Abstract: For flow-related design optimization problems, e.g., aircraft and automobile aerodynamic design, computational fluid dynamics (CFD) simulations are commonly used to predict flow fields and analyze performance. While important, CFD simulations are a resource-demanding and time-consuming iterative process. The expensive simulation overhead limits the opportunities for large design space exploration and prevents interactive design. In this paper, we propose FlowDNN, a novel deep neural network (DNN) to efficiently learn flow representations from CFD results. FlowDNN saves computational time by directly predicting the expected flow fields based on given flow conditions and geometry shapes. FlowDNN is the first DNN that incorporates the underlying physical conservation laws of fluid dynamics with a carefully designed attention mechanism for steady flow prediction. This approach not only improves the prediction accuracy, but also preserves the physical consistency of the predicted flow fields, which is essential for CFD. Various metrics are derived to evaluate FlowDNN with respect to the whole flow fields or regions of interest (RoIs) (e.g., boundary layers where flow quantities change rapidly). Experiments show that FlowDNN significantly outperforms alternative methods with faster inference and more accurate results. It speeds up a graphics processing unit (GPU) accelerated CFD solver by more than 14 000×, while keeping the prediction error under 5%.

FlowDNN：一种用于快速精确流场预测的物理启发深度神经网络

[1]Ahmed MYM, Qin N, 2009. Surrogate-based aerodynamic design optimization: use of surrogates in aerodynamic design optimization. Int Conf on Aerospace Sciences & Aviation Technology, p.1-26. doi: 10.21608/ASAT.2009.23442

[2]Amodio M, Krishnaswamy S, 2019. TraVeLGAN: image-to-image translation by transformation vector learning. IEEE/CVF Conf on Computer Vision and Pattern Recognition, p.8975-8984. doi: 10.1109/CVPR.2019.00919

[3]Balabanov VO, Giunta AA, Golovidov O, et al., 1999. Reasonable design space approach to response surface approximation. J Aircr, 36(1):308-315. doi: 10.2514/2.2438

[4]Bhatnagar S, Afshar Y, Pan S, et al., 2019. Prediction of aerodynamic flow fields using convolutional neural networks. Comput Mech, 64(2):525-545. doi: 10.1007/s00466-019-01740-0

[5]Blazek J, 2015. Computational Fluid Dynamics: Principles and Applications (3^rd Ed.). Butterworth-Heinemann, Oxford, UK, p.466.

[6]Constantin P, Foias C, 1988. Navier–Stokes Equations. The University of Chicago Press, Chicago, IL, USA, p.199.

[7]Daberkow DD, Mavris DN, 1998. New approaches to conceptual and preliminary aircraft design: a comparative assessment of a neural network formulation and a response surface methodology. World Aviation Congress & Exposition, Article 15. doi: 10.4271/985509

[8]Ernst MH, 1981. Nonlinear model-Boltzmann equations and exact solutions. Phys Rep, 78(1):1-171. doi: 10.1016/0370-1573(81)90002-8

[9]Farrashkhalvat M, Miles JP, 2003. Basic Structured Grid Generation: with an Introduction to Unstructured Grid Generation. Elsevier, Amsterdam, the Netherlands, p.190-226. doi: 10.1016/B978-075065058-8/50008-3

[10]Frankle J, Carbin M, 2019. The lottery ticket hypothesis: finding sparse, trainable neural networks. https://arxiv.org/abs/1803.03635v5

[11]Geneva N, Zabaras N, 2019. Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks. J Comput Phys, 383:125-147. doi: 10.1016/j.jcp.2019.01.021

[12]Guastoni L, Guemes A, Ianiro A, et al., 2020. Convolutional-network models to predict wall-bounded turbulence from wall quantities. https://arxiv.org/abs/2006.12483

[13]Guo XX, Li W, Iorio F, 2016. Convolutional neural networks for steady flow approximation. Proc 22^nd ACM SIGKDD Int Conf on Knowledge Discovery and Data Mining, p.481-490. doi: 10.1145/2939672.2939738

[14]Hamdan MKA, Rover DT, Darr MJ, et al., 2019. Mass estimation from images using deep neural network and sparse ground truth. http://arxiv.org/abs/1908.04387

[15]Hu J, Shen L, Sun G, 2018. Squeeze-and-excitation networks. IEEE/CVF Conf on Computer Vision and Pattern Recognition, p.7132-7141. doi: 10.1109/CVPR.2018.00745

[16]Isola P, Zhu JY, Zhou TH, et al., 2017. Image-to-image translation with conditional adversarial networks. IEEE Conf on Computer Vision and Pattern Recognition, p.5967-5976. doi: 10.1109/CVPR.2017.632

[17]Kim T, Cha M, Kim H, et al., 2017. Learning to discover cross-domain relations with generative adversarial networks. Proc 34^th Int Conf on Machine Learning, p.1857-1865.

[18]Lee S, You D, 2019. Data-driven prediction of unsteady flow over a circular cylinder using deep learning. J Fluid Mech, 879:217-254. doi: 10.1017/jfm.2019.700

[19]Li DL, Xu CF, Wang YX, et al., 2016. Parallelizing and optimizing large-scale 3D multi-phase flow simulations on the Tianhe-2 supercomputer. Concurr Comput, 28(5):1678-1692. doi: 10.1002/cpe.3717

[20]Ling JL, Kurzawski A, Templeton J, 2016. Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J Fluid Mech, 807:155-166. doi: 10.1017/jfm.2016.615

[21]Liu Z, Sun MJ, Zhou TH, et al., 2019. Rethinking the value of network pruning. https://arxiv.org/abs/1810.05270

[22]Long J, Shelhamer E, Darrell T, 2015. Fully convolutional networks for semantic segmentation. IEEE Conf on Computer Vision and Pattern Recognition, p.3431-3440. doi: 10.1109/CVPR.2015.7298965

[23]Molchanov P, Tyree S, Karras T, et al., 2017. Pruning convolutional neural networks for resource efficient inference. Int Conf on Learning Representations.

[24]Odena A, Dumoulin V, Olah C, 2016. Deconvolution and checkerboard artifacts. Distill, 1(10):e3. doi: 10.23915/distill.00003

[25]Park J, Woo S, Lee JY, et al., 2018. BAM: bottleneck attention module. https://arxiv.org/abs/1807.06514v1

[26]Raissi M, Perdikaris P, Karniadakis GE, 2017. Physics informed deep learning (part I): data-driven solutions of nonlinear partial differential equations. https://arxiv.org/abs/1711.10561

[27]Raissi M, Perdikaris P, Karniadakis GE, 2019. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys, 378:686-707. doi: 10.1016/j.jcp.2018.10.045

[28]Ronneberger O, Fischer P, Brox T, 2015. U-Net: convolutional networks for biomedical image segmentation. Medical Image Computing and Computer-Assisted Intervention, p.234-241. doi: 10.1007/978-3-319-24574-4_28

[29]Srinivasan PA, Guastoni L, Azizpour H, et al., 2019. Predictions of turbulent shear flows using deep neural networks. Phys Rev Fluids, 4:054603. doi: 10.1103/PhysRevFluids.4.054603

[30]Thuerey N, Weissenow K, Prantl L, et al., 2020. Deep learning methods for Reynolds-averaged Navier-ÍCStokes simulations of airfoil flows. AIAA J, 58(1):25-36. doi: 10.2514/1.J058291

[31]Wang R, Kashinath K, Mustafa M, et al., 2020. Towards physics-informed deep learning for turbulent flow prediction. Proc 26^th ACM SIGKDD Int Conf on Knowledge Discovery & Data Mining, p.1457-1466. doi: 10.1145/3394486.3403198

[32]Woo S, Park J, Lee JY, et al., 2018. CBAM: convolutional block attention module. European Conf on Computer Vision, p.3-9. doi: 10.1007/978-3-030-01234-2_1

[33]Zhou ZW, Siddiquee MMR, Tajbakhsh N, et al., 2018. UNet++: a nested U-Net architecture for medical image segmentation. 4^th Int Workshop on Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support, p.3-11. doi: 10.1007/978-3-030-00889-5_1

[34]Zhu JY, Park T, Isola P, et al., 2017. Unpaired image-to-image translation using cycle-consistent adversarial networks. IEEE Int Conf on Computer Vision, p.2242-2251. doi: 10.1109/ICCV.2017.244