Statistically-informed deep learning for gravitational wave parameter estimation

We introduce deep learning models to estimate the masses of the binary components of black hole mergers, $(m_1,m_2)$, and three astrophysical properties of the post-merger compact remnant, namely, the final spin, $a_f$, and the frequency and damping time of the ringdown oscillations of the fundamental $\ell=m=2$ bar mode, $(ω_R, ω_I)$. Our neural networks combine a modified $\texttt{WaveNet}$ architecture with contrastive learning and normalizing flow. We validate these models against a Gaussian conjugate prior family whose posterior distribution is described by a closed analytical expression. Upon confirming that our models produce statistically consistent results, we used them to estimate the astrophysical parameters $(m_1,m_2, a_f, ω_R, ω_I)$ of five binary black holes: $\texttt{GW150914}, \texttt{GW170104}, \texttt{GW170814}, \texttt{GW190521}$ and $\texttt{GW190630}$. We use $\texttt{PyCBC Inference}$ to directly compare traditional Bayesian methodologies for parameter estimation with our deep-learning-based posterior distributions. Our results show that our neural network models predict posterior distributions that encode physical correlations, and that our data-driven median results and 90$\%$ confidence intervals are similar to those produced with gravitational wave Bayesian analyses. This methodology requires a single V100 $\texttt{NVIDIA}$ GPU to produce median values and posterior distributions within two milliseconds for each event. This neural network, and a tutorial for its use, are available at the $\texttt{Data and Learning Hub for Science}$.