Artificial neural network approach for solving fuzzy differential equations

Abstract

The current research attempts to offer a novel method for solving fuzzy differential equations<br><br>with initial conditions based on the use of feed-forward neural networks. First, the<br><br>fuzzy differential equation is replaced by a system of ordinary differential equations. A trial<br><br>solution of this system is written as a sum of two parts. The first part satisfies the initial<br><br>condition and contains no adjustable parameters. The second part involves a feed-forward<br><br>neural network containing adjustable parameters (the weights). Hence by construction, the<br><br>initial condition is satisfied and the network is trained to satisfy the differential equations.<br><br>This method, in comparison with existing numerical methods, shows that the use of neural<br><br>networks provides solutions with good generalization and high accuracy. The proposed<br><br>method is illustrated by several examples