Reconciling Models with Data (System Identification).
It is in our nature to build ever more complex, higher-order
models: VHOMs, in other words. There are those for whom such
a program of model-building constitutes the program of reducing
the scientific uncertainties of today. There are also those
who, by their attachment to the pragmatism of seeking the robustly
preferred decision, above all else and, in particular, above
all the uncertainty of environmental modeling and management,
might tempt us to give up on eliminating ambiguity in the interpretation
of the past. Indeed, with an eye on a future in which VHOMs
will be available for reconciliation with high volume, high
quality (HVHQ) data, such as those we can now acquire with the
Environmental Process Control Laboratory (EPCL), the tasks of
system identification look daunting. There is a paradox. For
any given system, we can have a VHOM that is not capable of
being unambiguously reconciled with the observed record of the
past; yet we can have unambiguously identified low order models
(LOMs) incapable of supporting a satisfactory theoretical interpretation
of the data. Should we indeed give up our quest: to reconcile
a theoretically insightful model with the observed data? Our
current research is developing an approach to system identification
in which the gap between the two maximally different experiences
of the system's behavior, {Data} and {Theory}, is to be bridged
by a chain of transcriptions, from Data-based Mechanistic (DBM)
models to Theory-based Mechanistic (TBM) models. At some point
in the chain, in the parametric (not output) spaces of the two
types of model, a transcribed interpretation of the {Data} can
be compared with the transcribed interpretation of {Theory}.
What is more, this comparison may be made all the more effective
through the use of novel algorithms of recursive estimation,
in particular, those currently being developed around the Recursive
Prediction Error (RPE) and Fixed Interval Smoothing (FIS) algorithms.
And these, in turn, can have very practical outcomes, for the
detection of faults in the instrumentation of networks for monitoring
water quality in real time, specifically in the Lagoon of Venice
(through the Chair's collaboration with the University of Venice).