  Physical models often contain unknown functions and relations. The goal of
our work is to answer the question of how one should excite or control a system
under consideration in an appropriate way to be able to reconstruct an unknown
nonlinear relation. To answer this question, we propose a greedy reconstruction
algorithm within an offline-online strategy. We apply this strategy to a
two-dimensional semilinear elliptic model. Our identification is based on the
application of several space-dependent excitations (also called controls).
These specific controls are designed by the algorithm in order to obtain a
deeper insight into the underlying physical problem and a more precise
reconstruction of the unknown relation. We perform numerical simulations that
demonstrate the effectiveness of our approach which is not limited to the
current type of equation. Since our algorithm provides not only a way to
determine unknown operators by existing data but also protocols for new
experiments, it is a holistic concept to tackle the problem of improving
physical models.
