Learning turbulent flows with generative models for super resolution and sparse flow reconstruction.

Area of Science:

• Fluid Mechanics
• Machine Learning
• Turbulence Modeling

Background:

• Neural operators are effective for dynamical systems but struggle with turbulent flow details.
• Standard L2 losses in neural operators lead to oversmoothing of fine-scale turbulent structures.

Purpose of the Study:

• To overcome limitations of standard neural operators in turbulent flow analysis.
• To enhance spatio-temporal super-resolution, forecasting, and sparse flow reconstruction using combined operator learning and generative modeling.

Main Methods:

• Developed an adversarially trained neural operator (adv-NO) for super-resolution and forecasting.
• Employed a conditional generative model for sparse flow reconstruction.
• Tested methods on Schlieren jet super-resolution, 3D homogeneous isotropic turbulence, and cylinder wake flow reconstruction.

Main Results:

• adv-NO reduced energy-spectrum error by 15x for jet super-resolution, preserving sharp gradients.
• adv-NO achieved accurate 5-eddy-turnover time forecasts for turbulence with 114x speed-up.
• Conditional generative model accurately reconstructed 3D velocity and pressure fields from sparse data.

Conclusions:

• Combining operator learning with generative modeling effectively addresses limitations of standard neural operators in turbulence.
• The proposed methods enable accurate, low-compute-cost reconstruction and forecasting of turbulent flows.
• Advances bring near-real-time analysis and control within reach for fluid mechanics.