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

The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as "2nd-FASAM-L"), presented in this work, enables the most efficient computation of exactly obtained mathematical expressions of first- and second-order sensitivities of a generic system response with respect to the 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. This characteristic enables the 2nd-FASAM-L methodology to maximize the efficiency and accuracy of any other method for computing exact expressions of first- and second-order response sensitivities with respect to the model's features and/or primary uncertain parameters. The application of the 2nd-FASAM-L methodology is illustrated using a simplified energy-dependent neutron transport model of fundamental significance in nuclear reactor physics.