Download or read book The Second Order Adjoint Sensitivity Analysis Methodology written by Dan Gabriel Cacuci and published by CRC Press. This book was released on 2018-02-19 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Second Order Adjoint Sensitivity Analysis Methodology written by Dan Gabriel Cacuci and published by CRC Press. This book was released on 2018-02-19 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Sensitivity Uncertainty Analysis Volume 1 written by Dan G. Cacuci and published by CRC Press. This book was released on 2003-05-28 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book The nth Order Comprehensive Adjoint Sensitivity Analysis Methodology Volume II written by Dan Gabriel Cacuci and published by Springer Nature. This book was released on 2023-04-26 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The nth Order Comprehensive Adjoint Sensitivity Analysis Methodology Volume I written by Dan Gabriel Cacuci and published by Springer Nature. This book was released on 2022-07-19 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The nth Order Comprehensive Adjoint Sensitivity Analysis Methodology Volume III written by Dan Gabriel Cacuci and published by Springer Nature. This book was released on 2023-04-11 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book SECOND ORDER ADJOINT SENSITIVITY ANALYSIS METHODOLOGY written by DAN GABRIEL. CACUCI and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applications of Data Assimilation and Inverse Problems in the Earth Sciences written by Alik Ismail-Zadeh and published by Cambridge University Press. This book was released on 2023-06-30 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Adjoint Sensitivity Analysis of High Frequency Structures with MATLAB written by Mohamed H. Bakr and published by IET. This book was released on 2017-03-24 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique reference is the first to cover the theory of adjoint sensitivity analysis and explains how it can be applied to different types of electromagnetic structures. It is an invaluable book for anyone looking for an in-depth understanding of this useful theory for application in high-frequency electromagnetic problems. It uses the popular FDTD method to show how wideband sensitivities can be efficiently estimated for different types of materials and structures, and includes plenty of well-explained MATLAB(R) examples to help readers absorb the content more easily. Topics covered include a review of FDTD and an introduction to adjoint sensitivity analysis; sensitivity of the fields to changes in material parameters; sensitivity of S parameters; extension to dispersive material parameters, where the underlying FDTD algorithm must be modified; second-order sensitivity analysis; time-domain responses; and applications to nonlinear and anisotropic materials. This book will make the theory more understandable to the broadest possible audience. It will be useful for researchers and advanced students involved in computational techniques for electromagnetics, and other disciplines such as microwave, optics, acoustics, and semiconductor modelling.

Download or read book Advances in High Order Predictive Modeling written by Dan Gabriel Cacuci and published by CRC Press. This book was released on 2024-12-11 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing the author’s previous work on modeling, this book presents the most recent advances in high-order predictive modeling. The author begins with the mathematical framework of the 2nd-BERRU-PM methodology, an acronym that designates the “second-order best-estimate with reduced uncertainties (2nd-BERRU) predictive modeling (PM).” The 2nd-BERRU-PM methodology is fundamentally anchored in physics-based principles stemming from thermodynamics (maximum entropy principle) and information theory, being formulated in the most inclusive possible phase-space, namely the combined phase-space of computed and measured parameters and responses. The 2nd-BERRU-PM methodology provides second-order output (means and variances) but can incorporate, as input, arbitrarily high-order sensitivities of responses with respect to model parameters, as well as arbitrarily high-order moments of the initial distribution of uncertain model parameters, in order to predict best-estimate mean values for the model responses (i.e., results of interest) and calibrated model parameters, along with reduced predicted variances and covariances for these predicted responses and parameters.

Download or read book Adjoint Equations and Analysis of Complex Systems written by Guri I. Marchuk and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: New statements of problems arose recently demanding thorough ana lysis. Notice, first of all, the statements of problems using adjoint equations which gradually became part of our life. Adjoint equations are capable to bring fresh ideas to various problems of new technology based on linear and nonlinear processes. They became part of golden fund of science through quantum mechanics, theory of nuclear reactors, optimal control, and finally helped in solving many problems on the basis of perturbation method and sensitivity theory. To emphasize the important role of adjoint problems in science one should mention four-dimensional analysis problem and solution of inverse problems. This range of problems includes first of all problems of global climate changes on our planet, state of environment and protection of environ ment against pollution, preservation of the biosphere in conditions of vigorous growth of population, intensive development of industry, and many others. All this required complex study of large systems: interac tion between the atmosphere and oceans and continents in the theory of climate, cenoses in the biosphere affected by pollution of natural and anthropogenic origin. Problems of local and global perturbations and models sensitivity to input data join into common complex system.

Download or read book Theoretical Aspects of Industrial Design written by David Anthony Field and published by SIAM. This book was released on 1992-01-01 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Atmospheric Rivers written by F. Martin Ralph and published by Springer Nature. This book was released on 2020-07-10 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the standard reference based on roughly 20 years of research on atmospheric rivers, emphasizing progress made on key research and applications questions and remaining knowledge gaps. The book presents the history of atmospheric-rivers research, the current state of scientific knowledge, tools, and policy-relevant (science-informed) problems that lend themselves to real-world application of the research—and how the topic fits into larger national and global contexts. This book is written by a global team of authors who have conducted and published the majority of critical research on atmospheric rivers over the past years. The book is intended to benefit practitioners in the fields of meteorology, hydrology and related disciplines, including students as well as senior researchers.

Download or read book Engineering Research written by Herman Tang and published by John Wiley & Sons. This book was released on 2020-12-03 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Download or read book Global Sensitivity Analysis written by Andrea Saltelli and published by John Wiley & Sons. This book was released on 2008-02-28 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex mathematical and computational models are used in all areas of society and technology and yet model based science is increasingly contested or refuted, especially when models are applied to controversial themes in domains such as health, the environment or the economy. More stringent standards of proofs are demanded from model-based numbers, especially when these numbers represent potential financial losses, threats to human health or the state of the environment. Quantitative sensitivity analysis is generally agreed to be one such standard. Mathematical models are good at mapping assumptions into inferences. A modeller makes assumptions about laws pertaining to the system, about its status and a plethora of other, often arcane, system variables and internal model settings. To what extent can we rely on the model-based inference when most of these assumptions are fraught with uncertainties? Global Sensitivity Analysis offers an accessible treatment of such problems via quantitative sensitivity analysis, beginning with the first principles and guiding the reader through the full range of recommended practices with a rich set of solved exercises. The text explains the motivation for sensitivity analysis, reviews the required statistical concepts, and provides a guide to potential applications. The book: Provides a self-contained treatment of the subject, allowing readers to learn and practice global sensitivity analysis without further materials. Presents ways to frame the analysis, interpret its results, and avoid potential pitfalls. Features numerous exercises and solved problems to help illustrate the applications. Is authored by leading sensitivity analysis practitioners, combining a range of disciplinary backgrounds. Postgraduate students and practitioners in a wide range of subjects, including statistics, mathematics, engineering, physics, chemistry, environmental sciences, biology, toxicology, actuarial sciences, and econometrics will find much of use here. This book will prove equally valuable to engineers working on risk analysis and to financial analysts concerned with pricing and hedging.

Download or read book Adjoint Equations and Perturbation Algorithms in Nonlinear Problems written by Guri I. Marchuk and published by CRC Press. This book was released on 2018-04-24 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparked by demands inherent to the mathematical study of pollution, intensive industry, global warming, and the biosphere, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems is the first book ever to systematically present the theory of adjoint equations for nonlinear problems, as well as their application to perturbation algorithms. This new approach facilitates analysis of observational data, the application of adjoint equations to retrospective study of processes governed by imitation models, and the study of computer models themselves. Specifically, the book discusses: Principles for constructing adjoint operators in nonlinear problems Properties of adjoint operators and solvability conditions for adjoint equations Perturbation algorithms using the adjoint equations theory for nonlinear problems in transport theory, quasilinear motion, substance transfer, and nonlinear data assimilation Known results on adjoint equations and perturbation algorithms in nonlinear problems This groundbreaking text contains some results that have no analogs in the scientific literature, opening unbounded possibilities in construction and application of adjoint equations to nonlinear problems of mathematical physics.