A neural network approach for solving integral equations

Abstract

A strategy for solving integral equations using a Hopfield-type network is presented. The major advantage of this strategy is the guaranteed convergence to the globally optimum solution ensured by the causality property of the network and the continuous nature of the feedback to each node. The algorithm consists of deriving the two function minimization equations, one for the energy function of the network and the other for the least squares solution of the discretized integral equation with regularization conditions. By comparing similar terms of the two equations, the circuit parameters of the network are estimated. The network is then simulated to obtain the solution of the integral equation. Initial simulation results are presented.