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, (m1,m2), and three astrophysical properties of the post-merger compact remnant, namely, the final spin, af, and the frequency and damping time of the ringdown oscillations of the fundamental ℓ=m=2 bar mode, (ωR, ωI). Our neural networks combine a modified textttWaveNet 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 (m1,m2, af, ωR, ωI) of five binary black holes: textttGW150914, textttGW170104, textttGW170814, textttGW190521 and textttGW190630. We use textttPyCBC 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 textttNVIDIA 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 textttData and Learning Hub for Science.