Exact-to-precision generalized perturbation theory for source-driven systems

Presented in this manuscript are new developments to perturbation theory which are intended to extend its applicability to estimate, with quantifiable accuracy, the exact variations in all responses calculated by the model with respect to all possible perturbations in the model's input parameters. The new developments place high premium on reducing the associated computational overhead in order to enable the use of perturbation theory in routine reactor design calculations. By way of examples, these developments could be employed in core simulation to accurately estimate the few-group cross-sections variations resulting from perturbations in neutronics and thermal-hydraulics core conditions. These variations are currently being described using a look-up table approach, where thousands of assembly calculations are performed to capture few-group cross-sections variations for the downstream core calculations. Other applications include the efficient evaluation of surrogates for applications that require repeated model runs such as design optimization, inverse studies, uncertainty quantification, and online core monitoring. The theoretical background of these developments applied to source-driven systems and supporting numerical experiments are presented in this manuscript. Extension to eigenvalue problems will be presented in a future article.

► We present a new development in higher order generalized perturbation theory.
► The method addresses the explosion in the flux phase space, input parameters, and responses.
► The method hybridizes first-order GPT and proper orthogonal decomposition snapshots method.
► A simplified 1D and realistic 2D assembly models demonstrate applicability of the method.
► The accuracy of the method is compared to exact direct perturbations and first-order GPT.