We present a novel deep learning framework for flow field predictions in
irregular domains when the solution is a function of the geometry of either the
domain or objects inside the domain. Grid vertices in a computational fluid
dynamics (CFD) domain are viewed as point clouds and used as inputs to a neural
network based on the PointNet architecture, which learns an end-to-end mapping
between spatial positions and CFD quantities. Using our approach, (i) the
network inherits desirable features of unstructured meshes (e.g., fine and
coarse point spacing near the object surface and in the far field,
respectively), which minimizes network training cost; (ii) object geometry is
accurately represented through vertices located on object boundaries, which
maintains boundary smoothness and allows the network to detect small changes
between geometries; and (iii) no data interpolation is utilized for creating
training data; thus accuracy of the CFD data is preserved. None of these
features are achievable by extant methods based on projecting scattered CFD
data into Cartesian grids and then using regular convolutional neural networks.
Incompressible laminar steady flow past a cylinder with various shapes for its
cross section is considered. The mass and momentum of predicted fields are
conserved. We test the generalizability of our network by predicting the flow
around multiple objects as well as an airfoil, even though only single objects
and no airfoils are observed during training. The network predicts the flow
fields hundreds of times faster than our conventional CFD solver, while
maintaining excellent to reasonable accuracy.

本文提出了一种新颖的基于 PointNet 架构的深度学习框架，用于在几何形状无规则的区域中进行流场预测，该方法实现了在边界平滑性和小尺度几何变化检测方面的优化，并且能够比传统 CFD 解算器快数百倍且保持较高的准确度。

基于点云的深度学习框架在不规则几何形态流动场预测中的应用

A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow  Fields on Irregular Geometries

An approximation model based on convolutional neural networks (CNNs) is
proposed for flow field predictions. The CNN is used to predict the velocity
and pressure field in unseen flow conditions and geometries given the pixelated
shape of the object. In particular, we consider Reynolds Averaged Navier-Stokes
(RANS) flow solutions over airfoil shapes. The CNN can automatically detect
essential features with minimal human supervision and shown to effectively
estimate the velocity and pressure field orders of magnitude faster than the
RANS solver, making it possible to study the impact of the airfoil shape and
operating conditions on the aerodynamic forces and the flow field in near-real
time. The use of specific convolution operations, parameter sharing, and
robustness to noise are shown to enhance the predictive capabilities of CNN. We
explore the network architecture and its effectiveness in predicting the flow
field for different airfoil shapes, angles of attack, and Reynolds numbers.

本文提出了一种基于卷积神经网络（CNN）的近似模型，用于流场预测，该模型可以有效地估算速度和压力场，实现了对空气动力学力和流场的研究。