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Sparse identification of slow timescale dynamics.

Jason J Bramburger1, Daniel Dylewsky2, J Nathan Kutz3

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Summary
This summary is machine-generated.

This study introduces a new method to extract slow timescale dynamics from complex signals. It accurately identifies and models the emergent slow behavior in multiscale phenomena.

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Area of Science:

  • Physics and Applied Mathematics
  • Complex Systems Analysis
  • Data Science

Background:

  • Multiscale phenomena with distinct timescales are common in scientific fields.
  • Governing equations for fast scales are often known, but emergent slow scale dynamics remain challenging to determine.
  • Understanding slow timescale evolution is crucial for practical applications.

Purpose of the Study:

  • To present an accurate and efficient method for extracting slow timescale dynamics from signals with multiple timescales.
  • To develop a novel tool for analyzing and understanding emergent slow dynamics.
  • To provide a method applicable to signals amenable to averaging.

Main Methods:

  • Utilizing clustering techniques and dynamic mode decomposition (DMD) to discover the fast timescale period.
  • Tracking signals at intervals determined by the fast timescale period.
  • Employing sparse regression techniques to map data point iterations and discover continuous-time slow dynamics.

Main Results:

  • Successfully extracted slow timescale dynamics from signals exhibiting multiple timescales.
  • Demonstrated the accuracy and efficiency of the proposed method.
  • Showcased the ability to discover continuous-time slow dynamics for sufficiently disparate timescales.

Conclusions:

  • The developed method offers a novel approach for analyzing multiscale phenomena.
  • It provides a powerful tool for uncovering emergent slow dynamics that are often of greatest interest.
  • This technique enhances the understanding of complex systems across various scientific disciplines.