Benchmarking scientific machine-learning approaches for flow prediction around complex geometries.

Area of Science:

• Computational fluid dynamics
• Scientific Machine Learning (SciML)

Background:

• Accurate fluid dynamics simulations are vital for engineering and science.
• Current SciML models are often limited to simple geometries, hindering applications with complex shapes.

Purpose of the Study:

• To benchmark diverse SciML models for fluid flow prediction over intricate geometries.
• To evaluate the impact of geometric representations (SDF and binary masks) on model performance.
• To introduce a unified scoring framework for assessing SciML models in fluid dynamics.

Main Methods:

• Benchmarking neural operators and vision transformer-based foundation models.
• Utilizing a high-fidelity dataset of steady-state flow over complex geometries.
• Evaluating Signed Distance Fields (SDF) and binary masks as geometric representations.

Main Results:

• Foundation models significantly outperform neural operators, especially in data-limited settings.
• Binary masks improve vision transformer performance by up to 10%; SDFs enhance neural operator performance by up to 7%.
• All tested models exhibit limitations in out-of-distribution generalization.

Conclusions:

• Foundation models represent a significant advancement for SciML in complex fluid dynamics.
• Geometric representation choice critically influences model performance.
• Out-of-distribution generalization remains a key challenge for future SciML development in this domain.