# Approximating the operator of the wave equation using deep learning

## Palavras-chave:

Deep learning, Wave equation, Deep operator networks, Physics-informed neural networks## 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.