In this talk, we address the improvement of the physical and numerical interpretation of the information involved in data assimilation with modern and efficient model reduction strategies for systems held by PDEs. Specifically, the data assimilation task is related with the state estimation for stationary problems, especially neutronic state estimation in nuclear reactor applications. In the first part, we analyze and adapt the generalized empirical interpolation method (GEIM) and the parametrized-background data-weak (PBDW) approach to the state estimation problem. We formulate the stability analysis for GEIM/PBDW. Then, we propose the so-called constrained stabilized GEIM/PBDW (CS-GEIM/CS-PBDW) approaches to improve the stability performance with respect to noisy measurements. A closed form so-called regularized GEIM/PBDW (R-GEIM/R-PBDW) are also proposed to improve the computational efficiency. In the second part, we apply the developed techniques to real case problems provided by the industrial partner EDF, namely, i) sensor placement in a nuclear reactor core and ii) neutronic field reconstruction with noisy or noise-free measurements. Numerical tests confirm the feasibility of developed techniques to address the important and inevitable concern of noisy measurements in the field of data assimilation with reduced basis.
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