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This study demonstrates using physical constraints to model complex systems with unmeasurable variables. Sparse regression and interpolation overcome limitations in data-driven modeling, improving accuracy for turbulent flow dynamics.

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Area of Science:

  • Fluid dynamics
  • Complex systems modeling
  • Data-driven science

Background:

  • Spatially extended systems often contain crucial latent variables that are difficult to measure.
  • This poses a significant challenge for data-driven modeling and accurate dynamic description.
  • Weakly turbulent quasi-two-dimensional Kolmogorov flow serves as a relevant case study.

Purpose of the Study:

  • To illustrate the use of physical constraints for overcoming limitations in modeling systems with unmeasurable latent variables.
  • To develop a data-driven approach for modeling weakly turbulent Kolmogorov flow.
  • To investigate the impact of measurement noise on model reconstruction.

Main Methods:

  • Employing physical constraints to eliminate latent variable terms in governing partial differential equations by increasing equation order.
  • Utilizing local polynomial interpolation for data processing.
  • Applying sparse regression to reconstruct system dynamics from spatiotemporal data.
  • Simulating experimental measurement techniques like particle image velocimetry.

Main Results:

  • Successfully eliminated latent variables by increasing the order of the governing partial differential equations.
  • Demonstrated the effectiveness of local polynomial interpolation and sparse regression for handling experimental-like data.
  • Identified model sensitivity to measurement noise, particularly due to high-order derivatives.

Conclusions:

  • Physical constraints offer a viable method to incorporate unmeasurable variables into data-driven models.
  • The proposed method is effective for modeling complex fluid dynamics like Kolmogorov flow.
  • Careful consideration of measurement noise is crucial when applying high-order derivative-based models.