Abstraction By Time-Scale In Qualitative Simulation

Abstract

Qualitative simulation faces an intrinsic problem of scale: the number of limit hypotheses grows exponentially with the number of parameters approaching limits. We present a method called Time-Scale Abstraction for structuring a complex system as a hierarchy of smaller, interacting equilibrium mechanisms. Within this hierarchy, a given mechanism views a slower one as being constant, and a faster one as being instantaneous. A perturbation to a fast mechanism may be seen by a slower mechanism as a displacement of a monotonic function constraint. We demonstrate the time-scale abstraction hierarchy using the interaction between the water and sodium balance mechanisms in medical physiology, an example drawn from a larger, fully implemented, program. Where the structure of a large system permits decomposition by time-scale, this abstraction method permits qualitative simulation of otherwise intractibly complex systems.