Abstract
Recent progress of machine learning on graphs allowed to apply deep learning methods on spatial data such as meshes and point clouds. Geometric Deep Learning on meshes considers intrinsic properties of surfaces such as curvatures, inner angles and so on. We apply graph learning methods to the problem of mesh deformation that naturally arises in aircraft ice accretion applications. When ice heights on the surface are calculated using the finite elements method one needs to displace the node positions in order to reflect new surface shape that demonstrates the accreted ice layer. We consider simple yet effective traditional method called prism method and use it as a ground truth to train our Graph Neural Network (GNN) Model. We show that GNN can successfully learn the data by aggregating information from the local neighborhood of the target node.
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REFERENCES
T. Pfaff, M. Fortunato, A. Sanchez-Gonzalez, and P. W. Battaglia, ‘‘Learning mesh-based simulation with graph neural networks,’’ in Proceedings of the International Conference of Learning Representations (2020). https://openreview.net/forum?id=roNqYL0_XP.
A. Sanchez-Gonzalez, J. Godwin, T. Pfaff, R. Ying, J. Leskovec, and P. W. Battaglia, ‘‘Learning to simulate complex physics with graph networks,’’ in Proceedings of International Conference on Machine Learning (2020), pp. 8459–8468; arXiv: 2002.09405.
M. M. Bronstein, J. Bruna, Y. LeCun, A. Szlam, and P. Vandergheynst, ‘‘Geometric deep learning: Going beyond Euclidean data,’’ IEEE Signal Proces. Mag. 34 (4), 18–42 (2017); arxiv: 1611.08097.
M. Bronstein, J. Bruna, T. Cohen, P. Veličkovič, and P. W. Battaglia, ‘‘Geometric deep learning grids, groups, graphs, geodesics, and Gauges,’’ arXiv: 2104.13478 (2021).
I. Kostrikov, Zh. Jiang, D. Panozzo, D. Zorin, and J. Bruna, ‘‘Surface networks,’’ in Proceedings of the Conference on Computer Vision and Pattern Recognition CVPR (2018), pp. 2540–2548.
W. Tang and G. Qiu, ‘‘Dense graph convolutional neural networks on 3D meshes for 3D object segmentation and classification,’’ Image Vision Comput. 114, 104265 (2021). https://www.sciencedirect.com/science/article/pii/S0262885621001700.
Sh. Hattori T. Yatagawa, Y. Ohtake, and H. Suzuki, ‘‘Deep mesh prior: Unsupervised mesh restoration using graph convolutional networks,’’ arxiv: 2107.02909 (2021).
Ch. R. Qi, H. Su, K. Mo Leonidas, and L. J. Guibas, ‘‘PointNet: Deep learning on point sets for 3D classification and segmentation,’’ in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition CVPR (2017), pp. 652–660. https://openaccess.thecvf.com/content_cvpr_2017/html/Qi_PointNet_Deep_Learning_ CVPR_2017_paper.html.
Ch. R. Qi, Li Yi, H. Su, and L. J. Guibas, ‘‘PointNet++: Deep hierarchical feature learning on point sets in a metric space,’’ in Proceedings of the 30th Conference on Advances in Neural Information Processing Systems NIPS 2017.
Y. Wang, Y. Sun, Z. Liu, S. Sarma, M. Bronstein, and J. Solomon, ‘‘Dynamic graph CNN for learning on point clouds,’’ ACM Trans. Graphics 38 (5) (2018).
A. Hertz, R. Hanocka, R. Giryes, and D. Cohen-Or, ‘‘Deep geometric texture synthesis,’’ ACM Trans. Graphics 39 (4) (2020).
R. Hanocka, A. Hertz, N. Fish, R. Giryes, Sh. Fleishman, and D. Cohen-Or, ‘‘MeshCNN: A network with an edge,’’ ACM Trans. Graphics 38 (4) (2019).
Y. Shen, H. Fu, Zh. Du, X. Chen, E. Burnaev, D. Zorin, Zh. Zhou, and Y. Zheng, ‘‘GCN-denoiser: Mesh denoising with graph convolutional networks,’’ ACM Trans. Graphics 41 (1), 1–14 (2022). https://doi.org/10.1145/3480168
M. Armando, J.-S. Franco, and E. Boyer, ‘‘Mesh denoising with facet graph convolutions,’’ IEEE Trans. Visualiz. Comput. Graph. 28, 2999–3012 (2020).
Z. Wu, Sh. Pan, F. Chen, G. Long, Ch. Zhang, and Ph. S. Yu, ‘‘A comprehensive survey on graph neural networks,’’ IEEE Trans. Neural Networks Learn. Syst. 32 (1), 4–24 (2021); arXiv: 1901.00596.
J. Zhou, G. Cui, Zh. Zhang, C. Yang, Zh. Liu, L. Wang, Ch. Li, and M. Sun, ‘‘Graph neural networks: A review of methods and applications,’’ AI Open 1, 57–81 (2020).
X. Tong, D. Thompson, Q. Arnoldus, E. Collins, and E. Luke, ‘‘Three-dimensional surface evolution and mesh deformation for aircraft icing applications,’’ J. Aircraft 54, 1–17 (2016).
S. Bourgault-Côté, K. Hasanzadeh, P. Lavoie, and E. Laurendeau, ‘‘Multi-layer icing methodologies for conservative ice growth,’’ in Proceedings of the 7th European Conference for Aeronautics and Aerospace Sciences EUCASS (2017).
C. Morris, M. Ritzert, M. Fey, W. Hamilton, J. Lenssen, G. Rattan, and M. Grohe, ‘‘Weisfeiler and Leman go neural: Higher-order graph neural networks,’’ in Proceedings of the 33rd AAAI Conference on Artificial Intelligence (2019), pp. 4602–4609.
M. Fey and J. E. Lenssen, ‘‘Fast graph representation learning with PyTorch geometric,’’ in Proceedings of the International Conference on Learning Representations ICLR (2019); arxiv: 1903.02428.
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The work was carried out at the JSCC RAS as part of the government assignment (topic FNEF-2022-0016). Supercomputer MVS-10P was used in the research.
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(Submitted by A. M. Elizarov)
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Shumilin, S. Learning Ice Accretion with Graph Neural Networks. Lobachevskii J Math 43, 2887–2892 (2022). https://doi.org/10.1134/S1995080222130418
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DOI: https://doi.org/10.1134/S1995080222130418