Parametric neutron diffusion using proper generalized decomposition for uncertainty quantification

Uncertainty quantification (UQ) is the process of quantitatively determining the effect that uncertain parameters have on quantities of interest in a physical model. Parametric UQ considers these uncertain parameters by expanding the model into the parameter space. This parameterized model is inherently high-dimensional and evaluating it is often overtly burdensome. Proper generalized decomposition (PGD) is a reduced order modeling method that builds a small subspace on-the-fly to evaluating the model. This work applies PGD to steady-state, source-driven neutron diffusion where the material properties and source are parameterized. The result of system evaluation with PGD is a neutron flux that has unambiguous dependence on each material property. This PGD solution is then used to compute mean, variance, and probability distributions of several quantities of interest. Problems with various spatial and uncertain space dimensions are evaluated in order to illustrate PGD's ability to solve high-dimensional problems and analyze its convergence. (author)