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 real-time 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 OðmL þ mc fit Þ 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 effective-one-body 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 effective-one-body 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.

Tests of General Relativity with GW150914

“…[35] using NR waveforms from Ref. [36], enhanced with reduced-order modeling [37] to speed up waveform generation [38,39] (henceforth, EOBNR), and the single effective spin, precessing waveform model of Refs. [40][41][42] (henceforth, IMRPHENOM).…”

Transformations of asymptotic gravitational-wave data

“…For example, they will not be consistent with the usual postNewtonian waveforms; using the raw waveforms to construct hybrids with PN waveforms would result in mismatches between the modes. Using raw waveforms to calibrate effective-onebody waveforms [49][50][51], surrogate models [54,55], or other phenomenological waveform models [52,53] would degrade the quality of the numerous fits inherent to the calibration process, by subjecting them to effectively random noise in the input. A broader and deeper survey of the effects of these transformations on waveforms in the SXS catalog will be the subject of an upcoming paper [64].…”

“…If the numerical waveform has spurious features, the waveforms will appear to align poorly, so the calibration will be less than optimal and result in inaccurate waveforms. Other phenomenological waveform models [52,53] and surrogate models [54,55] would experience the same biases, trying to fit simple formulas to waveforms with effectively random gauge effects. Similarly, when constructing hybrid waveform models [48], the hybrids will be imperfect or even discontinuous in the region where one switches from analytical to numerical data.…”

Sources of Gravitational Waves: Theory and Observations

“…At present EOB waveforms for spinning BH binaries are computationally expensive to generate (although far faster than doing NR simulations) and hence not suitable for use in Markov Chain Monte Carlo-based parameter estimation methods. Quite importantly, accelerated waveform generation techniques that use reduced-order algorithms or singular-value decomposition techniques have been proposed to address such problems [411][412][413][414][415].…”