arXiv:2604.23350math.NAcs.LG2026-04

用物理约束生成高精度三维气动流场,解决传统方法失真问题。

GeoFunFlow-3D: A Physics-Guided Generative Flow Matching Framework for High-Fidelity 3D Aerodynamic Inference over Complex Geometries

论文配图:GeoFunFlow-3D: A Physics-Guided Generative Flow Matching Framework for High-Fidelity 3D Aerodynamic Inference over Complex Geometries
图 1 · 摘自论文原文
  • 基于最优传输构建生成路径,稳定训练过程
  • 引入无自动微分高阶离散引擎,缓解梯度僵化
  • 拓扑感知超分辨率模块精准捕捉激波等细节

深度生成模型与神经算子在三维气动推断中展现出巨大潜力,但常因谱偏差和控制方程中的梯度冲突导致物理一致性不足及高频特征丢失。为此,我们提出GeoFunFlow-3D——一种物理引导的生成流匹配框架。时间上,利用最优传输理论构建生成路径,确保训练稳定;频域上,采用无自动微分(No-AD)高阶离散引擎,降低梯度刚性;空间上,引入拓扑感知超分辨率模块(SATO),严格在激波等局部区域施加物理约束。在复杂工业数据集上评估:在BlendedNet数据集上,即使在稀疏数据下也避免模式崩溃;在NASA Rotor37测试中,准确捕获三维分离激波结构。相比传统算子,该框架显著提升精度,压力场相对均方根误差(RRMSE)降至0.0215,同时保持高效推理能力。本工作为高维流场生成提供了可靠、几何驱动的新范式。

原文摘要 · Abstract (English)

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.

三维气动生成模型物理引导流场生成

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