Intelligent prediction of manta ray flow field based on a denoising probabilistic diffusion model

BAI Jingyi; HUANG Qiaogao; GAO Pengcheng; WEN Xin; CHU Yong

doi:10.7498/aps.74.20241499

Abstract

The manta ray is a large marine species, which has the ability of gliding efficiently and flapping rapidly. It can autonomously switch between various motion modes, such as gliding, flapping, and group swimming, based on ocean currents and seabed conditions. To address the computational resource and time constraints of traditional numerical simulation methods in modeling the manta ray’s three-dimensional (3D) large-deformation flow field, this study proposes a novel generative artificial intelligence approach based on a denoising probabilistic diffusion model (surf-DDPM). This method predicts the surface flow field of the manta ray by inputting a set of motion parameter variables. Initially, we establish a numerical simulation method for the manta ray’s flapping mode by using the immersed boundary method and the spherical function gas kinetic scheme (IB-SGKS), generating an unsteady flow dataset comprising 180 sets under frequency conditions of 0.3–0.9 Hz and amplitude conditions of 0.1–0.6 body lengths. Data augmentation is then performed. Subsequently, a Markov chain for the noise diffusion process and a neural network model for the denoising generation process are constructed. A pretrained neural network embeds the motion parameters and diffusion time step labels into the flow field data, which are then fed into a U-Net for model training. Notably, a transformer network is incorporated into the U-Net architecture to enable the handling of long-sequence data. Finally, we examine the influence of neural network hyperparameters on model performance and visualize the predicted pressure and velocity fields for multi-flapping postures that were not included in the training set, followed by a quantitative analysis of prediction accuracy, uncertainty, and efficiency. The results demonstrate that the proposed model achieves fast and accurate predictions of the manta ray’s surface flow field, characterized by extensive high-dimensional upsampling. The minimum PSNR value and SSIM value of the predictions are 35.931 dB and 0.9524, respectively, with all data falling within the 95% prediction interval. Compared with CFD simulations, the single-condition simulations by using AI model show that the prediction efficiency is enhanced by 99.97%.

Keywords:

Authors and contacts

1.
School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China
2.
Unmanned Vehicle Innovation Center, Ningbo Institute of Northwestern Polytechnical University, Ningbo 315048, China

Corresponding author: HUANG Qiaogao, huangqiaogao@nwpu.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2022YFC2805200), the National Natural Science Foundation of China (Grant Nos. 52301387, 52201381, 12002282), the State Key Laboratory of Ocean Engineering of Shanghai Jiao Tong University, China (Grant No. GKZDO10089), the State Key Laboratory of High Temperature Gas Dynamics of Institute of Mechanics, Chinese Academy of Sciences, China (Grant No. 2023KF11), and the China Postdoctoral Science Foundation (Grant No. 2023M742851).

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References

[1]	王亮 2007 博士学位论文 (南京: 河海大学) Wang L 2007 Ph. D. Dissertation (Nanjing: Hehai University
[2]	Asada T, Furuhashi H 2024 Ocean Eng. 308 118261 Google Scholar
[3]	Xing C, Yin Z, Xu H, Cao Y, Qu Y, Huang Q 2024 Ocean Eng. 312 119039 Google Scholar
[4]	Bao T, Cao Y, Cao Y H, Lu Y, Pan G, Huang Q G 2024 Ocean Eng. 309 118377 Google Scholar
[5]	Dong H, Bozkurttas M, Mittal R, Madden P, Laude G V 2010 J. Fluid Mech. 645 34 Google Scholar
[6]	Huang Z, Menzer A, Guo J, Dong H 2024 Bioinspir Biomim 19 026004 Google Scholar
[7]	Wang S, Gao P, Huang Q G, Pan G, Tian X 2024 Ocean Eng. 294 116799 Google Scholar
[8]	Gao P C, Song B, Huang Q G, Tian X S, Pan G, Chu Y, Bai J Y 2024 Ocean Eng. 313 119415 Google Scholar
[9]	Gao P C, Huang Q G, Pan G, Cao Y, Luo Y 2023 Ocean Eng. 278 114389 Google Scholar
[10]	Miyanawala T P, Li Y, Law Y Z 2024 Ocean Eng. 306 118003 Google Scholar
[11]	Li G, Zhu H, Jian H 2023 J. Hydrol. 625 130025 Google Scholar
[12]	战庆亮, 葛耀君, 白春锦 2022 物理学报 71 074701 Google Scholar Zhan Q L, Ge Y J, Bai C J 2022 Acta Phys. Sin. 71 074701 Google Scholar
[13]	Wang Z, Zhang W 2023 Phys. Fluids 35 025124 Google Scholar
[14]	Qiu C C, Huang Q G, Pan G 2023 Phys. Fluids 35 017132 Google Scholar
[15]	Xia Y, Li T, Wang Q, Yue J, Peng B, Yi X 2024 Phys. Fluids 36 103313 Google Scholar
[16]	Li R, Song B, Chen Y 2024 Ocean Eng. 304 117857 Google Scholar
[17]	Caraccio P, Marseglia G, Lauria A 2024 Phys. Fluids 36 107120 Google Scholar
[18]	Qiu C C, Huang Q G, Pan G 2023 Ocean Eng. 281 114555 Google Scholar
[19]	Gao H, Gao L, Shi Z, Sun D, Sun X 2024 Aerosp. Sci. Technol. 147 108977 Google Scholar
[20]	Lin H, Jiang X, Deng X 2024 Thinking Skills and Creativity 54 101649 Google Scholar
[21]	Kartashov N, Vlassis N N 2024 arXiv: 2409.14473 [cs.CE]
[22]	Torem N, Ronen R, Schechner Y Y, Elad M 2023 Proceedings of the IEEE/CVF International Conference on Computer Vision Paris, France, October 2–6, 2023 p3810
[23]	Ho J, Jain A, Abbeel P 2020 Adv. Neural Inf. Process. Syst. 33 6840 Google Scholar
[24]	Rombach R, Blattmann A, Loren D, Esser P, Ommer B 2022 Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition New Orleans, LA, June 18–24, 2022 p10674
[25]	Song J, Meng C, Ermon S 2020 arXiv: 2010.02502 [cs.LG]
[26]	Nichol A, Dhariwal P, Ramesh A, Shyam P, Mishkin P, McGrew B 2021 arXiv: 2112.10741 [cs.CV]
[27]	Huang L, Zheng C, Chen Y 2024 Phys. Fluids 36 095113 Google Scholar
[28]	Rybchuk A, Hassanaly M, Hamilton N 2023 Phys. Fluids 35 126604 Google Scholar
[29]	Gao P C, Tian X, Huang Q G 2024 Phys. Fluids 36 011902 Google Scholar
[30]	Gao P C, Huang Q G, Pan G 2023 Phys. Fluids 35 061909 Google Scholar
[31]	张栋 2020 博士学位论文 (西安: 西北工业大学) Zhang D 2020 Ph. D. Dissertation (Xi’an: Northwestern Polytechnical University

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图 1 蝠鲼模型与流场网格划分

Figure 1. Manta ray model and flow field mesh partitioning.

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图 2 蝠鲼模型单周期运动

Figure 2. Single-cycle motion process of the manta ray simulation mode.

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图 3 仿真结果准确性验证

Figure 3. Accuracy validation of the simulation results.

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图 4 不同扑动频率对应CFD仿真时间步数

Figure 4. CFD simulation time steps corresponding to different flapping frequencies.

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图 5 蝠鲼表面流场数值模拟压力与速度场云图

Figure 5. Pressure and Velocity Field Contours in Numerical Simulation of Manta Ray Surface Flow Dynamics.

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图 6 原始数据填充与归一化处理结果对比

Figure 6. Comparison of original data padding and normalized processing results.

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图 7 去噪扩散概率模型原理

Figure 7. Principle of the denoising diffusion probabilistic model.

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图 8 surf-DDPM神经网络算法框图　(a)运动参数与噪声扩散时间步嵌入模块; (b) U-Net去噪生成模块; (c) Transformer自注意力机制模块

Figure 8. The surf-DDPM neural network algorithm flowchart: (a) Motion parameters and noise diffusion time step embedding module; (b) U-Net denoising generation module; (c) transformer self-attention mechanism module.

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图 9 超参数影响分析　(a)噪声调度时间表函数影响; (b) U-Net的网络层数影响; (c)噪声扩散步数影响

Figure 9. Hyperparameter impact analysis: (a) Effect of noise scheduling function on results; (b) impact of U-Net network depth on performance; (c) effect of noise diffusion steps on generation quality.

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图 10 内插测试工况压力与速度场预测结果与误差　(a), (d), (g)压力场CFD计算真值; (b), (e), (h) surf-DDPM人工智能模型预测结果; (c), (f), (i)预测值误差云图; (j), (m), (p)速度场CFD计算真值; (k), (n), (q) surf-DDPM人工智能模型预测结果; (l), (o), (r)预测值误差云图

Figure 10. Predicted results and errors of surface pressure and velocity fields for the interpolation test case: (a), (d), (g) True values of dynamic pressure field from CFD simulations; (b), (e), (h) pressure field predicted by surf-DDPM AI model; (c), (f), (i) absolute error contour of pressure field; (j), (m), (p) true values of velocity flow field from CFD simulations; (k), (n), (q) velocity field predicted by surf-DDPM AI model; (l), (o), (r) absolute error contour of velocity field.

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图 11 外推测试工况压力场与速度场预测结果与误差　(a), (d), (g)压力场CFD计算真值; (b), (e), (h) surf-DDPM人工智能模型预测结果; (c), (f), (i)预测值误差云图; (j), (m), (p)速度场CFD计算真值; (k), (n), (q) surf-DDPM人工智能模型预测结果; (l), (o), (r)预测值误差云图

Figure 11. Prediction results and errors of pressure and velocity fields in extrapolation test cases: (a), (d), (g) True values ofdynamic pressure field from CFD simulations; (b), (e), (h) pressure field predicted by surf-DDPM AI model; (c), (f), (i) absoluteer-ror contour of pressure field; (j), (m), (p) true values of velocity flow field from CFD simulations; (k), (n), (q) velocity fieldpre-dicted by surf-DDPM AI model; (l), (o), (r) absolute error contour of velocity field.

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图 12 翼尖位置网格节点流场预测结果95%置信区间　(a) d₁姿态压力场; (b) d₁姿态速度场; (c) d₃姿态压力场; (d) d₃姿态速度场

Figure 12. 95% Prediction intervals for flow field predictions at wingtip locations: (a) Dynamic pressure field for d₁ configuration; (b) velocity field for d₁ configuration; (c) dynamic pressure field for d₃ configuration; (d) velocity field for d₃ configuration.

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表 1 不同扑动频率对应数据提取起始与间隔时间步

Table 1. Starting times and interval steps for data extraction at different flapping frequencies.

扑动频率/Hz	起始时间步	间隔时间步
0.3	11390	57
0.5	6838	35
0.6	5698	29
0.7	4884	25
0.9	3799	19

DownLoad: CSV

表 2 流场预测结果准确性定量分析

Table 2. Quantitative analysis of accuracy in flow field predictions.

预测结果	内插测试工况			外推测试工况
预测结果	RMSE	PSNR/dB	SSIM	RMSE	PSNR/dB	SSIM
d₁-P	0.0224	37.031	0.9679	0.0263	36.085	0.9598
d₂-P	0.0122	38.203	0.9754	0.0233	36.556	0.9624
d₃-P	0.0214	37.486	0.9688	0.0208	36.387	0.9533
d₁-U	0.0245	36.475	0.9613	0.0272	35.902	0.9587
d₂-U	0.0146	38.811	0.9813	0.0261	35.241	0.9496
d₃-U	0.0250	35.931	0.9524	0.0301	35.158	0.9571

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表 3 CFD与人工智能方法预测流场效率对比

Table 3. Comparison of flow field prediction efficiency between CFD and surf-DDPM methods.

扑动频率/Hz	CFD/核时	AI训练/卡时	AI预测/s
0.3	120	24	30
0.5	72
0.6	60
0.7	48
0.9	36

DownLoad: CSV

[1]	王亮 2007 博士学位论文 (南京: 河海大学) Wang L 2007 Ph. D. Dissertation (Nanjing: Hehai University
[2]	Asada T, Furuhashi H 2024 Ocean Eng. 308 118261 Google Scholar
[3]	Xing C, Yin Z, Xu H, Cao Y, Qu Y, Huang Q 2024 Ocean Eng. 312 119039 Google Scholar
[4]	Bao T, Cao Y, Cao Y H, Lu Y, Pan G, Huang Q G 2024 Ocean Eng. 309 118377 Google Scholar
[5]	Dong H, Bozkurttas M, Mittal R, Madden P, Laude G V 2010 J. Fluid Mech. 645 34 Google Scholar
[6]	Huang Z, Menzer A, Guo J, Dong H 2024 Bioinspir Biomim 19 026004 Google Scholar
[7]	Wang S, Gao P, Huang Q G, Pan G, Tian X 2024 Ocean Eng. 294 116799 Google Scholar
[8]	Gao P C, Song B, Huang Q G, Tian X S, Pan G, Chu Y, Bai J Y 2024 Ocean Eng. 313 119415 Google Scholar
[9]	Gao P C, Huang Q G, Pan G, Cao Y, Luo Y 2023 Ocean Eng. 278 114389 Google Scholar
[10]	Miyanawala T P, Li Y, Law Y Z 2024 Ocean Eng. 306 118003 Google Scholar
[11]	Li G, Zhu H, Jian H 2023 J. Hydrol. 625 130025 Google Scholar
[12]	战庆亮, 葛耀君, 白春锦 2022 物理学报 71 074701 Google Scholar Zhan Q L, Ge Y J, Bai C J 2022 Acta Phys. Sin. 71 074701 Google Scholar
[13]	Wang Z, Zhang W 2023 Phys. Fluids 35 025124 Google Scholar
[14]	Qiu C C, Huang Q G, Pan G 2023 Phys. Fluids 35 017132 Google Scholar
[15]	Xia Y, Li T, Wang Q, Yue J, Peng B, Yi X 2024 Phys. Fluids 36 103313 Google Scholar
[16]	Li R, Song B, Chen Y 2024 Ocean Eng. 304 117857 Google Scholar
[17]	Caraccio P, Marseglia G, Lauria A 2024 Phys. Fluids 36 107120 Google Scholar
[18]	Qiu C C, Huang Q G, Pan G 2023 Ocean Eng. 281 114555 Google Scholar
[19]	Gao H, Gao L, Shi Z, Sun D, Sun X 2024 Aerosp. Sci. Technol. 147 108977 Google Scholar
[20]	Lin H, Jiang X, Deng X 2024 Thinking Skills and Creativity 54 101649 Google Scholar
[21]	Kartashov N, Vlassis N N 2024 arXiv: 2409.14473 [cs.CE]
[22]	Torem N, Ronen R, Schechner Y Y, Elad M 2023 Proceedings of the IEEE/CVF International Conference on Computer Vision Paris, France, October 2–6, 2023 p3810
[23]	Ho J, Jain A, Abbeel P 2020 Adv. Neural Inf. Process. Syst. 33 6840 Google Scholar
[24]	Rombach R, Blattmann A, Loren D, Esser P, Ommer B 2022 Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition New Orleans, LA, June 18–24, 2022 p10674
[25]	Song J, Meng C, Ermon S 2020 arXiv: 2010.02502 [cs.LG]
[26]	Nichol A, Dhariwal P, Ramesh A, Shyam P, Mishkin P, McGrew B 2021 arXiv: 2112.10741 [cs.CV]
[27]	Huang L, Zheng C, Chen Y 2024 Phys. Fluids 36 095113 Google Scholar
[28]	Rybchuk A, Hassanaly M, Hamilton N 2023 Phys. Fluids 35 126604 Google Scholar
[29]	Gao P C, Tian X, Huang Q G 2024 Phys. Fluids 36 011902 Google Scholar
[30]	Gao P C, Huang Q G, Pan G 2023 Phys. Fluids 35 061909 Google Scholar
[31]	张栋 2020 博士学位论文 (西安: 西北工业大学) Zhang D 2020 Ph. D. Dissertation (Xi’an: Northwestern Polytechnical University

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