Regression methods in waveform modeling: a comparative study

Abstract

Gravitational-wave astronomy of compact binaries relies on theoretical models of the gravitational-wave signal that is emitted as binaries coalesce. These models do not only need to be accurate, they also have to be fast to evaluate in order to be able to compare millions of signals in near real time with the data of gravitational-wave instruments. A variety of regression and interpolation techniques have been employed to build efficient waveform models, but no study has systematically compared the performance of these regression methods yet. Here we provide such a comparison of various techniques, including polynomial fits, radial basis functions, Gaussian process regression and artificial neural networks, specifically for the case of gravitational waveform modeling. We use all these techniques to regress analytical models of non-precessing and precessing binary black hole waveforms, and compare the accuracy as well as computational speed. We find that most regression methods are reasonably accurate, but efficiency considerations favour in many cases the most simple approach. We conclude that sophisticated regression methods are not necessarily needed in standard gravitational-wave modeling applications, although problems with higher complexity than what is tested here might be more suitable for machine-learning techniques and more sophisticated methods may have side benefits. ‡

Gravitational-wave surrogate models powered by artificial neural networks

“…In Ref. [48], the authors systematically explored several methods and ranked them in terms of accuracy, time to fit, and prediction time. They also experimented with ANNs but restricted to shallow networks with only two hidden layers and training/execution on CPUs only.…”

“…This is a multidimension interpolation or regression problem and has recently been investigated in Ref. [48], in which the authors systematically compared different interpolation and regression methods.…”

“…ANNs are a versatile tool [50] and have recently been applied to solve reduced-order modeling problems across multiple disciplines using a nonintrusive framework [51][52][53][54][55]. The use of ANNs in GW astronomy is increasing [48,[56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73]. In particular, the authors of [74] used ANNs to model the greedy reduced basis coefficients for a frequency domain inspiral post-Newtonian waveforms in the context of massive binary black holes (BBHs) that the space-based GW observatory LISA [75] will be sensitive to.…”

On ab initio-based, free and closed-form expressions for gravitational waves

“…In general, surrogate models for GWs have followed reduced order modeling (ROM) for parameterized systems and/or “standard” machine learning regression techniques 18 . Here we focus on the former, we will not delve into reviewing them but instead, as mentioned, refer to 17 .…”

Computational techniques for parameter estimation of gravitational wave signals

“…A fast reduced‐order quadrature allows to approximate posterior distributions at greatly reduced computational costs. A review of waveform acceleration techniques based on reduced order or surrogate models that speed up parameter estimation is provided in Setyawati, Pürrer, and Ohme (2020). Vinciguerra, Veitch, and Mandel (2017) exploit the chirping behavior of compact binary inspirals to sample sparsely for portions where the full frequency resolution is not required, Zackay, Dai, and Venumadhav (2018) and N. Cornish (2013) use relative binning and the heterodyning principle, respectively, for fast likelihood evaluation.…”