• close encounters
• deep learning
• gravitational waves
• normalizing flows

During the first three runs the Advanced LIGO and Virgo detectors have observed 90 transient events associated to coalescences of black holes and/or neutron stars in binary systems with quasi-circular orbits.

A yet undetected class of sources is represented by the so called Close Encounters (CEs) between compact objects in highly eccentric ($e\sim 1$) orbits. Those system are thought to be formed in highly dense stellar environments such as the cores of globular clusters.
\indent The aim of this work is to develop a model for a fast parameter estimation for these sources exploiting advanced Probabilistic Machine Learning techniques.
As these sources represent a unique opportunity to test General Relativity in the dynamical strong field regime and astrophysical formation channels, they are interesting sources to investigate. Furthermore, systems containing a neutron star could allow the placing of better constraints on the NS Equation of State as during the encounter as the f-modes on the surface can be excited, hence leaving a signature in the gravitational wave emitted. The expected CE signals are repeated short duration bursts emitted at each periastron passage and are expected to have a low Signal to Noise Ratio, with the current sensitivities. Therefore their detection and analysis is challenging for standard tools.

We focused on single bursts emission simulated in the current LIGO-Virgo detectors with colored noise from the O3 observing run.
The simulations are based on a recently developed analytic waveform model for the single burst emission.
These waveforms are obtained in a \textit{Effective fly-by} formalism by performing a re-summation on the Fourier series representation of the two-body problem at leading post-Newtonian order. Parameter Estimation on single burst could then be a valid tool to constrain models for the evolution of orbital parameters during the inspiral (timing models), which at the moment are not known with extreme accuracy.

This is an innovative work, in the field of GW, being based on a Bayesian Probabilistic Machine Learning model able to produce conditional probability distribution instead of a simple point estimate. In particular we made use of \textit{Conditional Normalizing Flows} which are able to model a complex probability distribution (the posterior for the CE's parameters) by means of a series of invertible transformations from a simple base density (a Multivariate Normal). By a simple change-of-variable formula, samples of the posterior can be directly obtained by evaluating the inverse of this transformation on samples from the base distribution.
The model developed makes use of Coupling Layers and Affine transformations in order to parametrize the bijection. An additional Deep Convolutional and Residual Network is used to extract information and features from the timeseries data and to compress them in a lower dimensional form to be given as a context to the flow. Both are trained together to maximize the Kullback-Leibler divergence between the true posterior and the one inferred by the flow. What makes Normalizing Flows such a valid alternative is that not only are they able to perform an extremely rapid inference, but their output can be directly compared with classic method's ones.

The developed model outperformed standard methods both in accuracy of the recovered parameters and inference time: $5\times 10^4$ samples produced in $\sim 0.5$ s against $\sim 5\times 10^3$ samples in $\mathcal{O}(10 \text{ hours})$ with traditional methods. We tested our model also on real data by analyzing the \textsc{GW190521} event which might have a dynamical origin with a yet unconfirmed CE progenitor.

The overall promising results here obtained constitute the first successful attempt for a fast and complete parameter estimation of Close Encounter systems. A future perspective is to make this work available to the \text{LIGO-Virgo-KAGRA} Collaboration in the form of a pipeline to perform inference on real-time data.