Modeling with differential equations of a great deal of dynamic systems may be
problematic due to either the incompleteness of the available knowledge about
the underlying mechanisms or the lack of an adequate observational data set.
In theory, input-output methods, which aim at the reconstruction of a
functional relationship between the input-output variables only from the
available data samples, could represent a valid alternative. The reconstruction
of such a function is a nonlinear regression problem which can be solved by
assuming that it belongs to opportune classes of approximation schemes, which
range from neural networks, to spline models, to fuzzy systems. But, in
practice, although such methods have been successfully applied to a variety of
domains, they fail when the data set is poor either in size or in quality.
Such a situation is not rare in the case of metabolic systems. We present
a hybrid approach which aims at overcoming the problems addressed above.
The method, which is half way between the differential and input-output
approach, integrates qualitative models and fuzzy systems. Qualitative
modeling methods, developed within the Artificial Intelligence research
framework, allow us to derive qualitative descriptions of the system dynamics
from a qualitative differential model, where both numeric values and
functional dependencies are not explicitely defined. The simulated qualitative
dynamics is then exploited to build a good initialization of a nonlinear
parametric regression model, where the regression function is approximated by
a fuzzy system. The method will be presented through a case study, namely
the intracellular thiamine kinetics in the intestine tissue, which does
present serious identification problems. The results obtained outperform,
in terms of efficiency and robustness, those obtained by the application
of traditional approaches. However, from a mathematical point of view, some
issues need further investigation and some problems are still open.
Copyright. All Rights Reserved.