Some Functional Network Models

In this chapter we present a collection of interesting functional network models that allow solving a wide range of real and interesting problems, as it will be shown in the following chapters. For each model, a detailed analyses of the simplification and the uniqueness of representation problems are presented. The initial functional network, arising from the physical or engineering problem being solved, can in many cases be improved. This means that the network structure can be simplified and the neuron functions reduced in their number of arguments. To this aim we use some results from functional equations, which have been described in Chapter 3. Once the functional network has been simplified, we analyze the uniqueness problem leading to important conditions to be satisfied for the estimation of the model to be correct. Again, functional equations give the key tools for solving this problem. Next, we describe the corresponding estimation methods, which are based on minimizing the sum of square errors between the expected and the actual outputs. Some illustrative examples are also given to clarify concepts and methods.