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Assimilation of statistical data into turbulent flows using physics-informed neural networks.

Sofía Angriman1,2, Pablo Cobelli1,2, Pablo D Mininni1,2

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This study introduces a physics-informed neural network method to assimilate experimental flow data into turbulent models when forcing information is unavailable. This approach generates valid turbulent states from accessible flow features, improving model accuracy.

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Area of Science:

  • Fluid dynamics
  • Computational physics
  • Machine learning

Background:

  • Turbulent flow modeling often lacks detailed forcing or boundary condition data.
  • Experimental data on flow features like mean velocity profiles are sometimes available.
  • Existing methods for assimilating such data can be complex or costly.

Purpose of the Study:

  • To develop a physics-informed neural network (PINN) approach for assimilating available flow conditions into turbulent states.
  • To enable the generation of valid turbulent flow states using partial or incomplete information.
  • To provide a flexible method applicable to experimental and atmospheric science problems.

Main Methods:

  • Utilizing physics-informed neural networks to enforce physical laws within the learning process.
  • Assimilating statistical moments and mean profiles of turbulent flows.
  • Implementing two resolution-scaling techniques: parallel neural networks and nudging with numerical solvers.

Main Results:

  • Demonstrated successful assimilation of various statistical conditions into turbulent flow states.
  • Showcased the generation of physically plausible turbulent flow approximations.
  • Validated the effectiveness of both parallel networks and nudging for resolution scaling.

Conclusions:

  • Physics-informed neural networks offer a powerful tool for data assimilation in turbulent flow modeling.
  • The proposed method effectively integrates experimental data, overcoming limitations of traditional approaches.
  • The developed techniques provide practical solutions for enhancing turbulent flow simulations with available observational data.