KAM: Automatic Planning and Interpretation of Numerical Experiments Using Geometrical Methods
Abstract
KAM is a computer program that can automatically plan, monitor, and interpret numerical experiments with Hamiltonian systems with two degrees of freedom. The program has recently helped solve an open problem in hydrodynamics - the prediction of onset of chaos in a resonantly excited rectangular wave tank of finite depth. Unlike other approaches to qualitative reasoning about physical system dynamics, KAM's ability to control numerical approaches to qualitative reasoning about physical system dynamics, KAM embodies a significant amount of knowledge about nonlinear dynamics. KAM's ability to control numerical experiments arises from the fact that it not only produces pictures for us to see, but also looks at (sic - in its mind's eye) the pictures it draws to guide its own actions. By combining techniques from computer vision with sophisticated dynamical invariants, KAM is able to exploit mathematical knowledge, represented in terms of a grammar that dictates consistency constraints on the structure of the phase space and parameter space. KAM is organized in three semantic levels: orbit recognition, phase space searching, and parameter space searching. Within each level spatial properties and relationships that are not explicitly represented in the initial representation are extracted by applying three operations - (1) aggregation, (2) partition, and (3) classification - iteratively. Keywords: Artificial intelligence; Hamiltonian mechanics; Numerical experiments.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1989
- Accession Number
- ADA216805
Entities
People
- Kenneth M. Yip
Organizations
- Massachusetts Institute of Technology