  In this paper we show how to efficiently achieve thermal cloaking from a
computational standpoint in several virtual scenarios by controlling a
distribution of active heat sources. We frame this problem in the setting of
PDE-constrained optimization, where the reference field is the solution of the
time-dependent heat equation in the absence of the object to cloak. The optimal
control problem then aims at actuating the space-time control field so that the
thermal field outside the obstacle is indistinguishable from the reference
field. In particular, we consider multiple scenarios where material's thermal
diffusivity, source intensity and obstacle's temperature are allowed to vary
within a user-defined range. To tackle the thermal cloaking problem in a rapid
and reliable way, we rely on a parametrized reduced order model built through
the reduced basis method, thus entailing huge computational speedups compared
to high-fidelity, full-order model exploiting the finite element method while
dealing both with complex target shapes and disconnected control domains.
