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Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Extracting dynamical equations from experimental data is NP hard.

Toby S Cubitt1, Jens Eisert, Michael M Wolf

  • 1Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, Ciudad Universitaria, 28040 Madrid, Spain.

Physical Review Letters
|May 1, 2012
PubMed
Summary
This summary is machine-generated.

Discovering the dynamical equations governing physical systems from experimental data is a computationally hard problem for both classical and quantum mechanics. This research proves the difficulty of identifying these fundamental laws, even with precise data.

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Area of Science:

  • Physics
  • Computer Science
  • Mathematics

Background:

  • Physical system behavior is dictated by dynamical equations.
  • Discovering these equations and their implications is a core physics pursuit.
  • Identifying underlying equations from data is crucial for scientific understanding.

Purpose of the Study:

  • To demonstrate the computational hardness of identifying dynamical equations from experimental data.
  • To provide complexity-theoretic solutions to the quantum and classical embedding problems.

Main Methods:

  • Computational complexity theory.
  • Analysis of experimental data for equation inference.
  • Theoretical computer science techniques.

Main Results:

  • Identifying dynamical equations from data is proven to be NP-hard for classical and quantum systems.
  • Complexity-theoretic solutions are provided for the long-standing quantum and classical embedding problems.

Conclusions:

  • Inferring fundamental physical laws from data is computationally intractable.
  • This work resolves open problems in mathematics with implications for physics and computer science.