Abstract:

Based on the function approximation theory and the Weierstrass approximation theorem, a novel 3input neural net activated by a group of products of Bernoulli polynomials (i.e., 3input Bernoulli polynomial neural net, 3IBPNN) was constructed in this paper. Furthermore, on the basis of the weightsdirectdetermination (WDD) method and the relationship between the number of hiddenlayer neurons and the approximation error of the neural net, three different weightsandstructuredetermination (WASD) algorithms were built up for the constructed 3IBPNN. Numerical experiment results further prove that all of the 3IBPNNs determined respectively by the three proposed algorithms perform excellently in training, testing and prediction.

Key words: Bernoulli polynomial neural net;weightsdirectdetermination method;weightsandstructuredetermination algorithm;algorithm;numerical experiment