Deep neural network-based reduced-order modeling of high-speed airfoil flow field

CHEN Zewei; LI Li; KONG Yinan; CHEN Gang

doi:10.7638/kqdlxxb-2024.0050

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Deep neural network-based reduced-order modeling of high-speed airfoil flow field

更新时间：2026-05-28

- Deep neural network-based reduced-order modeling of high-speed airfoil flow field
- Vol. 43, Issue 10, Pages: 33-43(2025)
- 作者机构：
  
  1. 西安交通大学，复杂服役环境重大装备结构强度与寿命全国重点实验室,西安,710049
  2. 西安交通大学航天航空学院，先进飞行器服役环境与控制陕西省重点实验室,西安,710049
  3. 中国航空工业集团公司西安航空计算技术研究所,西安,710000
  4. 西北工业大学计算机学院,西安,710129
  5. 中国空气动力研究与发展中心,绵阳,621000
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2024.0050
  CLC： V211.3
- Published：2025
- 稿件说明：
移动端阅览
陈泽伟, 李立, 孔轶男, 等. 基于深度神经网络的高速翼型流场降阶模型[J]. 空气动力学学报, 2025, 43(10): 33−43.

CHEN Zewei, LI Li, KONG Yinan, et al. Deep neural network-based reduced-order modeling of high-speed airfoil flow field[J]. 2025, 43(10): 33-43.
陈泽伟, 李立, 孔轶男, 等. 基于深度神经网络的高速翼型流场降阶模型[J]. 空气动力学学报, 2025, 43(10): 33−43. DOI： 10.7638/kqdlxxb-2024.0050

CHEN Zewei, LI Li, KONG Yinan, et al. Deep neural network-based reduced-order modeling of high-speed airfoil flow field[J]. 2025, 43(10): 33-43. DOI： 10.7638/kqdlxxb-2024.0050.

摘要

基于深度神经网络的流体建模近年来备受关注。然而，之前的研究主要集中在低速和亚声速流动上，对于高速流场的重构研究相对较少。为了解决高速翼型绕流的快速预测问题，本文提出了一种基于深度神经网络技术的流场降阶模型。该模型利用全连接神经网络和反卷积神经网络，能够建立翼型绕流工况与超声速流场之间的映射关系。首先，通过数值模拟方法构建翼型超声速流场数据集，其中攻角和来流马赫数作为输入数据，流场状态信息作为输出数据。其次，根据输入输出特征构建深度神经网络模型，并进行训练，损失函数均方根误差收敛至

0.0019

。最后，对模型的预测精度和泛化性能进行了分析。神经网络模型在测试集上的流场预测均方根误差低于0.004，最大相对误差值集中在0.03附近，且3个流场状态变量的相关系数均高于0.99。利用该模型对给定工况下的高速定常流场进行预测，结果与数值模拟结果形态高度一致，3个流场变量的相关系数均超过0.998，不同截面处的流场预测值与CFD预测值吻合良好，表明该模型具备良好的预测精度和内插泛化能力。此外，神经网络模型同样具备对数据集以外的马赫数工况进行流场预测的能力，在马赫数小于13的范围内具备一定的外推状态泛化能力。与CFD计算相比，深度神经网络降阶模型的预测速度提升了至少两个数量级，而且所需流场预测数据越多，深度神经网络模型效率优势越显著。

Abstract

The flow field prediction based on deep neural networks has attracted considerable attention in recent years. However

previous studies mainly focused on low-speed and subsonic conditions

whereas much less attention has been paid to reconstructing supersonic and hypersonic flow fields. To rapidly and accurately predict supersonic and hypersonic airfoil flows

this paper proposes a flow field reduc

ed-order model based on deep neural networks

utilizing fully-connected neural and deconvolutional neural networks to establish a mapping relationship between the flow conditions and flow fields. Firstly

a dataset of supersonic airfoil flow fields is constructed by numerical simulations in a wide range of the angles of attack and incoming Mach numbers. Secondly

a deep neural network model is constructed and trained

with the root mean square error of the loss function converged to 0.0019. Finally

the prediction accuracy and generalization performance of the model are analyzed. The root mean square error of the neural network model for the test set is less than 4×10

–3

the maximal relative error is about 0.03

and the correlation coefficients between true and predicted flow fields are higher than 0.99

indicating that the model has good prediction accuracy and interpolation generalization ability. In addition

the neural network model is also able to predict the flow fields for Mach numbers outside the dataset

exhibiting good generalization ability for extrapolated conditions in the range of the Mach number less than 13. Compared to numerical simulations

the prediction speed of the deep-neural-network-based reduced-order model is faster by at least two orders of magnitude

and the efficiency is proportional to the amount of predicted flow fields.

关键词

Keywords

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