Solving the Teukolsky equation with physics-informed neural networks

TL;DR

This paper demonstrates that physics-informed neural networks can accurately compute black hole quasi-normal modes from the Teukolsky equation, offering a flexible and efficient alternative to traditional numerical methods for gravitational wave analysis.

Contribution

The authors introduce a PINN-based approach to solve the Teukolsky equation, enabling rapid and accurate computation of black hole oscillation modes without complex numerical techniques.

Findings

PINNs accurately compute quasi-normal modes with below-percent error.

Method is effective for arbitrary black hole spins and masses.

Results are reliable for gravitational wave data analysis at high SNRs.

Abstract

We use physics-informed neural networks (PINNs) to compute the first quasi-normal modes of the Kerr geometry via the Teukolsky equation. This technique allows us to extract the complex frequencies and separation constants of the equation without the need for sophisticated numerical techniques, and with an almost immediate implementation under the \texttt{PyTorch} framework. We are able to compute the oscillation frequencies and damping times for arbitrary black hole spins and masses, with accuracy typically below the percentual level as compared to the accepted values in the literature. We find that PINN-computed quasi-normal modes are indistinguishable from those obtained through existing methods at signal-to-noise ratios (SNRs) larger than 100, making the former reliable for gravitational-wave data analysis in the mid term, before the arrival of third-generation detectors like LISA or the Einstein Telescope, where SNRs of ${\cal O}(1000)$ might be achieved.