Abstract
This work illustrates the application of the nth-order comprehensive adjoint sensitivity analysis methodology for response-coupled forward/adjoint linear systems (abbreviated as “nth-CASAM-L”) to a paradigm model that describes the transmission of particles (neutrons and/or photons) through homogenized materials, as encountered in radiation protection and shielding. The first-, second-, and third-order sensitivities of responses that depend on both the forward and adjoint particle fluxes are obtained exactly, in closed-form, underscoring the principles and methodology underlying the nth-CASAM-L. The results presented in this work underscore the fundamentally important role of the nth-CASAM-L in the quest to overcome the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling.
Highlights
The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems, which is presented in the accompanying work [1], enables the most efficient computation of exactly obtained expressions of arbitrarily-high-order sensitivities of a generic system response with respect to all of the parameters underlying the respective forward/adjoint systems
The application of the nth-CASAM-L is illustrated in this work by considering paradigm model which describes the transmission of particles produced by a distributed source through a shield which surrounds the source
The salient characteristics underlying the determination of the remaining 2nd-order sensitivities of the contributon-response flux ρ(φ, ψ; α) are summarized below: (i) As shown in Equation (151), the 1st-order sensitivity ∂ρ(φ, ψ; α)/∂q∗ depends on the 1st-level adjoint function a2(1)(z, ω), just like the sensitivity ∂ρ(φ, ψ; α)/∂b2
Summary
The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-. Coupled Forward/Adjoint Linear Systems (abbreviated as “nth-CASAM-L”), which is presented in the accompanying work [1], enables the most efficient computation of exactly obtained expressions of arbitrarily-high-order (nth-order) sensitivities of a generic system response with respect to all of the parameters (including boundary and initial conditions − the qualifier “comprehensive”) underlying the respective forward/adjoint systems. The application of the nth-CASAM-L is illustrated in this work by considering paradigm model which describes the transmission of particles produced by a distributed source through a shield which surrounds the source.
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