A neural network approach for solving integral equations

Author

Elshafiey, I. ; Udpa, L. ; Udpa, S.S.

Author_Institution

Dept. of Electr. Eng. & Comput. Eng., Iowa State Univ., Ames, IA, USA

fYear

1991

fDate

11-14 Jun 1991

Firstpage

1416

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

Keywords

convergence of numerical methods; integral equations; neural nets; Hopfield-type network; causality property; circuit parameters; discretized integral equation; energy function; function minimization equations; globally optimum solution; integral equations; least squares solution; neural network approach; regularization conditions; Circuit simulation; Electromagnetic measurements; Electromagnetic scattering; Geologic measurements; Geophysical measurements; Integral equations; Inverse problems; Neural networks; Seismic measurements; Shape;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 1991., IEEE International Sympoisum on

Print_ISBN

0-7803-0050-5

Type

conf

DOI

10.1109/ISCAS.1991.176638

Filename

176638