🤖 AI Summary
This work addresses the challenge that existing deep generative models struggle to simultaneously preserve physical consistency and high-frequency fidelity in three-dimensional aerodynamic inference, primarily due to spectral bias and gradient conflicts arising from governing equations. To overcome these limitations, the authors propose a physics-guided generative flow matching framework that constructs stable generation trajectories grounded in optimal transport theory. The approach incorporates a higher-order discrete numerical engine—operating without automatic differentiation—to alleviate gradient stiffness, and introduces a topology-aware super-resolution module (SATO) that rigorously embeds physical constraints in critical regions such as shock waves. Evaluated on the BlendedNet and NASA Rotor37 datasets, the method achieves a pressure field relative root-mean-square error of 0.0215 under sparse data conditions, significantly outperforming current neural operators while maintaining computational efficiency during inference.
📝 Abstract
Deep generative models and neural operators have demonstrated significant potential for 3D aerodynamic inference. However, they often face inherent challenges in maintaining physical consistency and preserving high-frequency features, primarily due to spectral bias and gradient conflicts within the governing equations. To address these issues, we propose GeoFunFlow-3D, a physics-guided generative flow matching framework. Temporally, we utilize optimal transport theory to build the generation path, ensuring stable training dynamics. Spectrally, we introduce a high-order discrete engine without automatic differentiation (No-AD) to reduce gradient stiffness. Spatially, a topology-aware super-resolution module (SATO) is employed to rigorously enforce physical laws in localized regions such as shock waves. We evaluated our framework on complex industrial datasets. On the BlendedNet dataset, the model successfully avoids mode collapse even under sparse data conditions. For the NASA Rotor37 test, it accurately captures 3D detached shock structures. Compared to conventional operators, GeoFunFlow-3D significantly improves accuracy, reducing the pressure field error (RRMSE) to 0.0215 while maintaining competitive inference efficiency. Ultimately, this work provides a reliable, geometry-driven approach for generating high-dimensional fluid fields.