This work addresses the problem of propagating uncertainty from group-wise
neutron cross-sections to the results of neutronics diffusion calculations.
Automatic differentiation based on dual number arithmetic was applied to
uncertainty propagation in the framework of local sensitivity analysis. As
an illustration, we consider a two-group diffusion problem in an infinite
medium, which has a solution in a closed form. We employ automatic
differentiation in conjunction with the sandwich formula for uncertainty
propagation in three ways. Firstly, by evaluating the analytical expression
for the multiplication factor using dual number arithmetic. Then, by solving
the diffusion problem with the power iteration algorithm and the algebra of
dual matrices. Finally, automatic differentiation is used to calculate the
partial derivatives of the production and loss operators in the perturbation
formula from the adjoint-weighted technique. The numerical solution of the
diffusion problem is verified against the analytical formulas and the
results of the uncertainty calculations are compared with those from the
global sensitivity analysis approach. The uncertainty values obtained in
this work differ from values given in the literature by less than 1?10?5.
Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation
