Inferring the Dynamic, Quantifying Physical Complexity

  • James P. Crutchfield
Part of the NATO ASI Series book series (NSSB, volume 208)


Through its formalization of inductive inference, computational learning theory provides a foundation for the inverse problem of chaotic data analysis: inferring the deterministic equations of motion underlying observed random behavior in physical systems. Integrating the geometric and statistical techniques of dynamical systems with learning theory provides a framework for consistently, although not absolutely, distinguishing between deterministic chaos and extrinsic fluctuations at a given level of computational resources. Two approaches to the inverse problem, estimating symbolic equations of motion and reconstructing minimal automata from chaotic data series, are reviewed from this point of view. With an inferred model dynamic the dynamical entropies and dimensions can be estimated. More interestingly, its structural properties give a measure of the intrinsic computational complexity of the underlying process.


Inverse Problem Inference Method Inductive Inference Dynamical System Theory Deterministic Chaos 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • James P. Crutchfield
    • 1
  1. 1.Physics DepartmentUniversity of CaliforniaBerkeleyUSA

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