LEADER 05737nam 22008175 450 001 9910698641303321 005 20250610110234.0 010 $a9783031227578 010 $a3031227573 024 7 $a10.1007/978-3-031-22757-8 035 $a(CKB)5590000001037871 035 $a(DE-He213)978-3-031-22757-8 035 $a(MiAaPQ)EBC7236714 035 $a(Au-PeEL)EBL7236714 035 $a(MiAaPQ)EBC7236378 035 $a(EXLCZ)995590000001037871 100 $a20230411d2023 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume III $eOvercoming the Curse of Dimensionality: Nonlinear Systems /$fby Dan Gabriel Cacuci 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (XII, 369 p. 148 illus., 20 illus. in color.) 311 08$a9783031227561 311 08$a3031227565 320 $aIncludes bibliographical references and index. 327 $aPart 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. 330 $aThis 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. 606 $aMathematical physics 606 $aComputer simulation 606 $aMathematical models 606 $aStatistics 606 $aEnergy policy 606 $aEnergy policy 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aNuclear physics 606 $aComputational Physics and Simulations 606 $aMathematical Modeling and Industrial Mathematics 606 $aStatistical Theory and Methods 606 $aEnergy Policy, Economics and Management 606 $aMathematical and Computational Engineering Applications 606 $aNuclear Physics 615 0$aMathematical physics. 615 0$aComputer simulation. 615 0$aMathematical models. 615 0$aStatistics. 615 0$aEnergy policy. 615 0$aEnergy policy. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 0$aNuclear physics. 615 14$aComputational Physics and Simulations. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aStatistical Theory and Methods. 615 24$aEnergy Policy, Economics and Management. 615 24$aMathematical and Computational Engineering Applications. 615 24$aNuclear Physics. 676 $a003.5 676 $a003.5 700 $aCacuci$b Dan Gabriel$0897247 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910698641303321 996 $aThe nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume III$94349685 997 $aUNINA