The Finite Element Neural Network And Its Applications To Forward And Inverse Problems

Abstract

In this paper, first we   refom1Ulated   the finite   element  model

(FEM)   into   a   neural   network   structure   using   a   simple   two   - dimensional problem. The structure of this neural network is described

, followed  by its   application   to   solving  the forward    and  inverse problems. This model is then extended to the general case and the advantages and  di sadvantages  of  this  approach  are  descri bed  along with an analysis  of  the sensi tivity   of  the algorithm  to errors  in the measurements. Consider  a typical  boundary  value  problem  with  the

govern ing  differential  equation:  Lcp  = f, where  L  is a  differential

operator,  f is the forcing function and cp  is the unknown quant ity. This

di fferential  equation  can  be  solved  in  conjunction   wi th  boundary conditi ons  on  the  boundary  r enclosing  the domain.  A commonly

used  approach  to  solve  this   problem  is  to  use  the  finite  element approach.