Parallel Computing and a Multi-Layer Neural Network Algorithm for Solving the Fractional Duffing System

Abstract

An effective neural network method is proposed to solve the fractional Duffing system in this paper. First, a multi-layer neural network is designed and the output is assumed as the solution. Secondly, by numerical discretization of the Caputo derivative using the L1 scheme, a discrete optimization problem is obtained. The famous Adam algorithm is used to train the neural network and parallel computing is suggested to reduce the computational cost. The neural network experimental results show that the analytical solution has a high accuracy and is in a good agreement with the numerical one.