  Deep operator networks (DeepONets) have demonstrated their capability of
approximating nonlinear operators for initial- and boundary-value problems. One
attractive feature of DeepONets is their versatility since they do not rely on
prior knowledge about the solution structure of a problem and can thus be
directly applied to a large class of problems. However, convergence in
identifying the parameters of the networks may sometimes be slow. In order to
improve on DeepONets for approximating the wave equation, we introduce the
Green operator networks (GreenONets), which use the representation of the exact
solution to the homogeneous wave equation in term of the Green's function. The
performance of GreenONets and DeepONets is compared on a series of numerical
experiments for homogeneous and heterogeneous media in one and two dimensions.
