THE NUMERICAL-SOLUTION OF LINEAR ORDINARY DIFFERENTIAL-EQUATIONS BY FEEDFORWARD NEURAL NETWORKS

It is demonstrated, through theory and examples, how it is possible to construct directly and noniteratively a feedforward neural network to approximate arbitrary linear ordinary differential equations. The met hod, using the hard limit transfer function, is linear in storage and processing time, and the L2 norm of the network approximation error de creases quadratically with the increasing number of hidden layer neuro ns. The construction requires imposing certain constraints on the valu es of the input, bias, and output weights, and the attribution of cert ain roles to each of these parameters. All results presented used the hard limit transfer function. However, the noniterative approach shoul d also be applicable to the use of hyperbolic tangents, sigmoids, and radial basis functions.