Towards beating the curse of dimensionality for gravitational waves using reduced basis

Abstract

Using the reduced basis approach, we efficiently compress and accurately represent the space of waveforms for nonprecessing binary black hole inspirals, which constitutes a four-dimensional parameter space (two masses, two spin magnitudes). Compared to the nonspinning case, we find that only a marginal increase in the (already relatively small) number of reduced basis elements is required to represent any nonprecessing waveform to nearly numerical round-off precision. Most parameters selected by the algorithm are near the boundary of the parameter space, leaving the bulk of its volume sparse. Our results suggest that the full eight-dimensional space (two masses, two spin magnitudes, four spin orientation angles on the unit sphere) may be highly compressible and represented with very high accuracy by a remarkably small number of waveforms, thus providing some hope that the number of numerical relativity simulations of binary black hole coalescences needed to represent the entire space of configurations is not intractable. Finally, we find that the distribution of selected parameters is robust to different choices of seed values starting the algorithm, a property which should be useful for indicating parameters for numerical relativity simulations of binary black holes. In particular, we find that the mass ratios ${m}_{1}/{m}_{2}$ of nonspinning binaries selected by the algorithm are mostly in the interval $[1,3]$ and that the median of the distribution follows a power-law behavior $\ensuremath{\sim}({m}_{1}/{m}_{2}{)}^{\ensuremath{-}5.25}$.