Fast Likelihood-free Reconstruction of Gravitational Wave Backgrounds

We apply state-of-the-art, likelihood-free statistical inference (machine-learning-based) techniques for reconstructing the spectral shape of a gravitational wave background (GWB). We focus on the reconstruction of an arbitrarily shaped signal by the LISA detector, but the method can be easily extended to either template-dependent signals, or to other detectors, as long as a characterisation of the instrumental noise is available. As proof of the technique, we quantify the ability of LISA to reconstruct signals of arbitrary spectral shape (${\it blind}$ reconstruction), considering a diversity of frequency profiles, and including astrophysical backgrounds in some cases. As a teaser of how the method can reconstruct signals characterised by a parameter-dependent template (${\it template}$ reconstruction), we present a dedicated study for power-law signals. While our technique has several advantages with respect to traditional MCMC methods, we validate it with the latter for concrete cases. This work opens the door for both fast and accurate Bayesian parameter estimation of GWBs, with essentially no computational overhead during the inference step. Our set of tools are integrated into the package ${\tt GWBackFinder}$, which is publicly available in https://github.com/AndronikiDimitriou/GWBackFinder.