Generative adversarial networks to infer velocity components in rotating turbulent flows

Area of Science:

• Fluid dynamics
• Turbulence research
• Computational physics

Background:

• Rotating turbulent flows present complex inference challenges.
• Accurate reconstruction of flow fields is crucial for scientific understanding and engineering applications.
• Existing methods like Extended Proper Orthogonal Decomposition (EPOD) have limitations in capturing intricate flow dynamics.

Purpose of the Study:

• To quantitatively benchmark the performance of Extended Proper Orthogonal Decomposition (EPOD), Convolutional Neural Networks (CNNs), and Generative Adversarial Networks (GANs).
• To evaluate their capabilities in reconstructing two-dimensional velocity components from partial measurements in rotating turbulent flows.
• To assess reconstruction accuracy for both strongly and weakly correlated velocity components.

Main Methods:

• Systematic quantitative benchmark of point-wise and statistical reconstruction.
• Comparison of linear EPOD, nonlinear CNN, and GAN methods.
• Analysis using standard validation metrics (e.g., L2 distance) and advanced multi-scale wavelet decomposition.
• Statistical validation using Jensen-Shannon divergence, spectral properties, and flatness.

Main Results:

• EPOD performs well only when velocity components are strongly correlated (in the plane orthogonal to rotation).
• CNN and GAN consistently outperform EPOD in both point-wise and statistical reconstructions.
• For weakly correlated components (one parallel to rotation), all methods struggle with point-wise reconstruction.
• GANs demonstrate the ability to statistically reconstruct weakly correlated flow fields.

Conclusions:

• CNNs and GANs offer superior performance over EPOD for inferring velocity components in rotating turbulent flows.
• GANs show significant potential for reconstructing statistical properties of complex, weakly correlated flow data.
• The choice of method depends on the correlation between input and output velocity components and the desired reconstruction fidelity (point-wise vs. statistical).