Reconstructing Rayleigh-Bénard flows out of temperature-only measurements using Physics-Informed Neural Networks.

Area of Science:

• Fluid Dynamics
• Computational Science
• Machine Learning

Background:

• Turbulent Rayleigh-Bénard convection is a fundamental problem in fluid dynamics.
• Data assimilation techniques are crucial for reconstructing flow fields from limited measurements.
• Physics-Informed Neural Networks (PINNs) offer a novel approach to integrate physical laws into neural networks.

Purpose of the Study:

• To evaluate the efficacy of PINNs in reconstructing turbulent Rayleigh-Bénard flows using solely temperature data.
• To quantitatively assess PINN performance under varying data densities and turbulence levels.
• To compare PINN capabilities against nudging, a conventional data assimilation method.

Main Methods:

• Utilizing Physics-Informed Neural Networks (PINNs) for flow reconstruction.
• Employing temperature measurements as the sole input data.
• Conducting quantitative analysis across different low-pass filtered information levels and turbulent intensities.
• Comparing PINN results with those from nudging, an equation-informed data assimilation technique.

Main Results:

• PINNs achieve high-precision reconstructions comparable to nudging at low Rayleigh numbers.
• At high Rayleigh numbers, PINNs outperform nudging but necessitate high spatial and temporal temperature data density for satisfactory velocity field reconstruction.
• PINN performance degrades significantly with sparse data, impacting both point-to-point accuracy and statistical properties (PDFs, energy spectra).

Conclusions:

• PINNs demonstrate significant potential for reconstructing turbulent flows from partial temperature data.
• The accuracy of PINN reconstructions is highly dependent on the density and quality of the input temperature data, especially at higher turbulence levels.
• While PINNs show promise, careful consideration of data acquisition strategies is essential for their effective application in complex flow scenarios.