Exact-to-precision generalzied perturbation theory for reactor design calculations

In this manuscript we have presented the application of exact-to-precision generalized perturbation theory (EPGPT) we recently developed to the reactor design calculations. EPGPT approach can be used to reconstruct the neutron flux and the responses of interest by means of a Neumann series expansion. Their application to reactor design calculations can be performed by pre-computing a set of forward fluxes and GPT fluxes, in this work the main details about how this is done are presented. The EPGPT approach makes use of both GPT approach and state reduction methods, i.e. proper orthogonal decomposition or POD of snapshots, to reduce the number of model executions and to allow one to calculate the higher-order variations in the responses of interest due to general parameters perturbations without having to re-execute the forward model. The computational cost is also inexpensive as it only involves simple inner products operations. This provides an enabling tool to analyze the impact of parameters variations on the responses variations as many times as needed for reactor design calculations.