Wideband Second-Order Adjoint Sensitivity Analysis Exploiting TLM

Nuclear Science and Engineering

2019

This work presents an application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the neutron transport Boltzmann equation that models a multiplying subcritical system comprising a nonfission neutron source to compute efficiently and exactly all of the first-and second-order functional derivatives (sensitivities) of a detector's response to all of the model's parameters, including isotopic number densities, microscopic cross sections, fission spectrum, sources, and detector response function. As indicated by the general theoretical considerations underlying the 2nd-ASAM, the number of computations required to obtain the first and second orders increases linearly in augmented Hilbert spaces as opposed to increasing exponentially in the original Hilbert space. The results presented in this work are currently being implemented in several production-oriented three-dimensional neutron transport code systems for analyzing specific subcritical systems.

Section: Introductionmentioning

confidence: 99%

Application of the Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology to Compute First- and Second-Order Sensitivities of Flux Functionals in a Multiplying System with Source

Nuclear Science and Engineering

2019

“…The "2 nd -ASAM for linear systems" considers nonlinear responses associated with physical systems modeled mathematically by systems of linear operator equations. The comparative discussion presented in [1] regarding the basic properties of the leading methods (deterministic and/or statistical) used for computing second-order sensitivities [2][3][4][5][6][7][8] and the fundamentally new and distinctive features of 2 nd -ASAM for linear systems introduced in [1] highlighted the unparalleled efficiency of the 2 nd -ASAM for linear systems for computing 2 nd -order sensitivities exactly. Since the comparative discussion presented in [1] continues to remain valid in the context of the new 2 nd -ASAM for nonlinear systems which will be introduced in this work, that discussion will not be repeated here.…”

Section: Introductionmentioning

confidence: 99%

The Second-Order Adjoint Sensitivity Analysis Methodology for Nonlinear Systems—I: Theory

Nuclear Science and Engineering

2016

This work presents the second-order adjoint sensitivity analysis methodology (2 nd -ASAM) for nonlinear systems, which yields exactly and efficiently the second-order functional derivatives of physical (engineering, biological, etc.) system responses (i.e., "system performance parameters") to the system's model parameters. The definition of "system parameters" used in this work includes all computational input data, correlations, initial and/or boundary conditions, etc. For a physical system comprising N α parameters responses, 1 , ,x

Second-order adjoint sensitivity analysis methodology (2nd-ASAM) for computing exactly and efficiently first- and second-order sensitivities in large-scale linear systems: I. Computational methodology

Journal of Computational Physics

2015

This work presents the second-order forward and adjoint sensitivity analysis procedures (SO-FSAP and SO-ASAP) for computing exactly and efficiently the second-order functional derivatives of physical (engineering, biological, etc.) system responses (i.e., "system performance parameters") to the system's model parameters. The definition of "system parameters" used in this work includes all computational input data, correlations, initial and/or boundary conditions, etc. For a physical system comprising N α parameters and r N responses, we note that the SO-FSAP requires a total of ( )computations for obtaining all of the first-and second-order sensitivities, for all r N system responses. On the other hand, the SO-ASAP requires a total of ( )large-scale computations for obtaining all of the first-and second-order sensitivities, for one functionaltype system responses. Therefore, the SO-FSAP should be used when r N N α  , while the SO-ASAP should be used when r N N α  . The original SO-ASAP presented in this work should enable the hitherto very difficult, if not intractable, exact computation of all of the second-order response sensitivities (i.e., functional Gateaux-derivatives) for large-systems involving many parameters, as usually encountered in practice. Very importantly, the implementation of the SO-ASAP requires very little additional effort beyond the construction of the adjoint sensitivity system needed for computing the first-order sensitivities.KEYWORDS: second-order adjoint sensitivity analysis procedure (SO-ASAP); exact and efficient computation of first-and second-order functional derivatives; large-scale systems.2