mlsanityData to 14 Oct 2026

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

arXiv 2604.23350 ↗First posted 25 Apr 2026math.NA cs.LG cs.NAcited by 0

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 18 of its 34 references that are in the map. First posted on arXiv 25 Apr 2026.

Builds on

18 of 34 references.

Closest ancestors · 3

Same direction, newest first

  1. 2026Flow Matching is Adaptive to Manifold Structures25 Feb
  2. 2022Flow Matching for Generative Modeling6 Oct
  3. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 15

  1. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,248
  2. 2017Squeeze-and-Excitation Networkscited by 4,789
  3. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,401
  4. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  5. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,223
  6. 20163D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotationcited by 1,476
  7. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  8. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 583
  9. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 303
  10. 2020PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domaincited by 174
  11. 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 148
  12. 2025Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domainscited by 62
3 more
  1. 2022wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation lawscited by 29
  2. 2025BlendedNet: A Blended Wing Body Aircraft Dataset and Surrogate Model for Aerodynamic Predictionscited by 16
  3. 2025LAMP: Data-Efficient Linear Affine Weight-Space Models for Parameter-Controlled 3D Shape Generation and Extrapolationcited by 4

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  1. 2026FluidFlow: a flow-matching generative model for fluid dynamics surrogates on unstructured meshes
  2. 2025GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometries
  3. 20253DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization
  4. 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints
  5. 2026Patched Flow Matching: Generative Wall-Pressure Reconstruction Beyond Training-Domain Scales from Sparse Sensors
  6. 2026VTV-FM: Flow Matching through Variational Terminal-Velocity Closure
  7. 2026High-fidelity Three-Dimensional Flow Field Reconstruction Driven by Turbulent Fluid Dynamics
  8. 2026PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics