SOLUTION OF NONLINEAR ORDINARY DIFFERENTIAL-EQUATIONS BY FEEDFORWARD NEURAL NETWORKS

It is demonstrated, through theory and numerical examples, how it is p ossible to directly construct a feedforward neural network to approxim ate nonlinear ordinary differential equations without the need for tra ining. The method, utilizing a piecewise linear map as the activation function, is linear in storage, and the L(2) norm of the network appro ximation error decreases monotonically with the increasing number of h idden layer neurons. The construction requires imposing certain constr aints on the values of the input, bias, and output weights, and the at tribution of certain roles to each of these parameters. All results pr esented used the piecewise linear activation function. However, the pr esented approach should also be applicable to the use of hyperbolic ta ngents, sigmoids, and radial basis functions.