Fast Prediction and Evaluation of Gravitational Waveforms Using Surrogate Models
Abstract
We propose a solution to the problem of quickly and accurately predicting gravitational waveforms within any given physical model. The method is relevant for both realtime applications and more traditional scenarios where the generation of waveforms using standard methods can be prohibitively expensive. Our approach is based on three offline steps resulting in an accurate reduced order model in both parameter and physical dimensions that can be used as a surrogate for the true or fiducial waveform family. First, a set of m parameter values is determined using a greedy algorithm from which a reduced basis representation is constructed. Second, these m parameters induce the selection of m time values for interpolating a waveform time series using an empirical interpolant that is built for the fiducial waveform family. Third, a fit in the parameter dimension is performed for the waveform's value at each of these m times. The cost of predicting L waveform time samples for a generic parameter choice is of order O(mL+mc_{fit}) online operations, where c_{fit} denotes the fitting function operation count and, typically, m ≪L. The result is a compact, computationally efficient, and accurate surrogate model that retains the original physics of the fiducial waveform family while also being fast to evaluate. We generate accurate surrogate models for effectiveonebody waveforms of nonspinning binary black hole coalescences with durations as long as 10^{5}M, mass ratios from 1 to 10, and for multiple spherical harmonic modes. We find that these surrogates are more than 3 orders of magnitude faster to evaluate as compared to the cost of generating effectiveonebody waveforms in standard ways. Surrogate model building for other waveform families and models follows the same steps and has the same low computational online scaling cost. For expensive numerical simulations of binary black hole coalescences, we thus anticipate extremely large speedups in generating new waveforms with a surrogate. As waveform generation is one of the dominant costs in parameter estimation algorithms and parameter space exploration, surrogate models offer a new and practical way to dramatically accelerate such studies without impacting accuracy. Surrogates built in this paper, as well as others, are available from GWSurrogate, a publicly available python package.
 Publication:

Physical Review X
 Pub Date:
 July 2014
 DOI:
 10.1103/PhysRevX.4.031006
 arXiv:
 arXiv:1308.3565
 Bibcode:
 2014PhRvX...4c1006F
 Keywords:

 04.30.w;
 04.25.dg;
 02.60.x;
 Gravitational waves: theory;
 Numerical studies of black holes and blackhole binaries;
 Numerical approximation and analysis;
 General Relativity and Quantum Cosmology;
 Computer Science  Computational Engineering;
 Finance;
 and Science
 EPrint:
 20 pages, 17 figures, uses revtex 4.1. Version 2 includes new numerical experiments for longer waveform durations, larger regions of parameter space and multimode models