“硬”边界低阶导数型物理信息神经网络:一种流动求解器

崔永赫; 张文耀; 闫慧龙; 钱芳; 王秋旺; 赵存陆

doi:10.7652/xjtuxb202209013

您当前的位置：

首页 >

文章列表页 >

“硬”边界低阶导数型物理信息神经网络:一种流动求解器

—————————————————————— | 更新时间：2025-07-09

- “硬”边界低阶导数型物理信息神经网络:一种流动求解器
- “Hard” Boundary Low-Order Derivative Physics Informed Neural Network: A Fluid Flow Solver
- 西安交通大学学报 2022年56卷第9期页码：123-133
- 作者机构：
  
  西安交通大学热流科学与工程教育部重点实验室,西安,710049
- 作者简介：
  
  : 2022-03-20。作者简介: 崔永赫(1996—),男,硕士生
  赵存陆(通信作者),男,教授,博士生导师。基金项目: 国家自然科学基金资助项目(51976157)
- 基金信息：
  
  : 2022-03-20。作者简介: 崔永赫(1996—),男,硕士生;赵存陆(通信作者),男,教授,博士生导师。基金项目: 国家自然科学基金资助项目(51976157);西安市科技局科技创新人才服务企业资助项目(2020KJRC0057);中央高校基本科研业务费资助项目(xzy012020075)
- DOI：10.7652/xjtuxb202209013
  中图分类号： TK124
- 网络首发：2022-09-10，
  
  纸质出版：2022
- 稿件说明：
移动端阅览
崔永赫, 张文耀, 闫慧龙, 等. “硬”边界低阶导数型物理信息神经网络:一种流动求解器[J]. 西安交通大学学报, 2022,56(9):123-133.

CUI Yonghe, ZHANG Wenyao, YAN Huilong, et al. “Hard” Boundary Low-Order Derivative Physics Informed Neural Network: A Fluid Flow Solver[J]. 2022, 56(9): 123-133.
崔永赫, 张文耀, 闫慧龙, 等. “硬”边界低阶导数型物理信息神经网络:一种流动求解器[J]. 西安交通大学学报, 2022,56(9):123-133. DOI： 10.7652/xjtuxb202209013.

CUI Yonghe, ZHANG Wenyao, YAN Huilong, et al. “Hard” Boundary Low-Order Derivative Physics Informed Neural Network: A Fluid Flow Solver[J]. 2022, 56(9): 123-133. DOI： 10.7652/xjtuxb202209013.

摘要

为加速求解流体力学问题的物理信息神经网络的训练过程

本文将Navier-Stokes方程转换成低阶导数形式

并以“硬”方式施加边界条件

构建了用于求解稳态不可压缩层流流动问题的“硬”边界低阶导数型物理信息神经网络(HLPINN)。应用HLPINN对变截面管道内的流动进行了数值模拟

并将结果与传统的“硬”边界物理信息神经网络(HPINN)结果对比。结果表明:HLPINN和HPINN均能精确模拟截面扩张和收缩管道内的流场; 相较于HPINN

HLPINN可以加速反向传播过程从而加速训练过程; 对于截面扩张和收缩两种工况

与HPINN相比

HLPINN的训练时间减少超60%; HLPINN可对两种优化算法进行加速

对于自适应矩估计(Adam)算法可提速超过200%

对于局部极小化(L-BFGS-B)算法可提速90%左右。此外

用于施加“硬”边界条件的距离函数的形式和值域对计算精度影响很大

但是对训练时间及优化算法计算速度的影响甚微。研究表明

连续、平缓和值域在合理范围的距离函数有助于提高计算精度。

Abstract

To accelerate the training of the physics informed neural network for solving fluid mechanics problems

a “hard” boundary low-order derivative physics informed neural network(HLPINN)is established by converting the Navier-Stokes equations into the low-order derivative form and imposing boundary conditions in a “hard” way to solve steady incompressible laminar flow problems. The HLPINN is used to simulate the flow in the pipes with a variable cross-section

and the results are compared with those obtained from the traditional “hard” boundary physics informed neural network(HPINN). The comparison results show that both HLPINN and HPINN can accurately simulate the flow fields in pipes with the expanding and contracting cross-section. Compared with the HPINN

HLPINN can accelerate the back-propagation process to accelerate the training. For either the cross-section expansion or the cross-section contraction

the training time of the HLPINN is reduced by more than 60% compared with that of HPINN with the same size. The HLPINN can accelerate the two optimization algorithms:adaptive moment estimation(Adam)algorithm and limited-memory BFGS-Bound(L-BFGS-B)algorithm by more than 200% and 90%

respectively. In addition

the form and value range of the distance function used to impose “hard” boundary conditions have a great impact on the calculation accuracy

but are of negligible influence on the training time and the calculation speed of both optimization algorithms. The results show that a continuous and smooth distance function with the reasonable value range can improve the calculation accuracy.

关键词

Keywords

references

吴立明, 王雷, 刘小民, 等. 仿海鸥翼型动静态气动特性的数值模拟 [J]. 西安交通大学学报, 2020, 54(12): 88-97.

WU Liming, WANG Lei, LIU Xiaomin, et al. Numerical simulation on the static and dynamic aerodynamic characteristics of bionic seagull airfoil [J]. Journal of Xi'an Jiaotong University, 2020, 54(12): 88-97.

韩馨仪, 赵松松, 刘斌, 等. 分体式空调室内气流组织CFD仿真优化 [J]. 制冷与空调, 2021, 21(11): 41-45.

HAN Xinyi, ZHAO Songsong, LIU Bin, et al. CFD simulation optimization of indoor air distribution in split air conditioner [J]. Refrigeration and Air-Conditioning, 2021, 21(11): 41-45.

樊桦, 吴东垠. 烟气挡板流动特性的数值模拟 [J]. 西安交通大学学报, 2021, 55(2): 93-99.

FAN Hua, WU Dongyin. Numerical simulation of the flow characteristics of a flue gas damper [J]. Journal of Xi'an Jiaotong University, 2021, 55(2): 93-99.

胡其会, 张鸣远, 李景银, 等. 轴流式血泵水动力特性和生物相容性的数值模拟 [J]. 西安交通大学学报, 2011, 45(8): 118-122.

HU Qihui, ZHANG Mingyuan, LI Jingyin, et al. Numerical simulation for hydrodynamics and biocompatibility in an axial blood pump [J]. Journal of Xi'an Jiaotong University, 2011, 45(8): 118-122.

TRIPATHY R K, BILIONIS I. Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification [J]. Journal of Computational Physics, 2018, 375: 565-588.

ZHU Yinhao, ZABARAS N. Bayesian deep convolutional encoder-decoder networks for surrogate modeling and uncertainty quantification [J]. Journal of Computational Physics, 2018, 366: 415-447.

JIN Xiaowei, CHENG Peng, CHEN Wenli, et al. Prediction model of velocity field around circular cylinder over various Reynolds numbers by fusion convolutional neural networks based on pressure on the cylinder [J]. Physics of Fluids, 2018, 30(4): 047105.

谢晨月, 王建春, 万敏平, 等. 基于人工神经网络的可压缩湍流大涡模拟模型 [J]. 航空学报, 2021, 42(9): 145-160.

XIE Chenyue, WANG Jianchun, WAN Minping, et al. Artificial neural network model for large-eddy simulation of compressible turbulence [J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(9): 145-160.

KIM J, LEE C. Prediction of turbulent heat transfer using convolutional neural networks [J]. Journal of Fluid Mechanics, 2020, 882: A18.

RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics informed deep learning: part I data-driven solutions of nonlinear partial differential equations [EB/OL]. [2022-03-13]. https:∥doi.org/10.48550/arXiv.1711.10561.

RAISSI M, PERDIKARIS P, KARNIADAKIS G E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations [J]. Journal of Computational Physics, 2019, 378: 686-707.

JIN Xiaowei, CAI Shengze, LI Hui, et al. NSFnets(Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations [J]. Journal of Computational Physics, 2021, 426: 109951.

侯龙锋, 朱兵, 张伟. 基于PINN神经网络算法的低雷诺数下槽道流模拟方法 [C]∥第三十一届全国水动力学研讨会论文集: 上册. 北京: 法律出版社, 2020: 1037-1044.

CAI Shengze, WANG Zhicheng, WANG Sifan, et al. Physics-informed neural networks for heat transfer problems [J]. Journal of Heat Transfer, 2021, 143(6): 060801.

CAI Shengze, WANG Zhicheng, FUEST F, et al. Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks [J]. Journal of Fluid Mechanics, 2021, 915: A102.

SUN Luning, GAO Han, PAN Shaowu, et al. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data [J]. Computer Methods in Applied Mechanics and Engineering, 2020, 361: 112732.

BERG J, NYSTRÖM K. A unified deep artificial neural network approach to partial differential equations in complex geometries [J]. Neurocomputing, 2018, 317: 28-41.

陆至彬, 瞿景辉, 刘桦, 等. 基于物理信息神经网络的传热过程物理场代理模型的构建 [J]. 化工学报, 2021, 72(3): 1496-1503.

LU Zhibin, QU Jinghui, LIU Hua, et al. Surrogate modeling for physical fields of heat transfer processes based on physics-informed neural network [J]. CIESC Journal, 2021, 72(3): 1496-1503.

ZHU Qiming, LIU Zeliang, YAN Jinhui. Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks [J]. Computational Mechanics, 2021, 67(2): 619-635.

RAO Chengping, SUN Hao, LIU Yang. Physics-informed deep learning for incompressible laminar flows [J]. Theoretical and Applied Mechanics Letters, 2020, 10(3): 207-212.

LAUBSCHER R, ROUSSEAU P. Application of a mixed variable physics-informed neural network to solve the incompressible steady-state and transient mass, momentum, and energy conservation equations for flow over in-line heated tubes [J]. Applied Soft Computing, 2022, 114: 108050.

BAYDIN A G, PEARLMUTTER B A, RADUL A A, et al. Automatic differentiation in machine learning: a survey [J]. Journal of Machine Learning Research, 2018, 18(153): 1-43.

GLOROT X, BENGIO Y. Understanding the difficulty of training deep feedforward neural networks [C]∥Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics. Chia Laguna Resort, Sardinia, Italy: PMLR, 2010: 249-256.

KINGMA D P, BA J. Adam: a method for stochastic optimization [EB/OL]. [2022-03-13]. https:∥doi. org/10.48550/arXiv.1412.6980.

KESKAR N, WÄCHTER A. A limited-memory quasi-Newton algorithm for bound-constrained non-smooth optimization [J]. Optimization Methods and Software, 2019, 34(1): 150-171.

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

电子级超纯氮深冷空分流程节能优化研究

水蒸气掺混对氨裂解气旋流燃烧与排放特性的影响研究

语义区分和子图整合驱动的知识图谱表示学习方法

面向高海拔空冷发电机防晕性能演化规律的电热耦合研究

采用试验设计方法的第三代CO2气体箔轴承箔片几何参数敏感性分析