State-Based Adjoint Method for Reduced Order Modeling

Introduced here is an adjoint state-based method for model reduction, which provides a single solution to two classes of reduction methods that are currently in the literature. The first class, which represents the main subject of this manuscript, is concerned with linear time invariant problems where one is interested in calculating linear responses variations resulting from initial conditions perturbations. The other class focuses on perturbations introduced in the operator, which result in nonlinear responses variations. Unlike existing adjoint-based methods where an adjoint function is calculated based on a given response, the state-based method employs the state variations to set up a number of adjoint problems, each corresponding to a pseudoresponse. This manuscript extends the applicability of state-based method to generate reduced order models for linear time invariant problems. Previous developments focusing on operator perturbations are reviewed briefly to highlight the common features of the state-based algorithm as applied to these two different classes of problems. Similar to previous developments, the state-based reduction is shown to set an upper-bound on the maximum discrepancy between the reduced and original model predictions. The methodology is applied and compared to other state-of-the-art methods employing several nuclear reactor diffusion and transport models.