  Solving large complex partial differential equations (PDEs), such as those
that arise in computational fluid dynamics (CFD), is a computationally
expensive process. This has motivated the use of deep learning approaches to
approximate the PDE solutions, yet the simulation results predicted from these
approaches typically do not generalize well to truly novel scenarios. In this
work, we develop a hybrid (graph) neural network that combines a traditional
graph convolutional network with an embedded differentiable fluid dynamics
simulator inside the network itself. By combining an actual CFD simulator (run
on a much coarser resolution representation of the problem) with the graph
network, we show that we can both generalize well to new situations and benefit
from the substantial speedup of neural network CFD predictions, while also
substantially outperforming the coarse CFD simulation alone.
