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.

翻译：深度算子网络（DeepONets）已展现出逼近初边值问题非线性算子的能力。DeepONets的一个显著优势在于其通用性——由于不依赖问题的解结构先验知识，因此可直接应用于广泛的问题类别。然而，在辨识网络参数时，收敛速度有时较慢。为改进DeepONets对波动方程的逼近性能，我们提出格林算子网络（GreenONets），该方法利用格林函数形式表示齐次波动方程的精确解。通过一系列一维和二维均匀/非均匀介质的数值实验，我们比较了GreenONets与DeepONets的性能表现。