  Numerical relativity (NR) simulations of binary black hole (BBH) systems
provide the most accurate gravitational wave predictions, but at a high
computational cost -- especially when the black holes have nearly extremal
spins (i.e. spins near the theoretical upper limit) or very unequal masses.
Recently, the technique of Reduced Order Modeling (ROM) has enabled the
construction of surrogate models trained on an existing set of NR waveforms.
Surrogate models enable the rapid computation of the gravitational waves
emitted by BBHs. Typically these models are used for interpolation to compute
gravitational waveforms for BBHs with mass ratios and spins within the bounds
of the training set. Because simulations with nearly extremal spins are so
technically challenging, surrogate models almost always rely on training sets
with only moderate spins. In this paper, we explore how well surrogate models
can extrapolate to nearly extremal spins when the training set only includes
moderate spins. For simplicity, we focus on one-dimensional surrogate models
trained on NR simulations of BBHs with equal masses and equal, aligned spins.
We assess the performance of the surrogate models at higher spin magnitudes by
calculating the mismatches between extrapolated surrogate model waveforms and
NR waveforms, by calculating the differences between extrapolated and NR
measurements of the remnant black-hole mass, and by testing how the surrogate
model improves as the training set extends to higher spins. We find that while
extrapolation in this one-dimensional case is viable for current detector
sensitivities, surrogate models for next-generation detectors should use
training sets that extend to nearly extremal spins.
