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 non-precessing binary black hole inspirals, which constitutes a four dimensional parameter space (two masses, two spin magnitudes). Compared to the non-spinning case, we find that only a {\it marginal} increase in the (already relatively small) number of reduced basis elements is required to represent any non-precessing 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 {\it 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 non-spinning binaries selected by the algorithm are mostly in the interval $[1,3]$ and that the median of the distribution follows a power-law behavior $\sim (m_1/m_2{)}^{-5.25}$.

References in corpus (9)

• Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors
• Phenomenological template family for black-hole coalescence waveforms
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• An improved analytical description of inspiralling and coalescing black-hole binaries
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-precessing, spinning, equal-mass black holes
• Singular value decomposition applied to compact binary coalescence gravitational-wave signals
• Estimating the parameters of non-spinning binary black holes using ground-based gravitational-wave detectors: Statistical errors
• The Final Merger of Black-Hole Binaries
• Statistical constraints on binary black hole inspiral dynamics

Cited by in corpus (23)

• Black holes, gravitational waves and fundamental physics: a roadmap
• Surrogate model of hybridized numerical relativity binary black hole waveforms
• Fast prediction and evaluation of gravitational waveforms using surrogate models
• Frequency domain reduced order models for gravitational waves from aligned-spin compact binaries
• Fast and Accurate Inference on Gravitational Waves from Precessing Compact Binaries
• A Surrogate Model of Gravitational Waveforms from Numerical Relativity Simulations of Precessing Binary Black Hole Mergers
• Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration
• Accelerated gravitational-wave parameter estimation with reduced order modeling
• An effectual template bank for the detection of gravitational waves from inspiralling compact binaries with generic spins
• Gravitational wave parameter estimation with compressed likelihood evaluations
• Effective-one-body waveforms for binary neutron stars using surrogate models
• A hybrid post-Newtonian -- effective-one-body scheme for spin-precessing compact-binary waveforms
• Two-step greedy algorithm for reduced order quadratures
• Measuring eccentricity of binary black holes in GWTC-1 by using inspiral-only waveform
• Singular value decomposition in parametrised tests of post-Newtonian theory
• Reduced Order and Surrogate Models for Gravitational Waves
• A sparse representation of gravitational waves from precessing compact binaries
• Improving performance of SEOBNRv3 by $\sim$300x
• A Note on QR-Based Model Reduction: Algorithm, Software, and Gravitational Wave Applications
• Enhancing gravitational waveform models through dynamic calibration
• Fast prediction and evaluation of eccentric inspirals using reduced-order models
• On ab initio-based, free and closed-form expressions for gravitational waves
• Estimating effective higher order terms in the post-Newtonian binding energy and gravitational-wave flux: Non-spinning compact binary inspiral