  While projection-based reduced order models can reduce the dimension of full
order solutions, the resulting reduced models may still contain terms that
scale with the full order dimension. Hyper-reduction techniques are
sampling-based methods that further reduce this computational complexity by
approximating such terms with a much smaller dimension. The goal of this work
is to introduce a points selection algorithm developed by Shin and Xiu [SIAM J.
Sci. Comput., 38 (2016), pp. A385--A411], as a hyper-reduction method. The
selection algorithm is originally proposed as a stochastic collocation method
for uncertainty quantification. Since the algorithm aims at maximizing a
quantity S that measures both the column orthogonality and the determinant, we
refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate
the performance of S-OPT and to compare its performance with an over-sampled
Discrete Empirical Interpolation (DEIM) algorithm. We found that using the
S-OPT algorithm is shown to predict the full order solutions with higher
accuracy for a given number of indices.
