“Learning three-dimensional flow for interactive aerodynamic design” by Umetani and Bickel

  • ©Nobuyuki Umetani and Bernd Bickel



Entry Number: 089

Session Title:

    Taking Flight


    Learning three-dimensional flow for interactive aerodynamic design



    We present a data-driven technique to instantly predict how fluid flows around various three-dimensional objects. Such simulation is useful for computational fabrication and engineering, but is usually computationally expensive since it requires solving the Navier-Stokes equation for many time steps. To accelerate the process, we propose a machine learning framework which predicts aerodynamic forces and velocity and pressure fields given a three-dimensional shape input. Handling detailed free-form three-dimensional shapes in a data-driven framework is challenging because machine learning approaches usually require a consistent parametrization of input and output. We present a novel PolyCube maps-based parametrization that can be computed for three-dimensional shapes at interactive rates. This allows us to efficiently learn the nonlinear response of the flow using a Gaussian process regression. We demonstrate the effectiveness of our approach for the interactive design and optimization of a car body.


    1. Pierre Baqué, Edoardo Remelli, François Fleuret, and Pascal Fua. 2018. Geodesic Convolutional Shape Optimization. CoRR abs/1802.04016 (2018). arXiv:1802.04016 http://arxiv.org/abs/1802.04016Google Scholar
    2. B. Bonev, L. Prantl, and N. Thuerey. 2017. Pre-computed Liquid Spaces with Generative Neural Networks and Optical Flow. ArXiv e-prints (April 2017). arXiv:cs.GR/1704.07854Google Scholar
    3. R. Buchheim, R. Unger, P. Jousserandot, E. Mercker, F. K. Schenkel, Y. Nishimura, and D. J. Wilsden. 1983. Comparison Tests Between Major European and North American Automotive Wind Tunnels. In SAE Technical Paper. SAE International.Google Scholar
    4. A. X. Chang, T. Funkhouser, L. Guibas, P. Hanrahan, Q. Huang, Z. Li, S. Savarese, M. Savva, S. Song, H. Su, J. Xiao, L. Yi, and F. Yu. 2015. ShapeNet: An Information-Rich 3D Model Repository. ArXiv e-prints (Dec. 2015). arXiv:cs.GR/1512.03012Google Scholar
    5. Mengyu Chu and Nils Thuerey. 2017. Data-Driven Synthesis of Smoke Flows with CNN-based Feature Descriptors. Transaction on Graphics (SIGGRAPH) 36(4) (Apr 2017), 14. Google ScholarDigital Library
    6. Jonathan M Cohen, Sarah Tariq, and Simon Green. 2010. Interactive fluid-particle simulation using translating Eulerian grids. In Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games. ACM, 15–22. Google ScholarDigital Library
    7. Tyler De Witt, Christian Lessig, and Eugene Fiume. 2012. Fluid Simulation Using Laplacian Eigenfunctions. ACM Trans. Graph. 31, 1, Article 10 (Feb. 2012), 11 pages. Google ScholarDigital Library
    8. Xianzhong Fang, Weiwei Xu, Hujun Bao, and Jin Huang. 2016. All-hex Meshing Using Closed-form Induced Polycube. ACM Trans. Graph. 35, 4, Article 124 (July 2016), 9 pages. Google ScholarDigital Library
    9. Michael S. Floater. 2003. Mean Value Coordinates. Comput. Aided Geom. Des. 20, 1 (March 2003), 19–27. Google ScholarDigital Library
    10. Igor Guskov, Kiril Vidimče, Wim Sweldens, and Peter Schröder. 2000. Normal Meshes. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’00). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 95–102. Google ScholarDigital Library
    11. Kurt Hornik. 1991. Approximation Capabilities of Multilayer Feedforward Networks. Neural Netw. 4, 2 (March 1991), 251–257. Google ScholarDigital Library
    12. Jin Huang, Tengfei Jiang, Zeyun Shi, Yiying Tong, Hujun Bao, and Mathieu Desbrun. 2014. ℓ1Basedd Construction of Polycube Maps from Complex Shapes. ACM Trans. Graph. 33, 3, Article 25 (June 2014), 11 pages. Google ScholarDigital Library
    13. Hucho. 1998. Aerodynamics of road vehicles: from fluid mechanics to vehicle engineering. Society of Automotive Engineers, Warrendale, PA.Google Scholar
    14. Tao Ju, Scott Schaefer, and Joe Warren. 2005. Mean Value Coordinates for Closed Triangular Meshes. ACM Trans. Graph. 24, 3 (July 2005), 561–566. Google ScholarDigital Library
    15. Theodore Kim and John Delaney. 2013. Subspace Fluid Re-simulation. ACM Trans. Graph. 32, 4, Article 62 (July 2013), 9 pages. Google ScholarDigital Library
    16. L’ubor Ladický, SoHyeon Jeong, Barbara Solenthaler, Marc Pollefeys, and Markus Gross. 2015. Data-driven Fluid Simulations Using Regression Forests. ACM Trans. Graph. 34, 6, Article 199 (Oct. 2015), 9 pages. Google ScholarDigital Library
    17. Tobias Martin, Nobuyuki Umetani, and Bernd Bickel. 2015. OmniAD: Data-driven Omni-directional Aerodynamics. ACM Trans. Graph. 34, 4, Article 113 (July 2015), 12 pages. Google ScholarDigital Library
    18. Mojang. 2009. Minecraft. (2009).Google Scholar
    19. Charles Ruizhongtai Qi, Hao Su, Kaichun Mo, and Leonidas J. Guibas. 2016. PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation. CoRR abs/1612.00593 (2016). arXiv:1612.00593 http://arxiv.org/abs/1612.00593Google Scholar
    20. Carl Edward Rasmussen and Christopher K. I. Williams. 2005. Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). The MIT Press. Google ScholarDigital Library
    21. Adriana Schulz, Jie Xu, Bo Zhu, Changxi Zheng, Eitan Grinspun, and Wojciech Matusik. 2017. Interactive Design Space Exploration and Optimization for CAD Models. ACM Trans. Graph. 36, 4, Article 157 (July 2017), 14 pages. Google ScholarDigital Library
    22. Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. 2014. Dropout: A Simple Way to Prevent Neural Networks from Overfitting. Journal of Machine Learning Research 15 (2014), 1929–1958. http://jmlr.org/papers/v15/srivastava14a.html Google ScholarDigital Library
    23. Matt Stanton, Ben Humberston, Brandon Kase, James F. O’Brien, Kayvon Fatahalian, and Adrien Treuille. 2014. Self-refining Games Using Player Analytics. ACM Trans. Graph. 33, 4, Article 73 (July 2014), 9 pages. Google ScholarDigital Library
    24. Matt Stanton, Yu Sheng, Martin Wicke, Federico Perazzi, Amos Yuen, Srinivasa Narasimhan, and Adrien Treuille. 2013. Non-polynomial Galerkin Projection on Deforming Meshes. ACM Trans. Graph. 32, 4, Article 86 (July 2013), 14 pages. Google ScholarDigital Library
    25. Hang Su, Subhransu Maji, Evangelos Kalogerakis, and Erik Learned-Miller. 2015. Multiview Convolutional Neural Networks for 3D Shape Recognition. In Proceedings of the 2015 IEEE International Conference on Computer Vision (ICCV) (ICCV ’15). IEEE Computer Society, Washington, DC, USA, 945–953. Google ScholarDigital Library
    26. Marco Tarini, Kai Hormann, Paolo Cignoni, and Claudio Montani. 2004. PolyCube-Maps. ACM Trans. Graph. 23, 3 (Aug. 2004), 853–860. Google ScholarDigital Library
    27. Jonathan Tompson, Kristofer Schlachter, Pablo Sprechmann, and Ken Perlin. 2016. Accelerating Eulerian Fluid Simulation With Convolutional Networks. CoRR abs/1607.03597 (2016). arXiv:1607.03597 http://arxiv.org/abs/1607.03597Google Scholar
    28. Adrien Treuille, Andrew Lewis, and Zoran Popović. 2006. Model Reduction for Real-time Fluids. ACM Trans. Graph. 25, 3 (July 2006), 826–834. Google ScholarDigital Library
    29. K. Um, X. Hu, and N. Thuerey. 2017. Liquid Splash Modeling with Neural Networks. ArXiv e-prints (April 2017). arXiv:cs.GR/1704.04456Google Scholar
    30. Nobuyuki Umetani. 2017. Exploring Generative 3D Shapes Using Autoencoder Networks. In SIGGRAPH Asia 2017 Technical Briefs (SA ’17). ACM, New York, NY, USA, Article 24, 4 pages. Google ScholarDigital Library
    31. Nobuyuki Umetani, Yuki Koyama, Ryan Schmidt, and Takeo Igarashi. 2014. Pteromys: Interactive Design and Optimization of Free-formed Free-flight Model Airplanes. ACM Trans. Graph. 33, 4, Article 65 (July 2014), 10 pages. Google ScholarDigital Library
    32. Peng-Shuai Wang, Yang Liu, Yu-Xiao Guo, Chun-Yu Sun, and Xin Tong. 2017. O-CNN: Octree-based Convolutional Neural Networks for 3D Shape Analysis. ACM Trans. Graph. 36, 4, Article 72 (July 2017), 11 pages. Google ScholarDigital Library
    33. Martin Wicke, Matt Stanton, and Adrien Treuille. 2009. Modular Bases for Fluid Dynamics. ACM Trans. Graph. 28, 3, Article 39 (July 2009), 8 pages. Google ScholarDigital Library
    34. Zhirong Wu, Shuran Song, Aditya Khosla, Xiaoou Tang, and Jianxiong Xiao. 2014. 3D ShapeNets for 2.5D Object Recognition and Next-Best-View Prediction. CoRR abs/1406.5670 (2014). http://arxiv.org/abs/1406.5670Google Scholar
    35. Kai Xu, Vladimir G Kim, Qixing Huang, Niloy Mitra, and Evangelos Kalogerakis. 2016. Data-driven shape analysis and processing. In SIGGRAPH ASIA 2016 Courses. ACM, 4. Google ScholarDigital Library
    36. Olek C Zienkiewicz, Robert L Taylor, and P. Nithiarasu. 2013. The Finite Element Method for Fluid Dynamics, Seventh Edition (7 ed.). Butterworth-Heinemann. http://amazon.com/o/ASIN/1856176355/Google Scholar

ACM Digital Library Publication: