Reference: Iwasaki, Y. Two Model Abstraction Techniques Based on Temporal Grain Size: Aggregation and Mixed Models. Knowledge Systems Laboratory, August, 1990.
Abstract: Many real world dynamic systems involve such a large number of variables and interconnections that it is difficult to grasp them mentally in their entirety. Abstracting a detailed description to produce a simpler description becomes essential as the complexity of the subject system increases. For example, an abstraction hierarchy of models is necessary to control the combinatorial explosion of envisionment process [4]. The author has investigated how different techniques for generating an abstract model from a detailed dynamic model of a system. One technique is generation of a model of a coarse temporal grain size from a model of a finer grain size by making assumptions about the relative adjustment speeds of the equations in the model [1]. The other technique is aggregating a dynamic system model to generate an aggregate model when the original model is nearly decomposable [8]. This paper compares the two abstraction techniques to show that they are actually closely related. The paper also discusses how the notion of causality relates to that of model abstraction. Both abstraction techniques are means of going bottom-up from a detailed description of a system to a description at a higher level of abstraction. There is an alternative, top-down, way of looking at the situation. When we model a complex system, we carry our modeling only down to some level of components. Above that level, structure and the interrelations of components are explicit. Below that level, the components are black boxes with no detailed internal structure. Suppose that we determine the causal structure of the model but decide subsequently that some part of the model must be elaborated in greater detail. Will the new model, incorporating this elaboration, have the same causal structure as the more aggregated model, or do we have to reexamine the causal ordering from the beginning? Section 2 will show that it is not necessary to reexamine the causal ordering of the aggregated model after elaborating a part of an aggregated model. Kuipers uses abstraction by time-scale in order to control the exponential growth of the number of possible courses of behavior in qualitative simulation [4]. Kuipers has a hierarchy of constraint networks of very fast to very slow mechanisms. When simulating a fast mechanism, variables controlled by slower mechanisms are considered constant, and when simulating a slow mechanism, equilibrium among variables controlled by faster mechanisms is considered to be reached instataneously. This idea of abstraction by time-scale is similar to the notion of abstraction discussed in this paper. The abstraction techniques discussed in this paper can be used to generate a hieracrchy of models of different time scales.