Demonstration of prospective application of the dual number automatic differentiation for uncertainty propagation in neutronic calculations

Bokov, Pavel M.; Groenewald, Suzanne A.; Botes, Danniëll; Adetula, Bolade A.

doi:10.1016/j.anucene.2020.107925

Cited by 5 publications

(3 citation statements)

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“…The complex-and dual-step differentiation methods have been implemented in many areas, including nuclear engineering, for first-order derivative calculations. 7,8 Multidual differentiation is a major extension of complex-and dual-step differentiation because it allows one to compute arbitrary-order sensitivities with machine precision. However, this method requires multidual variables with multiple imaginary axes and a requisite numerical library to support multidual algebraic operations.…”

Section: Discussionmentioning

confidence: 99%

“…Also, the dual number differentiation method was used in Ref. 8 to calculate firstorder partial derivatives for a sensitivity and uncertainty analysis for a diffusion problem, again for the k-eigenvalue.…”

Section: Introductionmentioning

confidence: 99%

“…While complex and dual variables have been used to compute first-order derivatives, 7,8 this paper computes higher-order derivatives using multidual numbers. This extension is significant.…”

Section: Introductionmentioning

confidence: 99%

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Multidual Sensitivity Method in Ray-Tracing Transport Simulations

Balcer

Millwater

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2021

Nuclear Science and Engineering

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The multidual differentiation method has been implemented in a ray-tracing transport simulation for the purpose of calculating arbitrary-order sensitivities of the uncollided particle leakage. This method extends dual number differentiation by perturbing variables along multiple nonreal axes to calculate arbitrary-order derivatives. Numerical results of first-through third-order multidual sensitivities of the uncollided particle leakage with respect to isotope densities, microscopic cross sections, source emission rates, and material interface locations (including the outer boundary) are shown for a two-region sphere. The relative error of first and second partial derivatives with respect to isotopic parameters and first partial derivatives of the leakage with respect to interface locations are within 9.8E−10% of existing adjoint-based sensitivities. Higher-order multidual-based derivatives that are not available with the adjoint method are in excellent agreement with central difference approximations.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%