  We propose a parametric sampling strategy for the reduction of large-scale
PDE systems with multidimensional input parametric spaces by leveraging models
of different fidelity. The design of this methodology allows a user to
adaptively sample points ad hoc from a discrete training set with no prior
requirement of error estimators. It is achieved by exploiting low-fidelity
models throughout the parametric space to sample points using an efficient
sampling strategy, and at the sampled parametric points, high-fidelity models
are evaluated to recover the reduced basis functions. The low-fidelity models
are then adapted with the reduced order models ( ROMs) built by projection onto
the subspace spanned by the recovered basis functions. The process continues
until the low-fidelity model can represent the high-fidelity model adequately
for all the parameters in the parametric space. Since the proposed methodology
leverages the use of low-fidelity models to assimilate the solution database,
it significantly reduces the computational cost in the offline stage. The
highlight of this article is to present the construction of the initial
low-fidelity model, and a sampling strategy based on the discrete empirical
interpolation method (DEIM). We test this approach on a 2D steady-state heat
conduction problem for two different input parameters and make a qualitative
comparison with the classical greedy reduced basis method (RBM), and further
test on a 9-dimensional parametric non-coercive elliptic problem and analyze
the computational performance based on different tuning of greedy selection of
points.
