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Reconstruction of normal forms by learning informed observation geometries from data.

Or Yair1, Ronen Talmon2, Ronald R Coifman3

  • 1Viterbi Faculty of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel.

Proceedings of the National Academy of Sciences of the United States of America
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Scientists can now discover underlying physical laws from data using geometry learning. This method reconstructs dynamical systems

Keywords:
data analysisdynamical systemsempirical modelsgeometrygraph theory

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Area of Science:

  • * Physics and Engineering
  • * Applied Mathematics
  • * Dynamical Systems Theory

Background:

  • * Discovering physical laws from empirical data is fundamental to science and engineering.
  • * Physical laws are often expressed as nonlinear differential equations.
  • * Dynamical systems theory characterizes system behaviors using normal forms.

Purpose of the Study:

  • * To develop a method for directly reconstructing normal forms from empirical observations.
  • * To create a quantitative mapping from data to prototypical dynamical regimes.
  • * To infer state variables and parameters intrinsically from observed data.

Main Methods:

  • * Implementation of data-informed geometry learning.
  • * Direct reconstruction of normal forms.
  • * Quantitative mapping of empirical observations to dynamical realizations.

Main Results:

  • * Successfully reconstructed normal forms directly from empirical data.
  • * Developed a method to map observations to intrinsic dynamical parameterizations.
  • * Inferred state variables and parameters without prior physical knowledge.

Conclusions:

  • * Data-informed geometry learning offers a novel approach to discovering physical laws.
  • * This method intrinsically parametrizes system dynamics from observations alone.
  • * Enables understanding of underlying dynamics without explicit reference to fundamental quantities.