Adaptive Functional Networks Loop Structures And Learning Algorithm

The Banach contraction theorem was proposed by S.Banach.It is not only play a vital role in functional analysis, but also an important theoretical basis for the algebraic equations of numerical analysis, the existence and uniqueness of ordinary differential equations and the integral equation of mathematical analysis. It is one of the most common methods in mathematical and engineering calculations. Neural network(NN) is a highly nonlinear dynamic systems. The Functional network(FN) is the generalization of NN , and deal with the general functional model problems. Adaptive structures with algebraic loops is both a feedforward and feedback pathway neural network architecture and can effectively deal with time-series related to the context of information, The Banach contraction theorem provides the basis of mathematical theory for the adaptive structures with algebraic loops.In this paper, adaptive functional networks loop structures are designed based on the Banach contraction theorem and the learning algorithm is presented. These structures are used for the approximation of the fixed point of unknown functional relations (mappings) represented by training sets. Finally, the simulation results demonstrate that the structure presented in the paper has high precision and stable. The results obtained in this paper are very important for research the methods of neural computation.Functional network like neural networks, nowadays, so far, there is no system designing method for designing approximation functional networks structure. Therefor, a new genetic programming designing neuron functions, combining genetic programming and evolutionary algorithm, was proposed for hybrid identification of functional network structure and functional parameters by performing global optimal search in the complex solution space where the structures and parameters coexist and interact. These results also show that the proposed method in this paper can produce very compact network structure and the functional networks convergent precisions are improved greatly.