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Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE,General Relativity and Quantum Cosmology, gr-qc
Abstract:
Models of gravitational waveforms play a critical role in detecting and
characterizing the gravitational waves (GWs) from compact binary coalescences.
Waveforms from numerical relativity (NR), while highly accurate, are too
computationally expensive to produce to be directly used with Bayesian
parameter estimation tools like Markov-chain-Monte-Carlo and nested sampling.
We propose a Gaussian process regression (GPR) method to generate accurate
reduced-order-model waveforms based only on existing accurate (e.g. NR)
simulations. Using a training set of simulated waveforms, our GPR approach
produces interpolated waveforms along with uncertainties across the parameter
space. As a proof of concept, we use a training set of IMRPhenomD waveforms to
build a GPR model in the 2-d parameter space of mass ratio $q$ and
equal-and-aligned spin $\chi_1=\chi_2$. Using a regular, equally-spaced grid of
120 IMRPhenomD training waveforms in $q\in[1,3]$ and $\chi_1 \in [-0.5,0.5]$,
the GPR mean approximates IMRPhenomD in this space to mismatches below
$4.3\times 10^{-5}$. Our approach can alternatively use training waveforms
directly from numerical relativity. Beyond interpolation of waveforms, we also
present a greedy algorithm that utilizes the errors provided by our GPR model
to optimize the placement of future simulations. In a fiducial test case we
find that using the greedy algorithm to iteratively add simulations achieves
GPR errors that are $\sim 1$ order of magnitude lower than the errors from
using Latin-hypercube or square training grids.
