Functional Networks with Applications
Artificial neural networks have been
recognized as a powerful tool to learn and reproduce systems in various fields of applications. Neural net works are inspired
by the brain behavior and consist of one or several layers of neurons, or computing units, connected by links. Each artificial
neuron receives an input value from the input layer or the neurons in the previ ous layer. Then it computes a scalar output
from a linear combination of the received inputs using a given scalar function (the activation function), which is assumed
the same for all neurons. One of the main properties of neural networks is their ability to learn from data. There are two
types of learning: structural and parametric. Structural learning consists of learning the topology of the network, that is,
the number of layers, the number of neurons in each layer, and what neurons are connected. This process is done by trial and
error until a good fit to the data is obtained. Parametric learning consists of learning the weight values for a given topology
of the network. Since the neural functions are given, this learning process is achieved by estimating the connection weights
based on the given information. To this aim, an error function is minimized using several well known learning methods, such
as the backpropagation algorithm. Unfortunately, for these methods: (a) The function resulting from the learning process has
no physical or engineering interpretation. Thus, neural networks are seen as black boxes.
I: Neural Networks. 1. Introduction
to Neural Networks. II: Functional Networks. 2. Introduction to Functional Networks. 3. Functional Equations. 4. Some Functional
Network Models. 5. Model Selection. III: Applications. 6. Applications to Time Series. 7. Applications to Differential Equations.
8. Applications to CAD. 9. Applications to Regression. IV: Computer Programs. 10. Mathematica Programs. 11. A Java Applet.
Notation. References. Index.
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