A machine learning approach to parameter inference in gravitational-wave signal analysis

Gravitational Wave (GW) physics is now in its golden age thanks to modern interferometers. The fourth observing run is now ongoing with two of the four second-generation detectors, collecting GW signals coming from Compact Binary Coalescences (CBCs). These systems are formed by black holes and/or neutron stars which lose energy and angular momentum in favour of GW emission, spiraling toward each other until they merge. The characteristic waveform has a chirping behaviour, with a frequency increasing with time. These GW signals are gold mines of physical information on the emitting system. The data analysis of these signals has two main aspects: detection and parameter estimation. For what concerns detection, two approaches are used right now: matched filtering, which compares numerical waveform with raw interferometers' output to highlight the signal, and the study of bursts, which highlights the coherence of arbitrary signals in different detectors. Both these techniques need to be fast enough to allow for electromagnetic follow-up with a relatively short delay. The offline parameter inference process is based on Bayesian techniques and is rather lengthy (individual processing Markov Chain Monte Carlo runs can take a month or more). My thesis has the goal of introducing a fast parameter estimation for unmodeled (burst) methods which produce only phenomenological, de-noised waveforms with, at best, a rough estimate of only a few parameters. The implementation of an approach for fast parameter inference in this unmodeled analysis, taking as input the reconstructed waveform, could be extremely useful for multimessenger observations. In this context, Keith et al. (2021a) proposed to use Physics Informed Neural Networks (PINNs) in GW data analysis. These PINNs are a machine learning approach which includes physical prior information in the algorithm itself. Taking a clean chirping waveform as input, the algorithm of Keith et al. (2021a) demonstrated a successful application of this concept and was able to reconstruct the compact object's orbits before coalescence with great detail, starting only from a parameterized Post-Newtonian model. The PINN environment could become a key tool to infer parameters from GW signals with a simple physical ansatz. As part of my thesis work, I reviewed in detail GW physics and the PINN environment and I updated the algorithm described in Keith et al. (2021a). Their ground-breaking work introduces PINNs for the first time in the analysis of GW signals, however it does so without considering some important details. In particular, I noted that the algorithm of Keith et al. (2021a) spans a very constrained parameter space. In this thesis I introduce some of the missing details and I recode the algorithm from scratch. My implementation includes the learning of the phenomenological differential equation that describes the frequency evolution over time of the chirping GW, within a different, but more physical, parameter space. As a test, starting from a waveform as training data, and from the Newtonian approximation of the GW chirp, I infer the chirp mass, the GW phase and the frequency exponent in the differential equation. The resulting algorithm is robust and uses realistic physical conditions. This is a necessary first step to realize parameter inference with PINNs on real gravitational wave data.