# Statistically-informed deep learning for gravitational wave parameter estimation

## TL;DR

This paper presents a deep learning approach combining WaveNet, contrastive learning, and normalizing flow to efficiently estimate gravitational wave parameters, matching traditional Bayesian results with significantly reduced computation time.

## Contribution

Introduces a novel neural network model for gravitational wave parameter estimation that is fast, accurate, and encodes physical correlations, validated against analytical posteriors.

## Key findings

- Neural network predictions are statistically consistent with Bayesian analyses.
- The model produces results within milliseconds per event.
- Posterior distributions accurately reflect physical parameter correlations.

## Abstract

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, $(\omega_R, \omega_I)$. 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 $(m_1,m_2, a_f, \omega_R, \omega_I)$ 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 $\texttt{Data and Learning Hub for Science}$.