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Initialization of Artificial Neural Network Training Using Mathematical Models
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Andrew J. Meade, Jr., Gregory S. Lind and Boris A. Zeldin,

Submitted to *Journal of Guidance, Control, and Dynamics*, 1996.

**Keywords:**:
neural networks, neural computation, mathematical modelling, mechanical systems.

**Abstract**:
An initiation method is developed for networks trained to model physical systems. The construction requires imposing certain constraints on the values of the input, bias, and output weights. The attribution of certain roles to each of these parameters allows for mapping a polynomial approximation into an artificial neural network architecture. Attention is focused on time-dependent linear and non-linear partial differential equations modelled by the recurrent artificial neural network architecture, in conjunction with the popular hyperbolic tangent transfer function. Moreover, this approach is shown to be capable of incorporating other smooth neuron transfer functions. Numerical examples are presented illustrating the accuracy and utility of the method.

This work was supported under NASA grant NGT 51230 and Office of Naval Research grant N00014-95-1-0741.