“Hard” Boundary Low-Order Derivative Physics Informed Neural Network: A Fluid Flow Solver

CUI Yonghe; ZHANG Wenyao; YAN Huilong; QIAN Fang; WANG Qiuwang; ZHAO Cunlu

doi:10.7652/xjtuxb202209013

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“Hard” Boundary Low-Order Derivative Physics Informed Neural Network: A Fluid Flow Solver

更新时间：2025-07-09

- “Hard” Boundary Low-Order Derivative Physics Informed Neural Network: A Fluid Flow Solver
- Vol. 56, Issue 9, Pages: 123-133(2022)
- 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：
- 基金信息：
- DOI：10.7652/xjtuxb202209013
  CLC： TK124
- Online First：10 September 2022，
  
  Published：2022
- 稿件说明：
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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：

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.

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