High fidelity simulations in nuclear reactor physics inherently lie in high-parameter spaces and commonly suffer from the "curse of dimensionality". Current methods used to overcome this computational expense for transient neutron transport include lower-order moments-based angular treatments, fewer-group energy discretizations, and spatial homogenization / upscaling. However, the effect of errors and uncertainties associated with these approaches increase when they are coupled to other physical systems (i.e. fluid dynamics, structural mechanics, material models, etc).
The combination of high parametric space and increasing need for high-fidelity calculations has led to a developing interest in applications of contemporary reduced order modeling methods. Due to the inherent high-dimensionality of many nuclear reactor physics problems, obtaining high quality experimental or simulation data can be difficult and costly; thus making the use of more developed a-posteriori data-driven methods (such as Proper Orthogonal Decomposition) infeasible.
This work focuses on employing what is known as Proper Generalized Decomposition (PGD) for transient neutron diffusion. PGD is an a-priori decomposition based method that seeks a solution to a differential equation that is represented through a series expansion whose components are products of separable functions in each dimension of interest. The exponential nature of the "curse of dimensionality" is reduced to a linear relationship. It can be shown that for a transient simulation in 1D space, an L2 difference of 0.0913 between a reference analytical solution and the approximated PGD solution can be produced. An overview of the PGD algorithm will be presented along with results for transient problems in 1D space as well as preliminary results for problems in 2D space.