Convolutional Neural Networks for Steady Flow Approximation

ABSTRACT

In aerodynamics related design, analysis and optimization problems, flow fields are simulated using computational fluid dynamics (CFD) solvers. However, CFD simulation is usually a computationally expensive, memory demanding and time consuming iterative process. These drawbacks of CFD limit opportunities for design space exploration and forbid interactive design. We propose a general and flexible approximation model for real-time prediction of non-uniform steady laminar flow in a 2D or 3D domain based on convolutional neural networks (CNNs). We explored alternatives for the geometry representation and the network architecture of CNNs. We show that convolutional neural networks can estimate the velocity field two orders of magnitude faster than a GPU-accelerated CFD solver and four orders of magnitude faster than a CPU-based CFD solver at a cost of a low error rate. This approach can provide immediate feedback for real-time design iterations at the early stage of design. Compared with existing approximation models in the aerodynamics domain, CNNs enable an efficient estimation for the entire velocity field. Furthermore, designers and engineers can directly apply the CNN approximation model in their design space exploration algorithms without training extra lower-dimensional surrogate models.

References

1. M. Ahmed and N. Qin. Surrogate-Based Aerodynamic Design Optimization: Use of Surrogates in Aerodynamic Design Optimization. Aerospace Sciences and Aviation Technology, ASAT-13, 2009.
2. J. Anderson. Computational Fluid Dynamics. 1995.
3. V. Balabanov, A. Giunta, O. Golovidov, B. Grossman, H. Mason, T. Watson, and T. Haftkalf. Reasonable design space approach to response surface approximation. Journal of Aircraft, 1999.
4. M. Batill, A. Stelmack, and S. Sellar. Framework for multidisciplinary design based on response-surfaceapproximations. Journal of Aircraft, 1999.
5. Y. Bengio. Learning deep architectures for AI, Foundations and trends in Machine Learning. 2009.
6. L. Chittka, P. Skorupski, and E. Raine. Speed-accuracy tradeo s in animal decision making. Trends in Ecology and Evolution, 2009.
7. D. Daberkow and D. N. New Approaches to Conceptual and Preliminary Aircraft Design: A Comparative Assessment of a Neural Network Formulation and a Response Surface Methodology. World Aviation Conference, 1998.
8. A. Dosovitskiy, P. Fischer, E. Ilg, P. Hausser, C. Hazrba, V. Golkov, P. v.d. Smagt, D. Cremers, and T. Brox. Flownet: Learning optical ow with convolutional networks. In IEEE International Conference on Computer Vision (ICCV), 2015.
9. D. Eigen, C. Puhrsch, and R. Fergus. Depth map prediction from a single image using a multi-scale deep network. In Advances in neural information processing systems, 2014.
10. H. Fang, M. Rais-Rohani, Z. Liu, and M. Horstemeyer. A comparative study of metamodeling methods for multiobjective crashworthiness optimization. Computers & Structures, 2005.
11. G. Forsythe and W. Wasow. Finite-Difference Methods for Partial Di erential Equations. 1960.
12. A. Giunta. Aircraft Multidisciplinary Design Optimization Using Design of Experiments Theory and Response Surface Modeling Methods. 1997.
13. S. Gupta, R. Girshick, P. Arbelßez, and J. Malik. Learning rich features from RGB-D images for object detection and segmentation. In Computer Vision-ECCV. 2014.
14. D. Hartmann, M. Meinke, and W. Schörder. Differential equation based constrained reinitialization for level set methods. Journal of Computational Physics, 2008.
15. V. Heuveline and J. Latt. The OpenLB project: an open source and object oriented implementation of lattice Boltzmann methods. International Journal of Modern Physics, 2007.
16. S. Jeong, M. Murayama, and K. Yamamoto. Efficient optimization design method using kriging model. Journal of Aircraft, 2005.
17. Y. Jia, E. Shelhamer, J. Donahue, S. Karayev, J. Long, R. Girshick, and T. Darrell. Caffe: Convolutional architecture for fast feature embedding. In Proceedings of the ACM International Conference on Multimedia. 2014.
18. A. Keane and P. Nair. Computational approaches for aerospace design. 2005.
19. S. J. Leary, A. Bhaskar, and A. J. Keane. Global approximation and optimization using adjoint computational uid dynamics codes. AIAA journal, 2004.
20. Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 1998.
21. M. Mawson, G. Leaver, and A. Revell. Real-time flow computations using an image based depth sensor and GPU acceleration. 2013.
22. G. R. McNamara and G. Zanetti. Use of the boltzmann equation to simulate lattice-gas automata. Physical Review Letters, 1988.
23. A. Mohamad. Lattice Boltzmann Method. 2011.
24. S. Patankar. Numerical heat transfer and fluid flow. CRC Press, 1980.
25. G. Russo and P. Smereka. A remark on computing distance functions. Journal of Computational Physics, 2000.
26. J. Schmidhuber. Deep learning in neural networks: An overview. Neural Networks, 2015.
27. R. Socher, B. Huval, B. Bath, C. D. Manning, and A. Y. Ng. Convolutional-recursive deep learning for 3d object classification. In Advances in Neural Information Processing Systems, 2012.
28. D. Tran, L. Bourdev, R. Fergus, L. Torresani, and M. Paluri. Deep end2end voxel2voxel prediction. arXiv preprint arXiv:1511.06681, 2015.
29. J. Turner, W. Clough, C. Martin, and J. Topp. Stiffness and deflection analysis of complex structures. Journal of the Aeronautical Sciences, 1956.
30. N. Umetani, Y. Koyama, R. Schmidt, and T. Igarashi. Pteromys: interactive design and optimization of free-formed free-flight model airplanes. ACM Trans. Graph., 2014.
31. K. Valderhaug. The Lattice Boltzmann Simulation on Multi-GPU Systems. 2011.
32. S. Wilkinson, G. Bradbury, and H. S. Reduced-Order Urban Wind Interference, Simulation: Transactions of the Society for Modeling and Simulation International. 2015

Index Terms

• Applied computing

  • Physical sciences and engineering

    • Engineering

• Computing methodologies

  • Machine learning

    • Learning paradigms

      • Supervised learning

    • Machine learning approaches

      • Neural networks