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(day) to a minute 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.

We develop a formalism to treat higher order (nonlinear) metric perturbations of the Kerr spacetime in a Teukolsky framework. We first show that solutions to the linearized Einstein equation with nonvanishing stress tensor can be decomposed into a pure gauge part plus a zero mode (infinitesimal perturbation of the mass and spin) plus a perturbation arising from a certain scalar (“Debye-Hertz”) potential, plus a so-called “corrector tensor.” The scalar potential is a solution to the spin $-2$ Teukolsky equation with a source. This source, as well as the tetrad components of the corrector tensor, are obtained by solving certain decoupled ordinary differential equations involving the stress tensor. As we show, solving these ordinary differential equations reduces simply to integrations in the coordinate $r$ in outgoing Kerr-Newman coordinates, so in this sense, the problem is reduced to the Teukolsky equation with source, which can be treated by a separation of variables ansatz. Since higher order perturbations are subject to a linearized Einstein equation with a stress tensor obtained from the lower order perturbations, our method also applies iteratively to the higher order metric perturbations, and could thus be used to analyze the nonlinear coupling of perturbations in the near-extremal Kerr spacetime, where weakly turbulent behavior has been conjectured to occur. Our method could also be applied to the study of perturbations generated by a pointlike body traveling on a timelike geodesic in Kerr, which is relevant to the extreme mass ratio inspiral problem.