用几何信息和梯度约束提升3D流场代理模型的精度与泛化能力。

Accurate modeling of fluid dynamics around complex geometries is critical for applications such as aerodynamic optimization and biomedical device design. While advancements in numerical methods and high-performance computing have improved simulation capabilities, the computational cost of high-fidelity 3D flow simulations remains a significant challenge. Scientific machine learning (SciML) offers an efficient alternative, enabling rapid and reliable flow predictions. In this study, we evaluate Deep Operator Networks (DeepONet) and Geometric-DeepONet, a variant that incorporates geometry information via signed distance functions (SDFs), on steady-state 3D flow over complex objects. Our dataset consists of 1,000 high-fidelity simulations spanning Reynolds numbers from 10 to 1,000, enabling comprehensive training and evaluation across a range of flow regimes. To assess model generalization, we test our models on a random and extrapolatory train-test splitting. Additionally, we explore a derivative-informed training strategy that augments standard loss functions with velocity gradient penalties and incompressibility constraints, improving physics consistency in 3D flow prediction. Our results show that Geometric-DeepONet improves boundary-layer accuracy by up to 32% compared to standard DeepONet. Moreover, incorporating derivative constraints enhances gradient accuracy by 25% in interpolation tasks and up to 45% in extrapolatory test scenarios, suggesting significant improvement in generalization capabilities to unseen 3D Reynolds numbers.