PHYSICS-ENHANCED DEEP LEARNING METHODS FOR MODELLING AND SIMULATING FLOW FIELDS
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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.Abstract: Fluid flows can be theoretically described by the Navier−Stokes equations. However, due to the nonlinear convection term, analytical solutions of the equations can only be obtained for a few cases. For complex engineering flow problems at high Reynolds numbers, it is difficult to calculate the flow field efficiently and accurately by numerical simulation, and it is difficult to obtain rich details by experiment or field measurement. With the rapid development of artificial intelligence technology, data-driven technologies such as deep learning can make use of flexible network structures and efficient optimization algorithms to obtain strong approximating ability for high-dimensional and nonlinear problems, bringing opportunities for the development of computational methods for fluid mechanics. Different from traditional data-driven deep learning modeling methods for image classification and natural language processing, the flow fields predicted by deep learning models should obey physical laws of fluids, such as the Navier−Stokes equations and typical energy spectrum. Recently, physics-enhanced deep learning methods have developed rapidly and are gradually becoming a new research paradigm of fluid mechanics: the method of selecting network input features or designing network architecture according to the laws of fluid physics is called the physics-inspired deep learning method, and the method of explicitly integrating the laws of fluid physics into the network loss function or network architecture is called the physics-informed deep learning method. The research content covers the fields of reduced order modelling of fluid mechanics and solution of flow governing equations.
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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
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]
Sampling VP-NSFnet VV-NSFnet $ \epsilon_{u} $/% $ \epsilon_{v} $/% $ \epsilon_{p} $/% $ \epsilon_{u} $/% $ \epsilon_{v} $/% Random 0.0095 ± 0.0026 0.0823 ± 0.0167 0.0401 ± 0.0061 0.0254 ± 0.0058 0.0704 ± 0.0160 RAR 0.0056 0.0369 0.0315 0.0083 0.0280 
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