  Model order reduction usually consists of two stages: the offline stage and
the online stage. The offline stage is the expensive part that sometimes takes
hours till the final reduced-order model is derived, especially when the
original model is very large or complex. Once the reduced-order model is
obtained, the online stage of querying the reduced-order model for simulation
is very fast and often real-time capable. This work concerns a strategy to
significantly speed up the offline stage of model order reduction for large and
complex systems. In particular, it is successful in accelerating the greedy
algorithm that is often used in the offline stage for reduced-order model
construction. We propose multi-fidelity error estimators and replace the
high-fidelity error estimator in the greedy algorithm. Consequently, the
computational complexity at each iteration of the greedy algorithm is reduced
and the algorithm converges more than 3 times faster without incurring
noticeable accuracy loss.
