The nth-order comprehensive adjoint sensitivity analysis methodology. Volume III, Overcoming the curse of dimensionality : nonlinear systems / Dan Gabriel Cacuci.
Cacuci, Dan Gabriel, author.
2023
QA402.3 .C34 2023
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Title The nth-order comprehensive adjoint sensitivity analysis methodology. Volume III, Overcoming the curse of dimensionality : nonlinear systems / Dan Gabriel Cacuci.
Author Cacuci, Dan Gabriel, author.
ISBN 9783031227578 electronic book
3031227573 electronic book
9783031227561
3031227565
DOI https://doi.org/10.1007/978-3-031-22757-8
Published Cham, Switzerland : Springer, [2023]
Language English
Description 1 online resource (xii, 369 pages) : illustrations
Item Number 10.1007/978-3-031-22757-8 doi
Call Number QA402.3 .C34 2023
Dewey Decimal Classification 515/.642
Summary 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 models responses can be either scalar-valued functionals of the models 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-ASAMs 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on online resource; title from digital title page (viewed on May 25, 2023).
Available in Other Form Nth-order comprehensive adjoint sensitivity analysis methodology. Volume III, Overcoming the curse of dimensionality.
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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.

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