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The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (2nd-FASAM-L): Mathematical Framework and Illustrative Application to an Energy System
Cacuci, D.G. The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (2nd-FASAM-L): Mathematical Framework and Illustrative Application to an Energy System. Energies2024, 17, 2263.
Cacuci, D.G. The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (2nd-FASAM-L): Mathematical Framework and Illustrative Application to an Energy System. Energies 2024, 17, 2263.
Cacuci, D.G. The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (2nd-FASAM-L): Mathematical Framework and Illustrative Application to an Energy System. Energies2024, 17, 2263.
Cacuci, D.G. The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (2nd-FASAM-L): Mathematical Framework and Illustrative Application to an Energy System. Energies 2024, 17, 2263.
Abstract
This work presents the mathematical framework of the Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “2nd-CASAM-L”), which enables the most efficient computation of exactly obtained mathematical expressions of first- and second-order sensitivities of a generic system response with respect to functions (“features”) of model parameters. Subsequently, the first- and second-order sensitivities with respect to the model’s uncertain parameters, boundaries, and internal interfaces are obtained analytically and exactly, without needing large-scale computations. Within the 2nd-FASAM-L methodology, the number of large-scale computations is proportional to the number of model features (defined as functions of model parameters), as opposed to being proportional to the number of model parameters, which are considerably more than the number of features, being incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities (of any order) with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces. The application of the 2nd-CASAM-L methodology is illustrated using a simplified energy-dependent neutron transport model of fundamental significance in nuclear reactor physics.
Keywords
exact computation of first- and second-order sensitivities of model responses to features of model parameters; first- and second-level adjoint sensitivity systems; neutron slowing down and transport
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
