Approximating the operator of the wave equation using deep learning

Resumo

Deep operator networks (DeepONets) have demonstrated the 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. A comparison between the GreenONets and the DeepONets is shown on a series of
numerical experiments for homogeneous and heterogeneous medias.