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.
