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Data-Driven Model Reduction, Scientific Frontiers, and Applications ()

Zachary Prince, Department of Nuclear Engineering
Parametric Uncertainty Quantification Using Proper Generalized Decomposition Applied to Neutron Diffusion


In this work, a Proper Generalized Decomposition (PGD) approach is employed for uncertainty quantification purposes. The neutron diffusion equation with external sources, a diffusion-reaction problem, is used as the parametric model. The uncertainty parameters include the zone-wise 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 3D models are also considered. To achieve and analyze a parametric PGD solution, algorithms are developed to decompose the model's parametric space and semi-analytically integrate solutions for evaluating statistical moments. Varying dimensional problems are evaluated in order to showcase PGD's ability to solve high-dimensional problems and analyze its convergence.