{"product_id":"the-nth-order-comprehensive-adjoint-sensitivity-dan-gabriel-cacuci-9783030963637","title":"The Nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume I: Overcoming the Curse of Dimensionality: Linear Systems","description":"\u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003eThis 3-Volume monograph describes a \u003ci\u003ecomprehensive adjoint sensitivity analysis methodology\u003c\/i\u003e, 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. \u003c\/p\u003e \u003cp\u003eSince 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 \u003ci\u003en\u003csup\u003eth\u003c\/sup\u003e-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward\/Adjoint Linear Systems\u003c\/i\u003e (abbreviated as \"n\u003csup\u003eth\u003c\/sup\u003e-CASAM-L\"), which is conceived for the most efficient computation of \u003ci\u003eexactly obtained\u003c\/i\u003e mathematical expressions of arbitrarily-high-order (n\u003csup\u003eth\u003c\/sup\u003e-order) sensitivities of a generic system response with respect to \u003ci\u003eall\u003c\/i\u003e of the parameters underlying the respective forward\/adjoint systems. Volume 2 of this book presents the application of the n\u003csup\u003eth\u003c\/sup\u003e-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 n\u003csup\u003eth\u003c\/sup\u003e-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 \"\u003ci\u003en\u003csup\u003eth\u003c\/sup\u003e-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems\u003c\/i\u003e\" (abbreviation: n\u003csup\u003eth\u003c\/sup\u003e-CASAM-N) for the practical, efficient, and exact computation of arbitrarily-high ord\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Dan Gabriel Cacuci\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3030963632\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783030963637\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/20\/2022\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 362\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.55lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.88d\u003c\/p\u003e","brand":"Dan Gabriel Cacuci","offers":[{"title":"Hardcover","offer_id":44159370395903,"sku":"9783030963637","price":179.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_8ca2d551-3e29-40ed-9474-c93db673b167.jpg?v=1689082202","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-nth-order-comprehensive-adjoint-sensitivity-dan-gabriel-cacuci-9783030963637","provider":"WR Book House","version":"1.0","type":"link"}