Geodesic Convolutional Shape Optimization

Pierre Baque, Edoardo Remelli, Francois Fleuret, Pascal Fua
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:472-481, 2018.

Abstract

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 poly-cube 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-baque18a, title = {Geodesic Convolutional Shape Optimization}, author = {Baque, Pierre and Remelli, Edoardo and Fleuret, Francois and Fua, Pascal}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {472--481}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/baque18a/baque18a.pdf}, url = {https://proceedings.mlr.press/v80/baque18a.html}, abstract = {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 poly-cube 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.} }
Endnote
%0 Conference Paper %T Geodesic Convolutional Shape Optimization %A Pierre Baque %A Edoardo Remelli %A Francois Fleuret %A Pascal Fua %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-baque18a %I PMLR %P 472--481 %U https://proceedings.mlr.press/v80/baque18a.html %V 80 %X 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 poly-cube 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.
APA
Baque, P., Remelli, E., Fleuret, F. & Fua, P.. (2018). Geodesic Convolutional Shape Optimization. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:472-481 Available from https://proceedings.mlr.press/v80/baque18a.html.

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