Using physics-informed neural networks to compute quasinormal modes

Abstract: In recent years there has been an increased interest in neural networks, particularly with regard to their ability to approximate partial differential equations. In this regard, research has begun on so-called physics-informed neural networks (PINNs) which incorporate into their loss function the boundary conditions of the functions they are attempting to approximate. In this paper, we investigate the viability of obtaining the quasi-normal modes (QNMs) of non-rotating black holes in 4-dimensional space-time using PINNs, and we find that it is achievable using a standard approach that is capable of solving eigenvalue problems (dubbed the eigenvalue solver here). In comparison to the QNMs obtained via more established methods (namely, the continued fraction method and the 6th-order Wentzel, Kramer, Brillouin method) the PINN computations share the same degree of accuracy as these counterparts. In other words, our PINN approximations had percentage deviations as low as $(\delta\omega_{{Re}}, \delta\omega{_{Im}}) = (<0.01\%, <0.01\%)$. In terms of the time taken to compute QNMs to this accuracy, however, the PINN approach falls short, leading to our conclusion that the method is currently not to be recommended when considering overall performance.