Real-Time Gravitational Wave Science with Neural Posterior Estimation

We demonstrate unprecedented accuracy for rapid gravitational wave parameter estimation with deep learning. Using neural networks as surrogates for Bayesian posterior distributions, we analyze eight gravitational wave events from the first LIGO-Virgo Gravitational-Wave Transient Catalog and find very close quantitative agreement with standard inference codes, but with inference times reduced from $O(\mathrm{day})$ to 20 s per event. Our networks are trained using simulated data, including an estimate of the detector noise characteristics near the event. This encodes the signal and noise models within millions of neural-network parameters and enables inference for any observed data consistent with the training distribution, accounting for noise nonstationarity from event to event. Our algorithm—called “DINGO”—sets a new standard in fast and accurate inference of physical parameters of detected gravitational wave events, which should enable real-time data analysis without sacrificing accuracy.

Figure 1

DINGO flow chart. The posterior distribution is represented in terms of an invertible normalizing flow (orange), taking normally distributed random variables $u$ into posterior samples $\theta$. The flow itself depends on a (compressed) representation of the noise properties $S_n$ and the data $d$, as well as an estimate ${\tau }_I$ of the coalescence time in each detector $I$. The data are time shifted by ${\tau }_I$ to simplify the representation. For inference, the iterative GNPE algorithm is used to provide an estimate of ${\tau }_I$, as described in the main text.

Figure 2

$P–P$ plot for 1000 injections. The legend shows the $p$ values of the individual parameters, with a combined $p$ value of 0.46.

Figure 3

Comparison of (a) detector-frame component mass and (b) sky position posteriors from DINGO (colored) and lalinference (gray) for eight GWTC-1 events. 90% credible regions shown.

Figure 4

JSDs between DINGO and lalinference marginalized posteriors, averaged over 100 realizations. The mean JSD across all events and parameters is 0.0009 nat.