3D Neural Operator-Based Flow Surrogates around 3D geometries: Signed Distance Functions and Derivative Constraints

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.