Exact-to-precision generalized perturbation theory for neutron transport calculation

Abstract

This manuscript extends the exact-to-precision generalized perturbation theory (EPGPT), introduced previously, to neutron transport calculation whereby previous developments focused on neutron diffusion calculation only. The EPGPT collectively denotes new developments in generalized perturbation theory (GPT) that place premium on computational efficiency and defendable accuracy in order to render GPT a standard analysis tool in routine design and safety reactor calculations. EPGPT constructs a surrogate model with quantifiable accuracy that can replace the original neutron transport model for subsequent engineering analysis. This is achieved by reducing the effective dimensionality of the state variable (i.e. neutron angular flux) via projection onto an active subspace determined using reduced order modeling techniques. Confining the state variations to the active subspace allows one to recast the problem in terms of a small number of ‘pseudo’ responses which are solely dependent on the physics model rather than on the nominal number of responses, the input parameters, or the number of points in the state phase space. This renders a computationally efficient construction of the surrogate whose form is determined using a recursive relationship from the solution of the transport equation. Unlike conventional surrogate techniques, the EPGPT can upper-bound the errors resulting from its predictions with high probability, which can be preset by the user.