL. CACUCI
language : en
Publisher:
Release Date : 2017
Second Order Adjoint Sensitivity Analysis Methodology written by DAN GABRIEL. CACUCI and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
The Nth Order Comprehensive Adjoint Sensitivity Analysis Methodology Volume Ii
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Author : Dan Gabriel Cacuci
language : en
Publisher: Springer Nature
Release Date : 2023-04-26
The Nth Order Comprehensive Adjoint Sensitivity Analysis Methodology Volume Ii written by Dan Gabriel Cacuci and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-26 with Science categories.
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.
The Nth Order Comprehensive Adjoint Sensitivity Analysis Methodology Volume Iii
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Author : Dan Gabriel Cacuci
language : en
Publisher: Springer Nature
Release Date : 2023-04-11
The Nth Order Comprehensive Adjoint Sensitivity Analysis Methodology Volume Iii written by Dan Gabriel Cacuci and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-11 with Science categories.
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 model’s responses can be either scalar-valued functionals of the model’s parameters and state variables (as customarily encountered, e.g., in optimization problems) or general function-valued responses, which are often of interest but are currently not amenable to efficient sensitivity analysis. 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 text includes illustrative paradigm problems which are fully worked-out to enable the thorough understanding of the C-ASAM’s principles and their practical application. 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. It serves as a textbook or as supplementary reading for graduate course on these topics, in academic departments in the natural, biological, and physical sciences and engineering. This Volume Three, the third of three, covers systems that are nonlinear in the state variables, model parameters and associated responses. The selected illustrative paradigm problems share these general characteristics. A separate Volume One covers systems that are linear in the state variables.
The Nth Order Comprehensive Adjoint Sensitivity Analysis Methodology Volume I
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Author : Dan Gabriel Cacuci
language : en
Publisher: Springer Nature
Release Date : 2022-07-19
The Nth Order Comprehensive Adjoint Sensitivity Analysis Methodology Volume I written by Dan Gabriel Cacuci and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-19 with Science categories.
The computational models of physical systems comprise parameters, independent and dependent variables. Since the physical processes themselves are seldom known precisely and since most of the model parameters stem from experimental procedures which are also subject to imprecisions, the results predicted by these models are also imprecise, being affected by the uncertainties underlying the respective model. The functional derivatives (also called “sensitivities”) of results (also called “responses”) produced by mathematical/computational models are needed for many purposes, including: (i) understanding the model by ranking the importance of the various model parameters; (ii) performing “reduced-order modeling” by eliminating unimportant parameters and/or processes; (iii) quantifying the uncertainties induced in a model response due to model parameter uncertainties; (iv) performing “model validation,” by comparing computations to experiments to address the question “does the model represent reality?” (v) prioritizing improvements in the model; (vi) performing data assimilation and model calibration as part of forward “predictive modeling” to obtain best-estimate predicted results with reduced predicted uncertainties; (vii) performing inverse “predictive modeling”; (viii) designing and optimizing the system. This 3-Volume monograph describes a comprehensive adjoint sensitivity analysis methodology, developed by the author, which enables the efficient and exact computation of arbitrarily high-order sensitivities of model responses in large-scale systems comprising many model parameters. The qualifier “comprehensive” is employed to highlight that the model parameters considered within the framework of this methodology also include the system’s uncertain boundaries and internal interfaces in phase-space. The model’s responses can be either scalar-valued functionals of the model’s parameters and state variables (e.g., as customarily encountered in optimization problems) or general function-valued responses. Since linear operators admit bona-fide adjoint operators, responses of models that are linear in the state functions (i.e., dependent variables) can depend simultaneously on both the forward and the adjoint state functions. Hence, the sensitivity analysis of such responses warrants the treatment of linear systems in their own right, rather than treating them as particular cases of nonlinear systems. This is in contradistinction to responses for nonlinear systems, which can depend only on the forward state functions, since nonlinear operators do not admit bona-fide adjoint operators (only a linearized form of a nonlinear operator may admit an adjoint operator). Thus, Volume 1 of this book presents the mathematical framework of the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “nth-CASAM-L”), which is conceived for the most efficient computation of exactly obtained mathematical expressions of arbitrarily-high-order (nth-order) sensitivities of a generic system response with respect to all of the parameters underlying the respective forward/adjoint systems. Volume 2 of this book presents the application of the nth-CASAM-L to perform a fourth-order sensitivity and uncertainty analysis of an OECD/NEA reactor physics benchmark which is representative of a large-scale model comprises many (21,976) uncertain parameters, thereby amply illustrating the unique potential of the nth-CASAM-L to enable the exact and efficient computation of chosen high-order response sensitivities to model parameters. Volume 3 of this book presents the “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviation: nth-CASAM-N) for the practical, efficient, and exact computation of arbitrarily-high order sensitivities of responses to model parameters for systems that are also nonlinear in their underlying state functions. Such computations are not feasible with any other methodology. The application of the nth-CASAM-L and the nth-CASAM-N overcomes the so-called “curse of dimensionality” in sensitivity and uncertainty analysis, thus revolutionizing all of the fields of activities which require accurate computation of response sensitivities. Since this monograph includes many illustrative, fully worked-out, paradigm problems, it can serve as a textbook or as supplementary reading for graduate courses in academic departments in the natural sciences and engineering.
Applications Of Data Assimilation And Inverse Problems In The Earth Sciences
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Author : Alik Ismail-Zadeh
language : en
Publisher: Cambridge University Press
Release Date : 2023-07-06
Applications Of Data Assimilation And Inverse Problems In The Earth Sciences written by Alik Ismail-Zadeh and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-06 with Mathematics categories.
A comprehensive reference on data assimilation and inverse problems, and their applications across a broad range of geophysical disciplines, ideal for researchers and graduate students. It highlights the importance of data assimilation for understanding dynamical processes of the Earth and its space environment, and summarises recent advances.
Sensitivity Uncertainty Analysis Volume 1
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Author : Dan G. Cacuci
language : en
Publisher: CRC Press
Release Date : 2003-05-28
Sensitivity Uncertainty Analysis Volume 1 written by Dan G. Cacuci and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-28 with Mathematics categories.
As computer-assisted modeling and analysis of physical processes have continued to grow and diversify, sensitivity and uncertainty analyses have become indispensable investigative scientific tools in their own right. While most techniques used for these analyses are well documented, there has yet to appear a systematic treatment of the method based
Theoretical Aspects Of Industrial Design
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Author : David Anthony Field
language : en
Publisher: SIAM
Release Date : 1992-01-01
Theoretical Aspects Of Industrial Design written by David Anthony Field and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Art categories.
A companion to Geometric aspects . . . (see preceding entry). The 10 papers consider traditional applied mathematics emphasizing problems such as control and optimization in industrial design. No index. Acidic paper. Annotation copyright Book News, Inc. Portland, Or.
Berru Predictive Modeling
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Author : Dan Gabriel Cacuci
language : en
Publisher: Springer
Release Date : 2018-12-29
Berru Predictive Modeling written by Dan Gabriel Cacuci and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-29 with Technology & Engineering categories.
This book addresses the experimental calibration of best-estimate numerical simulation models. The results of measurements and computations are never exact. Therefore, knowing only the nominal values of experimentally measured or computed quantities is insufficient for applications, particularly since the respective experimental and computed nominal values seldom coincide. In the author’s view, the objective of predictive modeling is to extract “best estimate” values for model parameters and predicted results, together with “best estimate” uncertainties for these parameters and results. To achieve this goal, predictive modeling combines imprecisely known experimental and computational data, which calls for reasoning on the basis of incomplete, error-rich, and occasionally discrepant information. The customary methods used for data assimilation combine experimental and computational information by minimizing an a priori, user-chosen, “cost functional” (usually a quadratic functional that represents the weighted errors between measured and computed responses). In contrast to these user-influenced methods, the BERRU (Best Estimate Results with Reduced Uncertainties) Predictive Modeling methodology developed by the author relies on the thermodynamics-based maximum entropy principle to eliminate the need for relying on minimizing user-chosen functionals, thus generalizing the “data adjustment” and/or the “4D-VAR” data assimilation procedures used in the geophysical sciences. The BERRU predictive modeling methodology also provides a “model validation metric” which quantifies the consistency (agreement/disagreement) between measurements and computations. This “model validation metric” (or “consistency indicator”) is constructed from parameter covariance matrices, response covariance matrices (measured and computed), and response sensitivities to model parameters. Traditional methods for computing response sensitivities are hampered by the “curse of dimensionality,” which makes them impractical for applications to large-scale systems that involve many imprecisely known parameters. Reducing the computational effort required for precisely calculating the response sensitivities is paramount, and the comprehensive adjoint sensitivity analysis methodology developed by the author shows great promise in this regard, as shown in this book. After discarding inconsistent data (if any) using the consistency indicator, the BERRU predictive modeling methodology provides best-estimate values for predicted parameters and responses along with best-estimate reduced uncertainties (i.e., smaller predicted standard deviations) for the predicted quantities. Applying the BERRU methodology yields optimal, experimentally validated, “best estimate” predictive modeling tools for designing new technologies and facilities, while also improving on existing ones.
Engineering Research
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Author : Herman Tang
language : en
Publisher: John Wiley & Sons
Release Date : 2020-12-03
Engineering Research written by Herman Tang and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-03 with Technology & Engineering categories.
Master the fundamentals of planning, preparing, conducting, and presenting engineering research with this one-stop resource Engineering Research: Design, Methods, and Publication delivers a concise but comprehensive guide on how to properly conceive and execute research projects within an engineering field. Accomplished professional and author Herman Tang covers the foundational and advanced topics necessary to understand engineering research, from conceiving an idea to disseminating the results of the project. Organized in the same order as the most common sequence of activities for an engineering research project, the book is split into three parts and nine chapters. The book begins with a section focused on proposal development and literature review, followed by a description of data and methods that explores quantitative and qualitative experiments and analysis, and ends with a section on project presentation and preparation of scholarly publication. Engineering Research offers readers the opportunity to understand the methodology of the entire process of engineering research in the real word. The author focuses on executable process and principle-guided exercise as opposed to abstract theory. Readers will learn about: An overview of scientific research in engineering, including foundational and fundamental concepts like types of research and considerations of research validity How to develop research proposals and how to search and review the scientific literature How to collect data and select a research method for their quantitative or qualitative experiment and analysis How to prepare, present, and submit their research to audiences and scholarly papers and publications Perfect for advanced undergraduate and engineering students taking research methods courses, Engineering Research also belongs on the bookshelves of engineering and technical professionals who wish to brush up on their knowledge about planning, preparing, conducting, and presenting their own scientific research.