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The nth-order comprehensive adjoint ...

Cacuci, Dan Gabriel.

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The nth-order comprehensive adjoint sensitivity analysis methodology.. Volume III,. Overcoming the curse of dimensionality : nonlinear systems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The nth-order comprehensive adjoint sensitivity analysis methodology./ by Dan Gabriel Cacuci.
其他題名:	Overcoming the curse of dimensionality :
作者:	Cacuci, Dan Gabriel.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xii, 369 p. :ill., digital ;24 cm.
內容註:	Part A: Function-Valued Responses. Chapter 1: The First- and Second-Order Comprehensive Adjoint Sensitivity Analysis Methodologies for Nonlinear Systems with Function-Valued Responses -- Chapter 2: The Third-Order Comprehensive Adjoint Sensitivity Analysis Methodology (C-ASAM-3) for Nonlinear Systems with Function-Valued Responses -- Chapter 3: The Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (C-ASAM-4) for Nonlinear Systems with Function-Valued Responses -- Chapter 4: The Nth-Order Adjoint Sensitivity Analysis Methodology (C-ASAM-N) for Nonlinear Systems with Function-Valued Responses -- Part B: Scalar-Valued Responses -- Part B: Scalar-Valued Responses -- Chapter 5: The Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (C-ASAM-4) for Nonlinear Systems with Scalar-Valued Responses -- Chapter 6: The Nth-Order Adjoint Sensitivity Analysis Methodology (C-ASAM-N) for Nonlinear Systems with Scalar-Valued Responses -- Chapter 7: Applications of C-ASAM to Uncertainty Analysis.
Contained By:	Springer Nature eBook
標題:	Sensitivity theory (Mathematics) -
電子資源:	https://doi.org/10.1007/978-3-031-22757-8
ISBN:	9783031227578

The nth-order comprehensive adjoint sensitivity analysis methodology.. Volume III,. Overcoming the curse of dimensionality : nonlinear systems
Cacuci, Dan Gabriel.

The nth-order comprehensive adjoint sensitivity analysis methodology.Volume III,Overcoming the curse of dimensionality : nonlinear systems[electronic resource] /Overcoming the curse of dimensionality :nonlinear systemsby Dan Gabriel Cacuci. - Cham :Springer International Publishing :2023. - xii, 369 p. :ill., digital ;24 cm.

Part A: Function-Valued Responses. Chapter 1: The First- and Second-Order Comprehensive Adjoint Sensitivity Analysis Methodologies for Nonlinear Systems with Function-Valued Responses -- Chapter 2: The Third-Order Comprehensive Adjoint Sensitivity Analysis Methodology (C-ASAM-3) for Nonlinear Systems with Function-Valued Responses -- Chapter 3: The Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (C-ASAM-4) for Nonlinear Systems with Function-Valued Responses -- Chapter 4: The Nth-Order Adjoint Sensitivity Analysis Methodology (C-ASAM-N) for Nonlinear Systems with Function-Valued Responses -- Part B: Scalar-Valued Responses -- Part B: Scalar-Valued Responses -- Chapter 5: The Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (C-ASAM-4) for Nonlinear Systems with Scalar-Valued Responses -- Chapter 6: The Nth-Order Adjoint Sensitivity Analysis Methodology (C-ASAM-N) for Nonlinear Systems with Scalar-Valued Responses -- Chapter 7: Applications of C-ASAM to Uncertainty Analysis.

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.

ISBN: 9783031227578

Standard No.: 10.1007/978-3-031-22757-8doiSubjects--Topical Terms:

652195
Sensitivity theory (Mathematics)

LC Class. No.: QA402.3

Dewey Class. No.: 003.5

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520 $a 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.
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