05737nam 22008175 450 991069864130332120250610110234.09783031227578303122757310.1007/978-3-031-22757-8(CKB)5590000001037871(DE-He213)978-3-031-22757-8(MiAaPQ)EBC7236714(Au-PeEL)EBL7236714(MiAaPQ)EBC7236378(EXLCZ)99559000000103787120230411d2023 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierThe nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume III Overcoming the Curse of Dimensionality: Nonlinear Systems /by Dan Gabriel Cacuci1st ed. 2023.Cham :Springer International Publishing :Imprint: Springer,2023.1 online resource (XII, 369 p. 148 illus., 20 illus. in color.) 9783031227561 3031227565 Includes bibliographical references and index.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.Mathematical physicsComputer simulationMathematical modelsStatisticsEnergy policyEnergy policyEngineering mathematicsEngineeringData processingNuclear physicsComputational Physics and SimulationsMathematical Modeling and Industrial MathematicsStatistical Theory and MethodsEnergy Policy, Economics and ManagementMathematical and Computational Engineering ApplicationsNuclear PhysicsMathematical physics.Computer simulation.Mathematical models.Statistics.Energy policy.Energy policy.Engineering mathematics.EngineeringData processing.Nuclear physics.Computational Physics and Simulations.Mathematical Modeling and Industrial Mathematics.Statistical Theory and Methods.Energy Policy, Economics and Management.Mathematical and Computational Engineering Applications.Nuclear Physics.003.5003.5Cacuci Dan Gabriel897247MiAaPQMiAaPQMiAaPQBOOK9910698641303321The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume III4349685UNINA