A Multi-Scale Feature Enhanced Graph Neural Network for Fluid Dynamics Prediction in Complex Geometries

Jul 16, 2026

Industrial design in vehicle and aerospace relies on large-scale numerical simulations for fluid dynamics evaluation, often incurring heavy computational cost and slow iteration. This work introduces Multi-scale Feature Enhanced Graph Neural Network (ME-GNN) to improve efficiency on complex geometries and large meshes. ME-GNN uses a two-step message-passing GNN for local detail, combines an Attention U-Net with uniform grid discretization for fine-to-coarse feature extraction, and applies K-hop sampling to build subgraphs for scalable training. Experiments on three benchmarks achieve state-of-the-art errors across velocity and surface pressure prediction.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages15

Reading Time38 min

Introduction

Challenges in Graph-Based CFD

Complex Geometry and Flow Structures

Large Scale Irregular Data

Sampling and Aliasing

arXiv :2607 . 1 1672v 1 [ cs .LG] 13 Jul 2026 A MULTI-SCALE FEATURE ENHANCED GRAPH NEURAL NETWORK FOR FLUID DYNAMICS PREDICTION IN COMPLEX GEOMETRIES LI XIAO, TIANYU LI, YIYE ZOU, MINGJIE ZHANG, AND XIAOGANGD DENG ABSTRACT. Industrial design in fields such as vehicle and aerospace engineering often relies on largescale numerical simulations to evaluate fluid dynamics performance, which can incur substantial computational costs. Deep neural networks have shown promise in improving simulation efficiency, especially graph neural networks (GNNs), which demonstrate great potential due to their flexibility with unstructured data. However, GNNs face challenges when dealing with tasks involving complex geometries and large-scale meshes. In this paper, we propose the Multi-scale Feature Enhanced Graph Neural Network (ME-GNN) to tackle these challenges. ME-GNN employs a graph neural network with a two-step messagepassing mechanism to capture detailed local features effectively. Additionally, it integrates an Attention U-Net with uniform grid discretization, enabling the extraction of both fine and coarse features. The model also utilizes K-hop sampling to construct subgraphs, facilitating efficient training on large datasets while preserving detailed local features. We evaluated ME-GNN on three benchmark datasets and achieved stateof-the-art results: a relative L2 error of 0.0196 for the velocity field and 0.0556 for the surface pressure on ShapeNet-Car, a normalized mean squared error of 0.0033 for the flow field on AirfRANS, and a relative L2 error of 0.1416 for the surface pressure on DrivAerNet. 1. INTRODUCTION Accurate fluid dynamics prediction is crucial in the automotive and aerospace industries, as it significantly influence reliability, fuel efficiency, and safety. Additionally, it enables performance optimization, environmental sustainability, and innovative design. While traditional Computational Fluid Dynamics (CFD) methods deliver high accuracy, they are computationally expensive, time-intensive, and require specialized expertise. These limitations present significant challenges for iterative design processes and rapid prototyping, where swift fluid dynamics prediction are critical. Recent advances in deep learning offer promising alternatives that can significantly reduce computation time while maintaining high accuracy [13, 4] . Deep learning models can approximate complex nonlinear relationships and have demonstrated success in various fields, including computer vision and natural language processing. In the context of CFD, data-driven models can learn from simulation data to predict flow fields and aerodnamic forces[5, 21, 22], offering a potential solution to the computational bottlenecks of traditional methods. Graph-based neural network architectures offer flexibility for unstructured data, as they have the potential to learn from simulation data represented on a grid. However, developing a graph-based model for fluid dynamic prediction presents several challenges: Complex geometry and flow structures. Geometric surfaces exhibit intricate features across various spatial scales, ranging from smooth to sharp, distinct edges. Complex geometry exhibits features at different spatial scales. For example, a car has a large-scale overall shape and small-scale side mirrors. In addition, fluid flow problems also involve multi-scale phenomena, such as wake flows and vortices of various sizes. This requires neural networks to be able to extract features at different scales. Date: July 14, 2026 . *Li Xiao and Tianyu Li contributed equally to this work.†Corresponding author: Mingjie Zhang. 2 LI ET AL. Large Scale Irregular Data. In CFD, the datasets used to model fluid dynamics performance are often large and irregular, including high-resolution surface mesh with tons of points and intricate geometries [5] . Standalone neural network architectures, such as Multi-Layer Perceptrons (MLPs) and Convolutional Neur

FAQs

What problem does ME-GNN target in fluid dynamics prediction?

ME-GNN targets accurate and efficient prediction of fluid dynamics on complex geometries and large-scale meshes, where standard CFD is computationally expensive and existing graph models struggle with multi-scale features and scalability.

How does ME-GNN capture multi-scale information?

It uses a two-step message-passing mechanism to extract detailed local features and integrates an Attention U-Net with uniform grid discretization to obtain fine and coarse features.

Why does the paper use K-hop sampling during training?

K-hop sampling constructs subgraphs that enable efficient training on large datasets while preserving detailed local structures important for accurate predictions.

Jul 16, 2026

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