Generalized Empirical Interpolation Method With H1 Regularization: Application to Nuclear Reactor Physics

Abstract

The generalized empirical interpolation method (GEIM) can be used to estimate the physical field by combining observation data acquired from the physical system itself and a reduced model of the underlying physical system. In presence of observation noise, the estimation error of the GEIM is blurred even diverged. We propose to address this issue by imposing a smooth constraint, namely, to constrain the H1 semi-norm of the reconstructed field of the reduced model. The efficiency of the approach, which we will call the H1 regularization GEIM (R-GEIM), is illustrated by numerical experiments of a typical IAEA benchmark problem in nuclear reactor physics. A theoretical analysis of the proposed R-GEIM will be presented in future works.