学习流体仿真中的高效长时序运动预测

doi:10.16182/j.issn1004731x.joss.22-1507

摘要/Abstract

摘要：

快速准确的进行流体仿真是一个具有挑战性的任务，基于传统方法的流体仿真需要消耗大量的计算资源以获得准确的结果。深度学习方法快速发展，为基于数据的流体仿真和生成提供了可能。提出一种基于单帧的浓度场和一个序列的先验速度场的长时序流体仿真运动预测算法。这一模型专注于将通过神经网络预测的速度和密度场基于纳维-斯托克斯方程获得的仿真数据在宏观尺度上进行匹配。通过使用基于全卷积U型网络的自动编码器和基于LSTM网络的时序预测子网络，本文模型在时间演化过程中更好地保持了视觉宏观相似性，并实现了显著的计算速度提升。本文方法实现了对流体场演化的宏观分布的准确和快速的长时序运动预测。在一系列二维和三维的仿真数据的基准测试上证明了本文算法的有效性和高效性。

关键词: 运动预测, 流体, 长时序, 高效, 学习算法

Abstract:

Simulating the dynamics of fluid flows accurately and efficiently remains a challenging task nowadays, and traditional fluid simulation methods consume large computational resources to obtain accurate results. Deep learning methods have developed rapidly, which makes data-based fluid simulation and generation possible. In this paper, a motion prediction algorithm for long-term fluid simulation is proposed, which is based on a density field with a single frame and a previous velocity field of a sequence. The model focuses on matching the velocity and density fields predicted by the neural network with the simulated data based on the Navier-Stokes equation at a macroscopic level. With the help of fully convolutional U-Net-based autoencoders and LSTM-based time series prediction subnetworks, the model better maintains the visual macroscopic similarity during temporal evolutions and significantly improves computation speed. As a result, the proposed method achieves accurate and rapid long-term motion prediction for the macroscopic distributions of flow field evolution. In addition, the paper demonstrates the effectiveness and efficiency of the proposed algorithm on a series of benchmark tests based on two-dimensional (2D) and three-dimension (3D) simulation data.

Key words: motion prediction, fluid flow, long-term, high-performance, learning algorithm

中图分类号:

TP391.9

. 学习流体仿真中的高效长时序运动预测[J]. 系统仿真学报, 2023, 35(3): 435-453.

Jingyuan Zhu, Huimin Ma, Jian Yuan. Learning-Based High-Performance Algorithm for Long-Term Motion Prediction of Fluid Flows[J]. Journal of System Simulation, 2023, 35(3): 435-453.

图/表 19

参考文献 40

1	Kim B, Azevedo V C, Thuerey N, et al. Deep Fluids: A Generative Network for Parameterized Fluid Simulations[J]. Computer Graphics Forum (S0167-7055), 2019, 38(2): 59-70.
2	Pfaff T, Fortunato M, Sanchez-Gonzalez A, et al. Learning Mesh-Based Simulation with Graph Networks[C]// International Conference on Learning Representations. Vienna, Austria: arXiv: , 2021.
3	Xie Y, Franz E, Chu M, et al. TempoGAN: A Temporally Coherent, Volumetric GAN for Super-Resolution Fluid Flow[J]. ACM Transactions on Graphics (S1557-7368), 2018, 37(4CD): 95:1-95:15.
4	Werhahn M, Xie Y, Chu M, et al. A Multi-Pass GAN for Fluid Flow Super-Resolution[J]. Proceedings of ACM on Computer Graphics and Interactive Techniques (S2577-6193), 2019, 2(2): 10:1-10:21.
5	Prantl L, Chentanez N, Jeschke S, et al. Tranquil Clouds: Neural Networks for Learning Temporally Coherent Features in Point Clouds[C]// International Conference on Learning Representations. Addis Ababa, Ethiopia: arXiv: , 2020.
6	Wiewel S, Becher M, Thuerey N, et al. Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow[J]. Computer Graphics Forum (S0167-7055), 2019, 38(2): 71-82.
7	Wiewel S, Kim B, Azevedo V C, et al. Latent Space Subdivision: Stable and Controllable Time Predictions for Fluid Flow[J]. Computer Graphics Forum (S0167-7055), 2020, 39(8): 15-25.
8	Tompson J, Schlachter K, Sprechmann P, et al. Accelerating Eulerian Fluid Simulation with Convolutional Networks[C]// 34th International Conference on Machine Learning. Sydney, Australia: PMLR, 2017: 3424-3433.
9	Zhu Y, Zabaras N, Koutsourelakis P S, et al. Physics-Constrained Deep Learning for High-Dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data[J]. Journal of Computational Physics (S0021-9991), 2019, 394: 56-81.
10	Li Xiaosheng, Liu Le, Wu Wen, et al. Dynamic BFECC Characteristic Mapping Method for Fluid Simulations[J]. Visual Computer (S1432-2315), 2014, 30: 787-796.
11	Wang Xin, Liu Yingjie. Back and Forth Error Compensation and Correction Method for Linear Hyperbolic Systems with Application to the Maxwell's Equations[J]. Journal of Computational Physics: X, (S0021-9991), 2019, 1(4): 100014.
12	Fedkiw Ronald, Stam Jos, Henrik Wann Jensen. Visual Simulation of Smoke[C]// SIGGRAPH 2001: Computer Graphics Conference Proceedings. Los Angeles, California, USA: ACM, 2001: 15-22.
13	Ding W, Jia L, Jiao H, et al. A New Method of Smoke Simulation[C]// The 2010 International Conference on Educational and Network Technology (ICENT). Qinhuangdao, China: IEEE, 2010: 267-270.
14	Xu Y, Liu S, Wu L. Smoke Simulation with Two-Scale Vorticity Confinement[C]// International Conference on Multimedia and Signal Processing. Shanghai, China: Springer, 2012: 467-474.
15	He X, Luo L S. Theory of the Lattice Boltzmann Method: From the Boltzmann Equation to the Lattice Boltzmann Equation[J]. Physical Review E (S1539-3755), 1997, 56(6): 6811-6817.
16	Li W Z, Zhou X, Dong B, et al. A Thermal LBM Model for Studying Complex Flow and Heat Transfer Problems in Body-Fitted Coordinates[J]. International Journal of Thermal Sciences (S1290-0729). 2015, 98: 266-276.
17	Wen J, Ma H. Real-Time Smoke Simulation Based on Vorticity Preserving Lattice Boltzmann Method[J]. Visual Computer (S1432-2315), 2019, 35: 1279-1292.
18	Foster N, Fedkiw R. Practical Animation of Liquids[C]// SIGGRAPH 2001. Los Angeles, CA, USA: ACM, 2001: 23-30.
19	Zhu Y, Bridson R. Animating Sand as a Fluid[J]. ACM Transactions on Graphics (TOG) (S1557-7368), 2005, 24(3): 965-972.
20	Macklin M, Mueller M, Chentanez N, et al. Unified Particle Physics for Real-Time Applications[J]. ACM Transactions on Graphics (TOG) (S1557-7368), 2014, 33(4CD): 1-12.
21	Gissler C, Peer A, Band S, et al. Interlinked SPH Pressure Solvers for Strong Fluid-Rigid Coupling[J]. ACM Transactions on Graphics (TOG) (S1557-7368), 2019, 38(1): 1-13.
22	Huang L, Hdrich T, Michels D L. On the Accurate Large-Scale Simulation of Ferrofluids[J]. ACM Transactions on Graphics (TOG) (S1557-7368), 2019, 38(4): 1-15.
23	Nagasawa K, Suzuki T, Seto R, et al. Mixing Sauces: A Viscosity Blending Model for Shear Thinning Fluids[J]. ACM Transactions on Graphics (TOG) (S1557-7368), 2019, 38(4): 1-17.
24	Rumelhart D E, Hinton G E, Williams R J. Learning Representations by Back Propagating Errors[J]. Nature (S1476-4687). 1986, 323(6088): 533-536.
25	Ladick L, Jeong S H, Solenthaler B, et al. Data-Driven Fluid Simulations Using Regression Forests[J]. ACM Transactions on Graphics (TOG) (S1557-7368), 2015, 34(6): 1-9.
26	Thuerey N, Weienow K, Prantl L, et al. Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows[J]. AIAA Journal (S1533-385X), 2020, 58(4): 1-12.
27	Um K, Hu X, Thuerey N. Liquid Splash Modeling with Neural Networks[J]. Computer Graphics Forum (S0167-7055), 2018, 37(8): 171-182.
28	Hennigh O. Lat-Net: Compressing Lattice Boltzmann Flow Simulations Using Deep Neural Networks[J]. 10.48550/arXiv: , 2017.
29	Chu M, Thuerey N. Data-Driven Synthesis of Smoke Flows with CNN-Based Feature Descriptors[J]. ACM Transactions on Graphics (TOG) (S1557-7368), 2017, 36(4): 69:1-69:14.
30	Kani J N, Elsheikh A H. Reduced Order Modeling of Subsurface Multiphase Flow Models Using Deep Residual Recurrent Neural Networks[J]. Transport in Porous Media (S1573-1634), 2019, 126: 713-74.
31	Sanchez-Gonzalez A, Godwin J, Pfaff T, et al. Learning to Simulate Complex Physics with Graph Networks[C]// 37th International Conference on Machine Learning. Vienna, Austria: JMLR, 2020: 8459-8468.
32	Ummenhofer B, Prantl L, Thürey N, et al. Lagrangian Fluid Simulation with Continuous Convolutions[C]// International Conference on Learning Representations. Addis Ababa, Ethiopia: OpenReview.net, 2020.
33	Zhang M, Wang J, Tlhomole J, et al. Learning to Estimate and Refine Fluid Motion with Physical Dynamics[C]// 39th International Conference on Machine Learning. Baltimore, Maryland, USA: arXiv:, 2022.
34	Rasp P, Düben P D, Scher S, et al. WeatherBench: A Benchmark Data Set for Data-Driven Weather Forecasting[J]. Journal of Advances in Modeling Earth Systems (S1942-2466), 2020, 12(11): e2020MS002203.
35	Eivazi H, Veisi H, Naderi M H, et al. Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows[J]. Physics of Fluids (S1070-6631), 2020, 32(10): 105104: 1-105104:21.
36	Goodfellow I, Pouget-Abadie J, Mirza M, et al. Generative Adversarial Nets[C]// Neural Information Processing Systems. Montreal, Quebec, Canada: MIT Press, arXiv: , 2014.
37	Reed S, Akata Z, Yan X, et al. Generative Adversarial Text to Image Synthesis[C]//. International Conference on Machine Learning. New York City, NY, USA: Curran Associates, Inc., 2016: 1060-1069.
38	Chu M, Xie Y, Mayer J, et al. Learning Temporal Coherence Via Self-Supervision for GAN-Based Video Generation[J]. ACM Transactions on Graphics (TOG) (S1557-7368), 2020, 39(4): 75:1-75:13.
39	Wei W, Liu S. Interpolating Frames for Super-Resolution Smoke Simulation with GANs[C]// International Conference on Computer Animation and Social Agents (CASA). Bournemouth, UK: Springer, 2020: 14-21.
40	Kochkov D, Smith J A, Alieva A, et al. Machine Learning Accelerated Computational Fluid Dynamics[J]. Proceedings of the National Academy of Sciences (S0027-8424), 2021, 118(21): e2101784118.

Layer	Kernel	Stride	Activation	Output	Feature
f_e1	4	2	Linear	r /2	16t_i
f_e2	2	2	LeakyReLU	r /4	32t_i
f_e3	2	2	LeakyReLU	r /8	64t_i
f_e4	2	2	LeakyReLU	r /16	128t_i
f_e5	2	2	LeakyReLU	r /32	256t_i
f_d1	2	2	LeakyReLU	r /16	128t_o
f_d2	2	2	LeakyReLU	r /8	64t_o
f_d3	2	2	LeakyReLU	r /4	32t_o
f_d4	2	2	LeakyReLU	r /2	16t_o
f_d5	4	2	LeakyReLU	r	dt_o

Scene Type	Resolution	Scene	Frames
Single source smoke (3D)	64³	600	100
Single source smoke with obstacles (3D)	64³	600	200
Single source smoke (2D)	64²	600	200
Single source smoke (2D)	128²	600	200
Single source smoke with obstacles (2D)	64²	600	200
Single source smoke with obstacles (2D)	128²	600	200
Rising smoke (2D)	64²	1 000	200
Rising smoke(2D)	128²	1 000	200
Rotating cup (2D)	64²	600	200
Rotating and moving cup (2D)	64²	300	300

Datasets	Resolution	Long-term velocity			Long-term density
Datasets	Resolution	PSNR	Cos similarity	MSE	PSNR	Cos similarity	MSE
Single source smoke (3D)	64³	41.123	0.997	0.002 2	26.279	0.889	0.002 6
Single source smoke with obstacles (3D)	64³	32.289	0.993	0.006 6	35.717	0.993	0.000 2
Rotating cup (2D)	64²	20.430	0.835	0.008 0	23.244	0.970	0.002 9
Rotating and moving cup (2D)	64²	20.279	0.863	0.030 8	25.579	0.972	0.003 8
Single source smoke (2D)	64²	23.627	0.969	0.084 0	28.212	0.985	0.003 8
Single source smoke (2D)	128²	25.024	0.976	0.264 8	27.377	0.978	0.006 4
Single source smoke with obstacles (2D)	64²	23.810	0.966	0.070 8	28.866	0.986	0.003 4
Single source smoke with obstacles (2D)	128²	27.098	0.960	0.095 4	29.092	0.954	0.003 8

Datasets	Resolution	LSP model			Our model
Datasets	Resolution	PSNR	Cos similarity	MSE	PSNR	Cos similarity	MSE
Rising smoke (2D)	64²	9.588	0.750	0.816	13.929	0.888	0.264
Rising smoke (2D)	128²	6.138	0.697	2.523	15.802	0.907	0.279

Datasets	Resolution	Prediction with original velocity fields			Prediction with predicted velocity fields
Datasets	Resolution	PSNR	Cos similarity	MSE	PSNR	Cos similarity	MSE
Single source smoke (3D)	64³	26.279	0.889	0.003	26.738	0.865	0.004
Single source smoke with obstacles (3D)	64³	35.717	0.993	0.000 2	35.340	0.989	0.000 02
Single source smoke (2D)	64²	28.621	0.990	0.002	17.904	0.842	0.023
Single source smoke (2D)	128²	25.886	0.984	0.003	18.418	0.886	0.019
Rising smoke (2D)	64²	18.465	0.895	0.009	17.760	0.875	0.010
Rising smoke (2D)	128²	19.483	0.897	0.019	17.717	0.837	0.029