  The Empirical Interpolation Method (EIM) and its generalized version (GEIM)
can be used to approximate a physical system by combining data measured from
the system itself and a reduced model representing the underlying physics. 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 a least-squares projection with constrains involving a
some a priori knowledge of the geometry of the manifold formed by all the
possible physical states of the system. The efficiency of the approach, which
we will call Constrained Stabilized GEIM (CS-GEIM), is illustrated by numerical
experiments dealing with the reconstruction of the neutron flux in nuclear
reactors. A theoretical justification of the procedure will be presented in
future works.
