  Aerodynamic shape optimization has many industrial applications. Existing
methods, however, are so computationally demanding that typical engineering
practices are to either simply try a limited number of hand-designed shapes or
restrict oneself to shapes that can be parameterized using only few degrees of
freedom. In this work, we introduce a new way to optimize complex shapes fast
and accurately. To this end, we train Geodesic Convolutional Neural Networks to
emulate a fluidynamics simulator. The key to making this approach practical is
remeshing the original shape using a polycube map, which makes it possible to
perform the computations on GPUs instead of CPUs. The neural net is then used
to formulate an objective function that is differentiable with respect to the
shape parameters, which can then be optimized using a gradient-based technique.
This outperforms state- of-the-art methods by 5 to 20% for standard problems
and, even more importantly, our approach applies to cases that previous methods
cannot handle.
