nth-order feature adjoint sensitivity analysis methodology for response-coupled forward/adjoint linear systems: II. Illustrative application to a paradigm energy system

This work presents a representative application of the newly developed “nth-order feature adjoint sensitivity analysis methodology for response-coupled forward/adjoint linear systems” (abbreviated as “nth-FASAM-L”), which enables the most efficient computation of exactly obtained mathematical 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) underlying the respective forward/adjoint systems. The nth-FASAM-L has been developed to treat responses of linear systems that simultaneously depend on both the forward and adjoint state functions. Such systems cannot be considered particular cases of nonlinear systems, as illustrated in this work by analyzing an analytically solvable model of the energy distribution of the “contributon flux” of neutrons in a mixture of materials. The unparalleled efficiency and accuracy of the nth-FASAM-L stem from the maximal reduction in the number of adjoint computations (which are “large-scale” computations) for determining the exact expressions of arbitrarily high-order sensitivities since the number of large-scale computations when applying the nth-FASAM-N is proportional to the number of model features as opposed to the number of model parameters (which are considerably more than the number of features). Hence, the higher the order of computed sensitivities, the more efficient the nth-FASAM-N becomes compared to any other methodology. Furthermore, as illustrated in this work, the probability of encountering identically vanishing sensitivities is much higher when using the nth-FASAM-L than other methods.