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=Volume 9 - 2021

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 approximate a physical system by combining observation data acquired from the system itself and a reduced model representing the underlying physical system. In presence of noise, the good properties of the approach are blurred in the sense that the approximation error no longer converges but even diverges. We propose to address this issue by imposing a smooth constrains, namely, an H1 semi-norm to involving some a priori knowledge of the noise and the geometry of the manifold formed by all the possible physical states of the system. The efficiency of the approach, which we will call H1 regularization GEIM (H-GEIM) is illustrated by numerical experiments dealing with the reconstruction of some numerical test sample. A theoretical justification of the procedure will be presented in future works.