The finite element neural network and its applications to forward and inverse problems

Abstract EN

١٨ this paper, first we reformulated the ؛«[؛te 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.

'1'his model is then extended to the general case and the advantages and disadvantages of this approach are described along with an analysis of the sensitivity of the algorithm to errors in the measurements.

Consider a typical boundary value problem with the governing differential equation: L،p - f, where L is a differential operator, ؛'is the forcing function and (p is the unl،nown quantity.

'1'his differential equation can be solved ١٦؛ conjunetion with boundary conditions on the boundary ٢ enclosing the domain.

٨ commonly used approach to solve this problem is to use the finite clement approach-