Parametric uncertainty quantification using proper generalized decomposition applied to neutron diffusion

SummaryIn this paper, a proper generalized decomposition (PGD) approach is employed for uncertainty quantification purposes. The neutron diffusion equation with external sources, a diffusionreaction problem, is used as the parametric model. The uncertainty parameters include the zonewise constant material diffusion and reaction coefficients as well as the source strengths, yielding a large uncertain space in highly heterogeneous geometries. The PGD solution, parameterized in all uncertain variables, can then be used to compute mean, variance, and more generally probability distributions of various quantities of interest. In addition to parameterized properties, parameterized geometrical variations of threedimensional models are also considered in this paper. To achieve and analyze a parametric PGD solution, algorithms are developed to decompose the model's parametric space and semianalytically integrate solutions for evaluating statistical moments. Varying dimensional problems are evaluated to showcase PGD's ability to solve highdimensional problems and analyze its convergence.

Parametric uncertainty quantification using proper generalized decomposition applied to neutron diffusion Academic Article