Gabbard, Hunter
(2021)
*Advancing the search for gravitational waves using machine learning.*
PhD thesis, University of Glasgow.

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## Abstract

Over 100 years ago Einstein formulated his now famous theory of General Relativity. In his theory he lays out a set of equations which lead to the beginning of a brand-new astronomical field, Gravitational wave (GW) astronomy. The LIGO-Virgo-KAGRA Collaboration (LVK)’s aim is the detection of GW events from some of the most violent and cataclysmic events in the known universe. The LVK detectors are composed of large-scale Michelson Morley interferometers which are able to detect GWs from a range of sources including: binary black holes (BBHs), binary neutron stars (BNSs), neutron star black holes (NSBHs), supernovae and stochastic GWs. Although these GW events release an incredible amount of energy, the amplitudes of the GWs from such events are also incredibly small.

The LVK uses sophisticated techniques such as matched filtering and Bayesian inference in order to both detect and infer source parameters from GW events. Although optimal under many circumstances, these standard methods are computationally expensive to use. Given that the expected number of GW detections by the LVK will be of order 100s in the coming years, there is an urgent need for less computationally expensive detection and parameter inference techniques. A possible solution to reducing the computational expense of such techniques is the exciting field of machine learning (ML).

In the first chapter of this thesis, GWs are introduced and it is explained how GWs are detected by the LVK. The sources of GWs are given, as well as methodologies for detecting various source types, such as matched filtering. In addition to GW signal detection techniques, the methods for estimating the parameters of detected GW signals is described (i.e. Bayesian inference). In the second chapter several machine learning algorithms are introduced including: perceptrons, convolutional neural networks (CNNs), autoencoders (AEs), variational autoencoders (VAEs) and conditional variational autoencoders (CVAEs). Practical advice on training/data augmentation techniques is also provided to the reader. In the third chapter, a survey on several ML techniques applied a variety of GW problems are shown.

In this thesis, various ML and statistical techniques were deployed such as CVAEs and CNNs in two first-of-their-kind proof-of-principle studies. In the fourth chapter it is described how a CNN may be used to match the sensitivity of matched filtering, the standard technique used by the LVK for detecting GWs. It was shown how a CNN may be trained using simulated BBH waveforms buried in Gaussian noise and signals with Gaussian noise alone. Results of the CNN classification predictions were compared to results from matched filtering given the same testing data as the CNN. In the results it was demonstrated through receiver operating characteristics and efficiency curves that the ML approach is able to achieve the same levels of sensitivity as that of matched filtering. It is also shown that the CNN approach is able to generate predictions in low-latency. Given approximately 25000 GW time series, the CNN is able to produce classification predictions for all 25000 in 1s.

In the fifth and sixth chapters, it is shown how CVAEs may be used in order to perform Bayesian inference. A CVAE was trained using simulated BBH waveforms in Gaussian noise, as well as the source parameter values of those waveforms. When testing, the CVAE is only supplied the BBH waveform and is able to produce samples from the Bayesian posterior. Results were compared to that of several standard Bayesian samplers used by the LVK including: Dynesty, ptemcee, emcee, and CPnest. It is shown that when properly trained the CVAE method is able to produce Bayesian posteriors which are consistent with other Bayesian samplers. Results are quantified using a variety of figures of merit such as probability-probability (p-p) plots in order to check the 1-dimensional marginalised posteriors from all approaches are self-consistent with the frequentist perspective. The Jensen—Shannon (JS)-divergence was also employed in order to compute the similarity of different posterior distributions from one another, as well as other figures of merit. It was also demonstrated that the CVAE model was able to produce posteriors with 8000 samples in under a second, representing a 6 order of magnitude increase in performance over traditional sampling methods.

Item Type: | Thesis (PhD) |
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Qualification Level: | Doctoral |

Keywords: | Gravitational waves, machine learning, variational inference. |

Subjects: | Q Science > QB Astronomy Q Science > QC Physics |

Colleges/Schools: | College of Science and Engineering > School of Physics and Astronomy |

Supervisor's Name: | Messenger, Dr. Chris and Heng, Professor Ik Siong |

Date of Award: | 2021 |

Depositing User: | Theses Team |

Unique ID: | glathesis:2021-82605 |

Copyright: | Copyright of this thesis is held by the author. |

Date Deposited: | 16 Dec 2021 09:35 |

Last Modified: | 08 Apr 2022 17:09 |

Thesis DOI: | 10.5525/gla.thesis.82605 |

URI: | http://theses.gla.ac.uk/id/eprint/82605 |

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