THE HOPFIELD NEURAL NETWORK AND ITS APPLICATION FOR DIRECT SOLUTION AND INVERSE OPTIMIZATION IN FINITE ELEMENT ANALYSIS

Abstract

The applicaion of artificial neural network technique and particularly the Hopfield neural network in ordinary finite element analysis is presented. Due to the main property of the Hopfield neural network to minimize the stored network energy, this type of neural network can easily find application in finite element analysis. In this paper two specific applications of the Hopfield neural network will be discussed: First, for obtaining the solution of finite element analysis directly by minimizing the energy of the network - same as minimization of energy functional in ordinary finite element analysis, and second, for obtaining the solution of inverse optimization problems also in connection with finite element analysis. Some basic mathematical calculus and correlations between neural network energy and energy functional that has to be minimized in finite element analysis are discussed. Some application examples to clarify the main idea are also presented.