KAM, a system for intelligently guiding numerical experimentation by computer
著者
書誌事項
KAM, a system for intelligently guiding numerical experimentation by computer
（The MIT Press series in artificial intelligence）
MIT Press, c1991
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
Scientists and engineers routinely use graphical reprsentations to organize their thoughts and as parts of the process of solving verbally presented problems. In a cross-disciplinary study that has important implications for research in artificial intelligence and complex nonlinear dynamics, Yip shows how to automate key aspects of this style of reasoning. He domonstrates the basic feasibility of intelligently guided numerical experimentation in a computational theory and a system for implementing the theory. The system, called KAM, is the first computer system that can intelligently guide numerical experimentation and interpret the numerical results in high-level, conceptual terms. KAM's ability to steer numerical experiments arises from the fact taht it not only produces images by also looks at 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, encoded as visual consistency constraints on the phase space and parameter space, to constrain its search for interesting behaviours.
The approach is applied to Hamiltonian systems with two degrees of freedom, an area that is currently of great physical interest, and its power is tested in a difficult problem in hydrodynamics, for which KAM helps derive previously unknown publishable results.
目次
- Part 1 Introduction: goal - automate part of a scientist's work
- Henon's area preserving map - an illustration
- what KAM does
- how KAM does it
- what does KAM build on?
- the rest of the story. Part 2 Overview of KAM: a session with KAM
- design criteria
- KAM overview - structure and processes. Part 3 Orbit recognition: what is orbit recognition?
- core idea - shape from minimal spanning trees
- implementation
- experiment - main illustration
- another experiment - orbit on the surface of a Torus
- evaluating the performance. Part 4 Phase space searching: what is phase space searching?
- core idea - consistency of neighbouring orbits
- rotation number - continuity of discrete flows
- orbit compatibility
- implementation
- experiment - main illustration
- other experiments
- a concise phase portrait description
- evaluating the performance. Part 5 Parameter space searching: what are bifurcations? core idea - structural stability
- generic bifurcations of fixed points
- phase portrait compatibility
- implementation
- experiment
- evaluating the performance
- executive summary of numerical experiments. Part 6 Exploring an open problem: scenario
- standing waves in a rectangular tank
- mathematical formulation
- numerical findings - making a Poincare section
- applying an analytical approximation method
- comparing analytical predictions with numerical findings
- how physical parameters affect chaos
- what have we learned? Part 7 Conclusion: what does KAM do?
- why does KAM work?
- what are the contributions
- what's next - enhancing KAM, a workbench approach to scientific computing
- user manual. (Part contents).
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