Universal approximation method for the solution of integral equations

Abstract

In this paper, we present a novel approach for approximating Hammerstein-Volterra delay integral equations (HVDIEs) by applying the universal approximation method through an artificial intelligence utility in a simple way. In this paper, neural network model (NNM) is applied as universal approximators for any nonlinear continuous functions. Here, neural network is considered as a part of large field called neural computing or soft computing. With this capability, the solution of HammersteinVolterra delay integral equation can be approximated by the appropriate NNM within an arbitrary accuracy.

DA-CapsNet: dual attention mechanism capsule network

“…In essence, the neural network is a function approver 26 . The structure of the neural network determines what kind of function it can fit 27 , 28 . Generally, A typical neural network can be implemented as a series of matrix multiplexes and element-wise non-linearities, where the elements of the input or eigenvectors interact only by addition 29 – 31 .…”