Artificial neural network technique for solution of nonlinear elliptic boundary value problems

Abstract

In this article, we present an artificial neural network technique to solve some of the two-point nonlinear elliptic boundary value problems arising in science and engineering. A trial solution of the differential equation is written in terms of a feed forward neural network with adjustable parameters weights or biases, and error function is prepared to use in the back-propagation algorithm to update the network parameters with momentum term. Comparison of the results obtained by the present method is done with analytical solution and other existing numerical methods which show the efficiency of Neural network method with high accuracy, fast convergence, and low use of memory for solving nonlinear elliptic boundary value problems. The main advantage of the proposed approach is that once the network is trained, it allows evaluation of the solution at any desired number of points instantaneously with spending negligible computing time.