Fast prediction and evaluation of gravitational waveforms using surrogate models

TL;DR

This paper introduces a surrogate modeling approach that significantly accelerates the prediction and evaluation of gravitational waveforms, enabling real-time applications and efficient parameter estimation in gravitational wave astronomy.

Contribution

The authors develop a three-step offline method to construct accurate surrogate models for gravitational waveforms, drastically reducing online evaluation time compared to traditional methods.

Findings

Surrogates are three orders of magnitude faster than standard waveform generation.

Method applies to effective one body waveforms of binary black hole coalescences.

Surrogates maintain high accuracy across a range of parameters.

Abstract

[Abridged] 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 in 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 that can be used as a surrogate for the true/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. 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 m L + m c_f online operations where c_f denotes the fitting function operation count and, typically, m << L. We generate accurate surrogate models for Effective One Body (EOB) waveforms of non-spinning binary black hole coalescences with durations as long as 10^5 M, mass ratios from 1 to 10, and for multiple harmonic modes. We find that these surrogates are three orders of magnitude faster to evaluate as compared to the cost of generating EOB waveforms in standard ways. Surrogate model building for other waveform models follow the same steps and have the same low online scaling cost. For expensive numerical simulations of binary black hole coalescences we thus anticipate 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.