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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems.

Steven L Brunton1, Joshua L Proctor2, J Nathan Kutz3

  • 1Department of Mechanical Engineering, University of Washington, Seattle, WA 98195; sbrunton@uw.edu.

Proceedings of the National Academy of Sciences of the United States of America
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Summary

This study introduces a machine learning approach to discover governing equations from data, even for complex systems. The method uses sparse regression to create accurate, parsimonious models, overcoming challenges in scientific modeling.

Keywords:
dynamical systemsmachine learningoptimizationsparse regressionsystem identification

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Area of Science:

  • Broad applicability across science and engineering disciplines.
  • Addresses data-rich but model-poor scenarios.

Background:

  • Extracting governing equations from measurement data is a fundamental challenge.
  • Abundant data exists in fields like climate science, neuroscience, and epidemiology, but underlying models are often elusive.

Purpose of the Study:

  • To develop a method for discovering governing equations from noisy measurement data.
  • To create parsimonious models that balance accuracy and complexity, avoiding overfitting.

Main Methods:

  • Combines sparsity-promoting techniques, machine learning, and nonlinear dynamical systems.
  • Utilizes sparse regression to identify the minimal set of terms governing system dynamics.
  • Assumes equations are sparse in the space of possible functions, a common characteristic of physical systems.

Main Results:

  • Successfully discovered governing equations for diverse systems, including oscillators, the Lorenz system, and fluid dynamics (vortex shedding).
  • Demonstrated ability to resolve complex fluid dynamics problems that previously took experts decades.
  • Showcased generalization to parameterized, time-varying, and externally forced systems.

Conclusions:

  • The developed method effectively discovers parsimonious governing equations from data.
  • Offers a powerful tool for scientific discovery in data-abundant fields.
  • Provides a robust approach for modeling complex and dynamic systems.