Aj. Meade et Aa. Fernandez, THE NUMERICAL-SOLUTION OF LINEAR ORDINARY DIFFERENTIAL-EQUATIONS BY FEEDFORWARD NEURAL NETWORKS, Mathematical and computer modelling, 19(12), 1994, pp. 1-25
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.