Neural Networks: An Overview - Neural Networks: Methodology and Applications - page 71

coe cient) whose variation as a function of concentration and temperature
is given by the free-volume theory, whose validity can be disputed;

• mass conservation at the surface: any solvent molecule that reaches the

surface, and evaporates, gives a contribution to the solvent partial pressure
in the gas; that law remains valid;

• the boundary condition at the coating-substrate interface: since the sub-

strate is impermeable to organic solvents and to water alike, that condition
does not change;

• the value of the partial pressure of the solvent in the gas is the “driving

force” of the whole process; it is given by an equation whose validity is not
disputed.

Therefore, it turns out that the variation of the diffusion coe cient must be ex-
pressed by a black-box neural network, within the whole physical model. That
has been done with the methodology that is described in detail in Chap. 2.
Note that the equations of the model are not ordinary differential equations,
but partial differential equations; that does not preclude the application of
the method.
The reader interested in the details of the model and in the results
will find them in [Oussar 2001]. Another industrial application of semi-
physical modeling—the automatic detection of faults in an industrial dis-
tillation column—can be found in [Ploix 1997]. It is worth mentioning that
applications or semi-physical modeling are in routine use in a major French
manufacturing company for the design of new materials and products.

1.4.11 Two Applications in Environment Control: Ozone Pollution
and Urban Hydrology

The two applications that are described in the present section are related to
the prevision of nonlinear phenomena in environmental science.

1.4.11.1 Prevision of Ozone Pollution Peaks

Ozone concentration measurements are more and more widespread, and elab-
orate knowledge-based models of atmospheric pollution become available, so
that the prediction of ozone peaks becomes feasible. The present section re-
ports an investigation that was carried out at ESPCI within a work group to
which measurements related to industrial area of Lyon (France) were made
available. The objective was to assess the e ciency of machine learning tech-
niques for designing black-box models for the prediction of ozone pollution
peaks in that area.
The available data set was made of hourly measurements of a reliable
ozone sensor between 1995 and 1998. Data pertaining to years 1995 to 1997
were used for training, and data of 1998 for validation. The task was to pre-
dict, 24 hours ahead of time, whether pollution would excess the legal alert
threshold (180 g/m 3 at the time of the investigation).

µ