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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  H  1  semi-norm of the reconstructed field of the reduced model. The efficiency of the approach, which we will call the  H  1  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.

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