Generating Global Behaviors Using Deep Knowledge of Local Dynamics

Kenneth Man-Kam Yip

Even with powerful numerical computers, exploring complex dynamical systems requires significant human effort and judgment to prepare simulations and to interpret numerical results. This paper describes one-aspect of a computer program, KAM, that can autonomously prepare numerical simulations, and can automatically generate high-level, qualitative interpretations of the quantitative results. Given a dynamical system, KAM searches in the phase space for regions where the system exhibits qualitatively distinct behaviors: periodic, almost-periodic, and chaotic motion. KAM uses its knowledge of dynamics to constrain its searches. This knowledge is encoded by a grammar of ' dynamical behavior in which the primitives are geometric orbits, and in which the rules of combination are orbit adjacency constraints. A consistency analysis procedure analogous to Waltz’s constraint satisfaction algorithm is implemented. The utility of the approach is demonstrated by exploring the dynamics of non-linear conservative systems with two degrees of freedom.

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