Application of model-order reduction of non-linear time-dependent neutronics via POD-Galerkin projection and matrix discrete empirical interpolation

Abstract

Presented here is an application of model-order reduction to non-linear neutronic transients. The effort described extends previous work (Elzohery and Roberts, 2021b) aimed to develop and assess a Reduced-order model (ROM) framework that can be used for different purposes, such as design optimization and propagating input parameter uncertainties like nuclear data. Here, the target applications is non-linear. The ROM was built with the use of the POD-Galerkin projection method and the matrix version of the Discrete Empirical Interpolation Method (MDEIM) for improved efficiency. Where applications of the ROM to the diffusion equation have been introduced before, this work focuses on treating the non-linearity induced by coupling with different physics. Previous work has used DEIM to approximate non-linear functions resulting from multiphysics coupling such as the temperature and the velocity field (German et al., 2019, 2022). Here, the MDEIM is used to approximate the projection of the problem operator that otherwise must be computed at each non-linear iteration within each time step, which increases the ROM cost. By applying the method to the LRA benchmark, speed ups from 6 to 40 were achieved depending on the full-order model (FOM) spatial fidelity. The maximum relative error in the assemblies power was in the order of 1×10−5%. Moreover, the ROM was parameterized by POD-greedy sampling, and a case study was performed where the kinetic data, i.e., the precursor decay constants and delayed-neutron fraction were assumed to be the model parameters of interest. For the parameterized ROM, the maximum relative error in the assembly power was 1×10−3%, The computational gain from the MDEIM-ROM was compared with that of a direct projection ROM and showed that employing the MDEIM is computationally advantageous, and the advantage grows with dimension of the problem. The method was implemented in the open-source deterministic transport code Detran (Roberts, 2014) where only access to the system operator was needed to construct the ROM, and; hence, the method is trivially invasive and could easily be implemented in many modern deterministic diffusion codes.