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物理增强的流场深度学习建模与模拟方法

金晓威 赖马树金 李惠

金晓威, 赖马树金, 李惠. 物理增强的流场深度学习建模与模拟方法. 力学学报, 2021, 53(10): 2616-2629 doi: 10.6052/0459-1879-21-373
引用本文: 金晓威, 赖马树金, 李惠. 物理增强的流场深度学习建模与模拟方法. 力学学报, 2021, 53(10): 2616-2629 doi: 10.6052/0459-1879-21-373
Jin Xiaowei, Laima Shujin, Li Hui. Physics-enhanced deep learning methods for modelling and simulating flow fields. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2616-2629 doi: 10.6052/0459-1879-21-373
Citation: Jin Xiaowei, Laima Shujin, Li Hui. Physics-enhanced deep learning methods for modelling and simulating flow fields. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2616-2629 doi: 10.6052/0459-1879-21-373

物理增强的流场深度学习建模与模拟方法

doi: 10.6052/0459-1879-21-373
基金项目: 国家自然科学基金(51921006, U1711265, 51878230)和广东省科技厅(2020B1212030001)资助项目
详细信息
    作者简介:

    赖马树金, 副教授, 主要研究方向: 智能流体力学与风工程. E-mail: laimashujin@hit.edu.cn

  • 中图分类号: O368

PHYSICS-ENHANCED DEEP LEARNING METHODS FOR MODELLING AND SIMULATING FLOW FIELDS

  • 摘要: 流体运动理论上可用Navier−Stokes方程描述, 但由于对流项带来的非线性, 仅在少数情况可求得方程解析解. 对于复杂工程流动问题, 数值模拟难以高效精准计算高雷诺数流场, 实验或现场测量难以获得流场丰富细节. 近年来, 人工智能技术快速发展, 深度学习等数据驱动技术可利用灵活网络结构, 借助高效优化算法, 获得对高维、非线性问题的强大逼近能力, 为研究流体力学计算方法带来新机遇. 有别于传统图像识别、自然语言处理等典型人工智能任务, 深度学习模型预测的流场需满足流体物理规律, 如Navier−Stokes方程、典型能谱等. 近期, 物理增强的流场深度学习建模与模拟方法快速发展, 正逐渐成为流体力学全新研究范式: 根据流体物理规律选取网络输入特征或设计网络架构的方法称为物理启发的深度学习方法, 直接将流体物理规律显式融入网络损失函数或网络架构的方法称为物理融合的深度学习方法. 研究内容涵盖流体力学降阶模型、流动控制方程求解领域.

     

  • 图  1  基于LSTM的POD模型[51]

    Figure  1.  Architecture of LSTM-based POD model[51]

    图  2  流场重构神经网络架构: 多对一双向循环神经网络[55]

    Figure  2.  Architecture of many-to-one bidirectional RNN to reconstruct the flow field[55]

    图  3  Re = 2.4 × 104时的瞬时尾流场[55]

    Figure  3.  Instantaneous wake-flow field[55] for Re = 2:4 × 104

    图  4  用于建立压力−速度场模型的卷积神经网络架构. “conv”表示卷积层, “ReLU”是非线性激活函数, “pooling”表示最大池化层, “FC”表示全连接层, “concat”表示不同路径融合[62]

    Figure  4.  The architecture of the fusion CNN to establish the pressure−velocity model. “conv”denotes convolutional layer; “ReLU” denotes nonlinear rectified linear unit; “pooling” denotes max pooling layer; “FC” denotes fully-connected layer; “concat” denotes the concatenating of different paths[62]

    图  5  不同雷诺数下模型预测流场与CFD计算结果对比[62]. CFD计算结果: (a) Re = 65, (c) Re = 170, (e) Re = 500, (g) Re = 1000; 模型预测结果: (b) Re = 65, (d) Re = 170, (f) Re = 500, (h) Re = 1000

    Figure  5.  Comparisons of instantaneous flow fields between the model predictions and CFD results for various Reynolds numbers[62]. CFD results for (a) Re = 65, (c) Re = 170, (e) Re = 500, and (g) Re = 1000; model predictions for (b) Re = 65, (d) Re = 170, (f) Re = 500, and (h) Re = 1000

    图  6  NSFnets网络架构[66]

    Figure  6.  A schematic of NSFnets[66]

    图  7  圆柱绕流求解误差[66]: (a) 流向速度, (b) 横向速度和 (c) 压力的L2相对误差

    Figure  7.  Flow past a circular cylinder[66]: relative L2 errors of NSFnets simulations for (a) the streamwise velocity, (b) the crossflow velocity and (c) pressure

    图  8  基于深度强化学习的微分方程求解框架[74]

    Figure  8.  DRL framework for equation solution[74]

    表  1  采用RAR增加残差点时NSFnets求解的速度和压力L2相对误差[66]

    Table  1.   Relative L2 errors of velocity and pressure solutions for NSFnets with residual points added via RAR[66]

    SamplingVP-NSFnetVV-NSFnet
    $ \epsilon_{u} $/%$ \epsilon_{v} $/%$ \epsilon_{p} $/%$ \epsilon_{u} $/%$ \epsilon_{v} $/%
    Random0.0095 ± 0.00260.0823 ± 0.01670.0401 ± 0.00610.0254 ± 0.00580.0704 ± 0.0160
    RAR0.00560.03690.03150.00830.0280
    下载: 导出CSV
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  • 收稿日期:  2021-08-04
  • 录用日期:  2021-09-15
  • 网络出版日期:  2021-09-16
  • 刊出日期:  2021-10-26

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