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Transfer learning for nonlinear dynamics and its application to fluid turbulence.

Masanobu Inubushi1, Susumu Goto1

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Transfer learning accelerates predictions of chaotic dynamics using minimal data. This approach significantly improves inference accuracy for systems like Lorenz chaos and Navier-Stokes turbulence.

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Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Fluid mechanics
  • Machine learning

Background:

  • Predicting chaotic dynamics and turbulence often requires substantial data.
  • Transfer learning offers a promising approach to enhance data efficiency in complex systems.

Purpose of the Study:

  • To introduce and evaluate transfer learning for predicting nonlinear and chaotic dynamics.
  • To demonstrate the efficacy of transfer learning in improving inference accuracy with limited data.

Main Methods:

  • Applying transfer learning techniques to chaotic systems, specifically the Lorenz system.
  • Optimizing transfer rates for enhanced prediction accuracy.
  • Utilizing knowledge transfer from lower Reynolds number turbulence data to infer properties of Navier-Stokes turbulence.

Main Results:

  • Achieved an order of magnitude improvement in inference accuracy for Lorenz chaos compared to conventional methods.
  • Demonstrated that a small amount of learning is sufficient to infer the energy dissipation rate of Navier-Stokes turbulence.
  • Leveraged the small-scale universality of turbulence for effective knowledge transfer.

Conclusions:

  • Transfer learning significantly enhances the efficiency and accuracy of predicting chaotic dynamics.
  • The methodology shows promise for complex fluid dynamics problems, reducing data requirements through knowledge transfer.