AUTHOR=Gong Helin , Chen Zhang , Li Qing TITLE=Generalized Empirical Interpolation Method With H1 Regularization: Application to Nuclear Reactor Physics JOURNAL=Frontiers in Energy Research VOLUME=9 YEAR=2022 URL=https://www.frontiersin.org/journals/energy-research/articles/10.3389/fenrg.2021.804018 DOI=10.3389/fenrg.2021.804018 ISSN=2296-598X 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.