  The offline time of the reduced basis method can be very long given a large
training set of parameter samples. This usually happens when the system has
more than two independent parameters. On the other hand, if the training set
includes fewer parameter samples, the greedy algorithm might produce a
reduced-order model with large errors at the samples outside of the training
set. We introduce a method based on a surrogate error model to efficiently
sample the parameter domain such that the training set is adaptively updated
starting from a coarse set with a small number of parameter samples. A sharp a
posteriori error estimator is evaluated on a coarse training set. Radial Basis
Functions are used to interpolate the error estimator over a separate fine
training set. Points from the fine training set are added into the coarse
training set at every iteration based on a user defined criterion. In parallel,
parameter samples satisfying a defined tolerance are adaptively removed from
the coarse training set. The approach is shown to avoid high computational
costs by using a small training set and to provide a reduced-order model with
guaranteed accuracy over a fine training set. Further, we show numerical
evidence that the reduced-order model meets the defined tolerance over an
independently sampled test set from the parameter domain.
