  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.
