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Many relevant applications in gravitational wave physics share a significantcommon problem: the seven-dimensional parameter space of gravitationalwaveforms from precessing compact binary inspirals and coalescences is largeenough to prohibit covering the space of waveforms with sufficient density. Wefind that by using the reduced basis method together with a parametrization ofwaveforms based on their phase and precession, we can construct ultra-compactyet high-accuracy representations of this large space. As a demonstration, weshow that less than $100$ judiciously chosen precessing inspiral waveforms areneeded for $200$ cycles, mass ratios from $1$ to $10$ and spin magnitudes $\le0.9$. In fact, using only the first $10$ reduced basis waveforms yields amaximum mismatch of $0.016$ over the whole range of considered parameters. Wetest whether the parameters selected from the inspiral regime result in anaccurate reduced basis when including merger and ringdown; we find that this isindeed the case in the context of a non-precessing effective-one-body model.This evidence suggests that as few as $\sim 100$ numerical simulations ofbinary black hole coalescences may accurately represent the seven-dimensionalparameter space of precession waveforms for the considered ranges.

A sparse representation of gravitational waves from precessing compact binaries