Physics informed neural network in flowfield reconstruction

YAO Shaobo; HE Weifeng; CHEN Lihua; WU Changju; CHEN Weifang

doi:10.7638/kqdlxxb-2021.0080

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Physics informed neural network in flowfield reconstruction

更新时间：2026-05-28

- Physics informed neural network in flowfield reconstruction
- Vol. 40, Issue 5, Pages: 30-38(2022)
- 作者机构：
  
  浙江大学航空航天学院,杭州,310027
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2021.0080
  CLC： TP181;O357.5
- Published：2022
- 稿件说明：
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尧少波, 何伟峰, 陈丽华, 等. 融合物理的神经网络方法在流场重建中的应用[J]. 空气动力学学报, 2022, 40(5): 30−38.

YAO Shaobo, HE Weifeng, CHEN Lihua, et al. Physics informed neural network in flowfield reconstruction[J]. 2022, 40(5): 30-38.
尧少波, 何伟峰, 陈丽华, 等. 融合物理的神经网络方法在流场重建中的应用[J]. 空气动力学学报, 2022, 40(5): 30−38. DOI： 10.7638/kqdlxxb-2021.0080

YAO Shaobo, HE Weifeng, CHEN Lihua, et al. Physics informed neural network in flowfield reconstruction[J]. 2022, 40(5): 30-38. DOI： 10.7638/kqdlxxb-2021.0080.

摘要

神经网络融合物理先验知识能极大提高其拟合复杂变量的能力，其中融合神经网络和物理控制方程的物理融合神经网络模型（physical-informed neural network

PINN），赋予传统神经网络所不具备的先验知识和可解释性。结合课题组对PINN方法的研究和应用，本文介绍了融合N-S方程的PINN神经网络模型预测能力。首先借助三维超声速槽道湍流的直接数值计算数据，耦合神经网络和可压缩N-S方程，应用PINN方法对槽流的瞬时流场的物理量进行预测，并对瞬时量及其统计平均值与DNS对应结果进行对比来验证训练所获PINN模型的可靠性。其次，借助不可压缩圆柱绕流与三维可压缩槽道流动的计算数据，利用PINN模型进行了N-S控制方程待定系数与待定项的重建，结果显示其在重建流场流动信息的同时可逼近方程的待定系数。研究结果证实了PINN方法可为建立流动物理模型提供工具和算法支撑。

Abstract

A novel physics-informed neural network named PINN was proposed recently by Karniadakis G. E.(2017). It combined the neural network and partial differential equation to endow the traditional machine learning algorithm with prior knowledges and interpretability. Its performance has attracted lots of research interest

and this paper presents the predictions based on PINN and direct numerical simulation results for two cases. Combing the neural networks and compressible Navier-Stokes equations

the turbulent instantaneous flow field of a fully developed turbulent channel flow was reconstructed

a good agreement has been achieved between the DNS results and predictive results for both instantaneous and the statistical mean profiles of flow quantities. The method was also used to predict the undetermined coefficient of the N-S equation for the 2-dimensional circular cylinder and the undetermined item of the N-S equation for the 3-dimensional compressible channel flow with different initial values

the results matched the exact data very well. These results proved that the physics-informed neural network had a strong capability for physics problems.

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references

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