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

2025-03-21

AI Summary

High-fidelity 3D flow field simulation is computationally prohibitive for real-time applications such as aerodynamic optimization and medical device design. To address this, we propose Geometric-DeepONet, a surrogate model integrating geometric priors with physical constraints. Specifically, we embed Signed Distance Functions (SDFs) as geometric encodings into the DeepONet architecture and introduce velocity gradient penalization and incompressibility-derived regularization to explicitly enforce Navier–Stokes physical consistency. Trained on 1,000 steady-state, high-fidelity 3D flow fields spanning Reynolds numbers Re = 10–1000, the model reduces boundary-layer prediction error by 32%. Gradient prediction accuracy improves by 25% (interpolation) and 45% (extrapolation), significantly enhancing generalization to unseen Reynolds numbers.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Deep Neural Architectures and Foundation Models

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Accurate 3D fluid flow modeling around complex geometries
• High computational cost of 3D flow simulations
• Improving physics consistency in 3D flow prediction

Innovation

• Uses Geometric-DeepONet with SDFs
• Incorporates derivative-informed training strategy
• Improves boundary-layer and gradient accuracy