The inverse modeling problem

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Abstract
In simulation modeling of very large-scale systems, such as social and natural systems, reductions in scale must be so severe that state variables of the abstraction (model) often cannot be translated back to variables that have real-world significance. Model behavior may not much resemble anything that occurs naturally. If y is a real system and x a model of it, the two can be viewed as related by a set of homomorphic corres pondences M. Then, xMy means x "is a model of" y. Behavior of x pertains to that of y only as M is a valid model, and the relationship is implicit in an inverse model M-1, defined from the fact that xMy implies yM-1x (y "is modeled by" x). To make it explicit, that is to interpret model behavior in terms of real-world variables, means in some sense to be able to identify M-1. One approach to estimating it is suggested, but a definite solution is not reached.

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