Numerical Solution of Partial Differential Equations by using Modified Artificial Neural Network

Abstract

In this paper, we introduce a novel approach based on modified artificial neural network and optimization teqnique to solve partial differential equations. Using modified artificial neural network makes that training points should be selected over an open interval  without training the network in the range of first and end points. Therefore, the calculating volume involving computational error is reduced. In fact, the training points depending on the distance selected for training neural network are converted to similar points in the open interval  by using a new approach, then the network is trained in these similar areas. In comparison with existing similar neural networks proposed model provides solutions with high accuracy. The proposed method is illustrated by two  numerical examples.

Keywords: Partial differential equation, Modified  neural network, Feed-forward neural network,BFGS Teqnique, Hyperbolic tangent activation function.