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

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.