A Precessing Numerical Relativity Waveform Surrogate Model for Binary Black Holes: A Gaussian Process Regression Approach

Abstract

Gravitational wave astrophysics relies heavily on the use of matched filtering both to detect signals in noisy data from detectors, and to perform parameter estimation on those signals. Matched filtering relies upon prior knowledge of the signals expected to be produced by a range of astrophysical systems, such as binary black holes. These waveform signals can be computed using numerical relativity techniques, where the Einstein field equations are solved numerically, and the signal is extracted from the simulation. Numerical relativity simulations are, however, computationally expensive, leading to the need for a surrogate model which can predict waveform signals in regions of the physical parameter space which have not been probed directly by simulation. We present a method for producing such a surrogate using Gaussian process regression which is trained directly on waveforms generated by numerical relativity. This model returns not just a single interpolated value for the waveform at a new point, but a full posterior probability distribution on the predicted value. This model is therefore an ideal component in a Bayesian analysis framework, through which the uncertainty in the interpolation can be taken into account when performing parameter estimation of signals.