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Discovering multiscale and self-similar structure with data-driven wavelets.

Daniel Floryan1, Michael D Graham2

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Summary
This summary is machine-generated.

This study introduces a data-driven wavelet decomposition method to uncover hierarchical structures in complex systems. The technique reveals scale-specific features, offering new insights into multiscale phenomena like turbulence.

Keywords:
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Area of Science:

  • Multiscale data analysis
  • Complex systems science
  • Applied mathematics

Background:

  • Many scientific and engineering systems exhibit features across multiple temporal and spatial scales.
  • Identifying and characterizing these multiscale features is challenging due to system-specific complexities.
  • Existing methods often struggle to capture the inherent hierarchical structure of such systems.

Purpose of the Study:

  • To develop a novel analysis method for discovering an energetic hierarchy of structures localized in scale and space.
  • To introduce a 'data-driven wavelet decomposition' that reflects the inherent structure of observational data.
  • To provide a model-free approach for characterizing localized hierarchical structures in multiscale systems.

Main Methods:

  • Development of a data-driven wavelet decomposition technique.
  • Application of the method to observational datasets, including turbulence.
  • Analysis of the resulting basis vectors to identify scale-localized structures.

Main Results:

  • The data-driven wavelet decomposition successfully identifies inherent structures in datasets, regardless of their complexity.
  • When applied to turbulence, the method reveals self-similar structures across a broad range of spatial scales.
  • This provides direct, model-free evidence supporting established phenomenological models of turbulence.

Conclusions:

  • The data-driven wavelet decomposition is an effective tool for characterizing localized hierarchical structures in multiscale systems.
  • This method offers a new perspective on understanding the 'building blocks' of complex phenomena.
  • The approach has broad applicability across various scientific and engineering domains dealing with multiscale data.