Modeling with Neural Networks: Principles and Model Design Methodology - Neural Networks: Methodology and Applications - page 85

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Modeling with Neural Networks:
Principles and Model Design Methodology
G. Dreyfus
In the previous chapter, we showed that neural networks are nonlinear mod-
els, either static or dynamic, either “black-box” or “gray-box”. The present
chapter provides an in-depth treatment of the principles of modeling, together
with a full model design methodology. For a new technology, the availability
of a methodology is a proof of maturity, and it is a crucial asset for success in
the development of applications.
2.1 What Is a Model?
A model is a representation of a part of the visible or observable world. In
the present topic, we consider only mathematical models, made of algebraic
or differential equations that relate causes (called variables, factors, or model
inputs) to effects (called quantities to be modeled, or quantities of interest,
or model outputs); all these quantities are numbers. Symbolic or linguistic
models, such as expert or fuzzy systems, will not be considered.
2.1.1 From Black-Box Models to Knowledge-Based Models
The black-box model is the most primitive form of a mathematical model: it
is based only on observations; it may have some predictive value, but it does
not provide any explanation. Thus, the Ptolemaic model of the universe was a
black-box model: it did not provide any explanation of the motion of planets,
but it did predict it, within the accuracy of experimental instruments that
were available at that time.
By contrast, a knowledge-based model, or white-box model, results from
an analysis of the physical, chemical, biological, etc., phenomena that gen-
erate the quantity to be modeled. Those phenomena are described by equa-
tions that depend on the theoretical knowledge that is available when the
model is designed. Therefore, such a model has the abilities of predicting