Statistically-informed deep learning for gravitational wave parameter estimation

Hongyu Shen, E. A. Huerta, Eamonn O'Shea, Prayush Kumar, Zhizhen Zhao

We introduce deep learning models for gravitational wave parameter estimation that combine a modified $\texttt{WaveNet}$ architecture with $\textit{constrastive learning}$ and $\textit{normalizing flow}$. To ascertain the statistical consistency of these models, we validated their predictions 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 of five binary black holes: $\texttt{GW150914}$, $\texttt{GW170104}$, $\texttt{GW170814}$, $\texttt{GW190521}$ and $\texttt{GW190630}$. Our findings indicate that our deep learning approach predicts posterior distributions that encode physical correlations, and that our data-driven median results and $90\%$ confidence intervals are consistent with those obtained 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 $\texttt{Data and Learning Hub for Science}$.

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