Benchmarking autoregressive conditional diffusion models for turbulent flow simulation.

Area of Science:

• Computational fluid dynamics
• Machine learning for scientific computing
• Turbulence modeling

Background:

• Simulating turbulent flows is vital across many scientific and engineering fields.
• Machine learning (ML) solvers are increasingly used for fluid dynamics simulations.
• A key challenge for ML solvers is maintaining temporal stability during long-term predictions.

Purpose of the Study:

• To evaluate conditional diffusion models as fully data-driven fluid solvers.
• To assess their capability in achieving temporal stability for extended rollout horizons.
• To benchmark their performance against established flow prediction methods.

Main Methods:

• Utilized autoregressive rollout based on conditional diffusion models for fluid solvers.
• Investigated accuracy, posterior sampling, spectral behavior, and temporal stability.
• Employed three challenging 2D scenarios: incompressible flow, transonic flow, and isotropic turbulence.
• Benchmarked against traditional flow prediction architectures and state-of-the-art stabilization techniques.

Main Results:

• Simple diffusion-based approaches demonstrated superior accuracy and temporal stability compared to several established methods.
• Performance was comparable to unrolling techniques used during training.
• Diffusion models offer probabilistic predictions aligned with physical statistics, unlike faster traditional architectures.
• The benchmarked datasets are suitable for probabilistic evaluation of flow prediction.

Conclusions:

• Conditional diffusion models are a viable option for data-driven fluid solvers, addressing temporal stability challenges.
• These models provide accurate and stable predictions, especially for generalizing beyond training data.
• While slower in inference, their probabilistic nature offers advantages for understanding flow physics.