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001448376 019__ $$a1336953520$$a1337066947
001448376 020__ $$a9783030963644$$q(electronic bk.)
001448376 020__ $$a3030963640$$q(electronic bk.)
001448376 020__ $$z9783030963637
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001448376 0247_ $$a10.1007/978-3-030-96364-4$$2doi
001448376 035__ $$aSP(OCoLC)1337159529
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001448376 1001_ $$aCacuci, Dan Gabriel,$$eauthor.$$1https://isni.org/isni/0000000116707826
001448376 24514 $$aThe nth-order comprehensive adjoint sensitivity analysis methodology.$$nVolume I,$$pOvercoming the curse of dimensionality : linear systems /$$cDan Gabriel Cacuci.
001448376 24630 $$aOvercoming the curse of dimensionality : linear systems
001448376 264_1 $$aCham :$$bSpringer,$$c[2022]
001448376 264_4 $$c©2022
001448376 300__ $$a1 online resource
001448376 336__ $$atext$$btxt$$2rdacontent
001448376 337__ $$acomputer$$bc$$2rdamedia
001448376 338__ $$aonline resource$$bcr$$2rdacarrier
001448376 504__ $$aIncludes bibliographical references and index.
001448376 5050_ $$aChapter 1. Introduction and Motivation: Breaking the Curse of Dimensionality in Sensitivity and Uncertainty Analysis. Part A: Function-Valued Responses -- Chapter 2. Part A: Function-Valued Responses-The First- and Second-Order Comprehensive Adjoint Sensitivity Analysis Methodologies for Linear Systems with Function-Valued Responses -- Chapter 3. The Third-Order Comprehensive Adjoint Sensitivity Analysis Methodology (C-ASAM-3) for Linear Systems with Function-Valued Responses -- Chapter 4. The Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (C-ASAM-4) for Linear Systems with Function-Valued Responses -- Chapter 5. The Nth-Order Adjoint Sensitivity Analysis Methodology (C-ASAM-N) for Linear Systems with Function-Valued Responses -- Chapter 6. Part B: Scalar-Valued Responses-The Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (C-ASAM-4) for Linear Systems with Scalar-Valued Responses -- Chapter 7. The Nth-Order Adjoint Sensitivity Analysis Methodology (C-ASAM-N) for Linear Systems with Scalar-Valued Responses.
001448376 506__ $$aAccess limited to authorized users.
001448376 520__ $$aThe 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?" 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" 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 systems uncertain boundaries and internal interfaces in phase-space. The models responses can be either scalar-valued functionals of the models 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.
001448376 588__ $$aDescription based on print version record.
001448376 650_0 $$aSensitivity theory (Mathematics)
001448376 650_0 $$aLarge scale systems.
001448376 650_0 $$aLinear systems.
001448376 650_6 $$aThéorie de la sensibilité (Mathématiques)$$0(CaQQLa)201-0313296
001448376 650_6 $$aSystèmes de grandes dimensions.$$0(CaQQLa)201-0128787
001448376 650_6 $$aSystèmes linéaires.$$0(CaQQLa)201-0041485
001448376 655_0 $$aElectronic books.
001448376 77608 $$iPrint version:$$aCacuci, Dan Gabriel.$$tNth-order comprehensive adjoint sensitivity analysis methodology. Volume I, Overcoming the curse of dimensionality : linear systems.$$dCham : Springer, 2022$$z9783030963637$$w(OCoLC)1308603467
001448376 852__ $$bebk
001448376 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-96364-4$$zOnline Access$$91397441.1
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001448376 980__ $$aBIB
001448376 980__ $$aEBOOK
001448376 982__ $$aEbook
001448376 983__ $$aOnline
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