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Learning dominant physical processes with data-driven balance models.

Jared L Callaham1, James V Koch2, Bingni W Brunton3

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This study introduces a data-driven approach to automatically identify dominant physical processes in complex systems. This method generalizes traditional physics-based modeling to non-asymptotic regimes, uncovering key mechanistic models across diverse scientific fields.

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Area of Science:

  • Physics-based modeling
  • Data-driven science
  • Computational science

Background:

  • Traditional physics-based modeling relies on approximations of dominant processes.
  • This approach is mathematically complex and limited to asymptotic regimes with scale separation.
  • A need exists for generalized methods applicable to non-asymptotic regimes.

Purpose of the Study:

  • To automate and generalize the identification of dominant physical balances.
  • To develop data-driven balance models for non-asymptotic regimes.
  • To uncover key mechanistic models in complex systems.

Main Methods:

  • Introduction of an 'equation space' concept.
  • Utilizing unsupervised learning to identify subspace clusters representing local balances.
  • Applying data-driven models to identify negligible terms in equations.

Main Results:

  • Successfully delineated dominant balance physics in a wider range of systems.
  • Demonstrated the efficacy of data-driven balance models.
  • Uncovered key mechanistic models in turbulence, combustion, nonlinear optics, geophysical fluids, and neuroscience.

Conclusions:

  • The proposed data-driven approach effectively automates and generalizes physics-based modeling.
  • This method overcomes limitations of traditional asymptotic approaches.
  • It offers a powerful tool for discovering fundamental physics in complex scientific domains.