#### 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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