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

Rapid and accurate simulations of fluid dynamics around complicated geometric bodies are critical in a variety of engineering and scientific applications. While scientific machine learning (SciML) has shown considerable promise, most studies in this field are limited to simple geometries. This paper addresses this gap by benchmarking diverse SciML models, including neural operators and vision transformer-based foundation models, for fluid flow prediction over intricate geometries. We evaluate the impact of geometric representations-Signed Distance Fields (SDF) and binary masks-on model accuracy, scalability, and generalization using a high-fidelity dataset of steady-state flow over complex geometries. We introduce a unified scoring framework that integrates metrics for global accuracy, boundary layer fidelity, and physical consistency. Our findings reveal that newer foundation models significantly outperform neural operators, particularly in data-limited scenarios. In addition, binary mask representation enhances the performance of vision transformer models by up to 10%, while SDF representations improve neural operator performance by up to 7%. Despite these promises, all models struggle with out-of-distribution generalization, highlighting a critical challenge for future SciML applications. Our work paves the way for robust and scalable ML solutions for fluid dynamics across complex geometries.