Neural Networks: An Overview - Neural Networks: Methodology and Applications - page 22

self-organizing maps (“Kohonen maps”), are powerful data visualization tech-
niques.
Chapter 7 of the present topic is devoted to unsupervised learning, with
emphasis on spectacular applications in satellite observation systems.

1.1.6 Recurrent Neural Networks for Black-Box Modeling,
Gray-Box Modeling, and Control

In an earlier section, devoted to recurrent neural networks, we showed that any
neural network can be cast into a canonical form, which is made of a feed-
forward neural network with external recurrent connections. Therefore, the
properties of recurrent neural networks with supervised learning are strongly
related to those of feedforward neural networks. The latter are used for static
modeling from examples; similarly, recurrent neural networks are used for dy-
namic modeling from examples, i.e., for finding, from measured sequences of
inputs and outputs, recurrent (discrete-time) equations that govern a process.
A sizeable part of Chap. 2, and Chap. 4, are devoted to dynamic process mod-
eling.
The design of a dynamic model may have several motivations.

• Use the model as a simulator in order to predict the evolution of a process

that is described by a model whose equations are inaccurate.

• Use the model as a simulator of a process whose knowledge-based model is

known and reliable, but cannot be solved accurately in real time because
it contains many coupled differential or partial differential equations that
cannot be solved numerically in real time with the desired accuracy: in such
circumstances, one can generate a training set from the software code that
solves the equations, and design a recurrent neural network that provides
accurate solutions within a much shorter computation time; furthermore, it
may be advantageous to take advantage of the differential equations of the
knowledge-based model, as guidelines to the design of the architecture of
the neural model: this is known as “gray-box” or “semi-physical” modeling,
described in Sect. 1.1.6.1.

• Use the model as a one-step-ahead predictor, integrated into a control

system.

1.1.6.1 Semiphysical Modeling

In the manufacturing industry, a knowledge-based model of a process of inter-
est is often available, but is not fully satisfactory, and it cannot be improved
through further analysis; this may be due to a variety of reasons:

• the model may be too inaccurate for the purpose that it should serve:

for instance, if it is desired to perform fault detection by analyzing the
difference between the state of the process that is predicted by the model