  A genetic algorithm procedure is demonstrated that refines the selection of
interpolation points of the discrete empirical interpolation method (DEIM) when
used for constructing reduced order models for time dependent and/or
parametrized nonlinear partial differential equations (PDEs) with proper
orthogonal decomposition. The method achieves nearly optimal interpolation
points with only a few generations of the search, making it potentially useful
for {\em online} refinement of the sparse sampling used to construct a
projection of the nonlinear terms. With the genetic algorithm, points are
optimized to jointly minimize reconstruction error and enable dynamic regime
classification. The efficiency of the method is demonstrated on two canonical
nonlinear PDEs: the cubic-quintic Ginzburg-Landau equation and the
Navier-Stokes equation for flow around a cylinder. Using the former model, the
procedure can be compared to the ground-truth optimal interpolation points,
showing that the genetic algorithm quickly achieves nearly optimal performance
and reduced the reconstruction error by nearly an order of magnitude.
