Algorithmically Designed Artificial Neural Networks (ADANNs): Higher Order Deep Operator Learning for Parametric Partial Differential Equations (opens in new tab)

In this article, we propose a new deep learning approach to approximate operators related to parametric partial differential equations (PDEs). In particular, we introduce a new strategy to design specific artificial neural network (ANN) architectures in conjunction with specific ANN initialization schemes which are tailor-made for the particular approximation problem under consideration. In the proposed approach, we combine efficient classical numerical approximation techniques with deep oper...