Stochastic Higher-Order Generalized Perturbation Theory for Neutron Diffusion and Transport Calculations

The role of scientific computing has been heavily promoted in many fields to improve understanding the physics of complex engineering systems in recent years while conduct the experiments can be time-consuming, inflexible, expensive and difficult to repeat, e.g. nuclear reactor systems. The ultimate goal of scientific computing is to provide more reliable predictions for engineering systems within certain acceptable tolerance. To realize the benefits of scientific computing, extensive effort has been devoted to the development of efficient algorithms for Sensitivity Analysis (SA) and Uncertainty Quantification (UQ) whose numerical errors is under control and understood. However, the repeated execution of the simulations with different samples is computationally intractable for large-scale system with large number of Degrees of Freedom (DOF). The object of this manuscript will be focus on presenting our own developments of stochastic higher-order generalized perturbation theory to address the explosion in the computational load burden. Additionally, an overview of the current state-of-the-art of SA/UQ will also be provided.