The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume III

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The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume III by Dan Gabriel Cacuci

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.

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher Description

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 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.

Back Cover

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.

Table of Contents

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.

Feature

Describes the innovative C-ASAM methodology Describes representative large-scale applications Treats models that are nonlinear in the state variables

Details ISBN3031227565 Author Dan Gabriel Cacuci Short Title The Nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume III Publisher Springer International Publishing AG Language English Year 2023 ISBN-10 3031227565 ISBN-13 9783031227561 Format Hardcover Subtitle Overcoming the Curse of Dimensionality: Nonlinear Systems DOI 10.1007/978-3-031-22757-8 Imprint Springer International Publishing AG Place of Publication Cham Country of Publication Switzerland Pages 369 Publication Date 2023-04-12 UK Release Date 2023-04-12 DEWEY 003.5 Edition Description 2023 ed. Edition 2023rd Country of Origin NL Product Class Description Physics Alternative 9783031227578 Illustrations 20 Illustrations, color; 128 Illustrations, black and white Audience Educational: Primary & Secondary
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