Performance of physical-informed neural network (PINN) for the key parameter inference in Langmuir turbulence parameterization scheme

Fangrui Xiu; Zengan Deng

doi:10.1007/s13131-024-2329-4

Volume 43 Issue 5

May 2024

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Fangrui Xiu, Zengan Deng. Performance of physical-informed neural network (PINN) for the key parameter inference in Langmuir turbulence parameterization scheme[J]. Acta Oceanologica Sinica, 2024, 43(5): 121-132. doi: 10.1007/s13131-024-2329-4

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Fangrui Xiu, Zengan Deng. Performance of physical-informed neural network (PINN) for the key parameter inference in Langmuir turbulence parameterization scheme[J]. Acta Oceanologica Sinica, 2024, 43(5): 121-132. doi: 10.1007/s13131-024-2329-4

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Performance of physical-informed neural network (PINN) for the key parameter inference in Langmuir turbulence parameterization scheme

doi: 10.1007/s13131-024-2329-4

Fangrui Xiu¹,
Zengan Deng^{1
,
,}

School of Marine Science and Technology, Tianjin University, Tianjin 300072, China

Funds: The National Key Research and Development Program of China under contract No. 2022YFC3105002; the National Natural Science Foundation of China under contract No. 42176020; the project from the Key Laboratory of Marine Environmental Information Technology, Ministry of Natural Resources, under contract No. 2023GFW-1047.

More Information

Corresponding author: E-mail: dengzengan@163.com
Received Date: 2024-02-11
Accepted Date: 2024-04-22

Available Online: 2024-05-23

Publish Date: 2024-05-30

Abstract

Abstract

The Stokes production coefficient (E₆) constitutes a critical parameter within the Mellor-Yamada type (MY-type) Langmuir turbulence (LT) parameterization schemes, significantly affecting the simulation of turbulent kinetic energy, turbulent length scale, and vertical diffusivity coefficient for turbulent kinetic energy in the upper ocean. However, the accurate determination of its value remains a pressing scientific challenge. This study adopted an innovative approach by leveraging deep learning technology to address this challenge of inferring the E₆. Through the integration of the information of the turbulent length scale equation into a physical-informed neural network (PINN), we achieved an accurate and physically meaningful inference of E₆. Multiple cases were examined to assess the feasibility of PINN in this task, revealing that under optimal settings, the average mean squared error of the E₆ inference was only 0.01, attesting to the effectiveness of PINN. The optimal hyperparameter combination was identified using the Tanh activation function, along with a spatiotemporal sampling interval of 1 s and 0.1 m. This resulted in a substantial reduction in the average bias of the E₆ inference, ranging from O(10¹) to O(10²) times compared with other combinations. This study underscores the potential application of PINN in intricate marine environments, offering a novel and efficient method for optimizing MY-type LT parameterization schemes.
- Langmuir turbulence,
- physical-informed neural network,
- parameter inference

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References(60)

References

Abbasi J, Andersen P Ø. 2023. Physical activation functions (PAFs): an approach for more efficient induction of physics into physics-informed neural networks (PINNs). arXiv: 2205.14630, doi: 10.48550/arXiv.2205.14630

Abdou M A. 2007. The extended tanh method and its applications for solving nonlinear physical models. Applied Mathematics and Computation, 190(1): 988–996, doi: 10.1016/j.amc.2007.01.070

Abueidda D W, Lu Qiyue, Koric S. 2021. Meshless physics-informed deep learning method for three-dimensional solid mechanics. International Journal for Numerical Methods in Engineering, 122(23): 7182–7201, doi: 10.1002/nme.6828

Bajaj C, McLennan L, Andeen T, et al. 2023. Recipes for when physics fails: recovering robust learning of physics informed neural networks. Machine Learning: Science and Technology, 4(1): 015013, doi: 10.1088/2632-2153/acb416

Baydin A G, Pearlmutter B A, Radul A A, et al. 2017. Automatic differentiation in machine learning: a survey. The Journal of Machine Learning Research, 18(1): 5595–5637

Bolandi H, Sreekumar G, Li Xuyang, et al. 2023. Physics informed neural network for dynamic stress prediction. Applied Intelligence, 53(22): 26313–26328, doi: 10.1007/s10489-023-04923-8

Bowman B, Oian C, Kurz J, et al. 2023. Physics-informed neural networks for the heat equation with source term under various boundary conditions. Algorithms, 16(9): 428, doi: 10.3390/a16090428

Cao Yu, Deng Zengan, Wang Chenxu. 2019. Impacts of surface gravity waves on summer ocean dynamics in Bohai Sea. Estuarine, Coastal and Shelf Science, 230: 106443, doi: 10.1016/j.ecss.2019.106443

Cedillo S, Núñez A G, Sánchez-Cordero E, et al. 2022. Physics-informed neural network water surface predictability for 1D steady-state open channel cases with different flow types and complex bed profile shapes. Advanced Modeling and Simulation in Engineering Sciences, 9: 10, doi: 10.1186/s40323-022-00226-8

Craik A D D, Leibovich S. 1976. A rational model for Langmuir circulations. Journal of Fluid Mechanics, 73(3): 401–426, doi: 10.1017/S0022112076001420

Depina I, Jain S, Mar Valsson S, et al. 2022. Application of physics-informed neural networks to inverse problems in unsaturated groundwater flow. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 16(1): 21–36, doi: 10.1080/17499518.2021.1971251

Doronina O A, Murman S M, Hamlington P E. 2020. Parameter estimation for RANS models using approximate bayesian computation. arXiv: 2011.01231, doi: 10.48550/arXiv.2011.01231

Fan Engui. 2000. Extended tanh-function method and its applications to nonlinear equations. Physics Letters A, 277(4/5): 212–218, doi: 10.1016/S0375-9601(00)00725-8

Faroughi S A, Soltanmohammadi R, Datta P, et al. 2024. Physics-informed neural networks with periodic activation functions for solute transport in heterogeneous porous media. Mathematics, 12(1): 63, doi: 10.3390/math12010063

Gimenez J M, Bre F. 2019. Optimization of RANS turbulence models using genetic algorithms to improve the prediction of wind pressure coefficients on low-rise buildings. Journal of Wind Engineering and Industrial Aerodynamics, 193: 103978, doi: 10.1016/j.jweia.2019.103978

Harcourt R R. 2013. A second-moment closure model of langmuir turbulence. Journal of Physical Oceanography, 43(4): 673–697, doi: 10.1175/JPO-D-12-0105.1

Harcourt R R. 2015. An improved second-moment closure model of langmuir turbulence. Journal of Physical Oceanography, 45(1): 84–103, doi: 10.1175/JPO-D-14-0046.1

Hemchandra S, Datta A, Juniper M P. 2023. Learning RANS model parameters from LES using bayesian inference. In: Proceedings of ASME Turbo Expo 2023: Turbomachinery Technical Conference and Exposition. Boston, USA: ASME, doi: 10.1115/GT2023-102159

Jagtap A D, Kawaguchi K, Karniadakis G E. 2020. Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. Journal of Computational Physics, 404: 109136, doi: 10.1016/j.jcp.2019.109136

Kantha L H, Clayson C A. 1994. An improved mixed layer model for geophysical applications. Journal of Geophysical Research: Oceans, 99(C12): 25235–25266, doi: 10.1029/94JC02257

Kantha L H, Clayson C A. 2004. On the effect of surface gravity waves on mixing in the oceanic mixed layer. Ocean Modelling, 6(2): 101–124, doi: 10.1016/S1463-5003(02)00062-8

Kantha L, Lass H U, Prandke H. 2010. A note on Stokes production of turbulence kinetic energy in the oceanic mixed layer: observations in the Baltic Sea. Ocean Dynamics, 60(1): 171–180, doi: 10.1007/s10236-009-0257-7

Kato H, Obayashi S. 2012. Statistical approach for determining parameters of a turbulence model. In: Proceedings of the 2012 15th International Conference on Information Fusion. Singapore: IEEE

Krishnapriyan A S, Gholami A, Zhe Shandian, et al. 2021. Characterizing possible failure modes in physics-informed neural networks. In: Proceedings of the 35th Conference on Neural Information Processing Systems. Vancouver, Canada: NeurIPS, 26548–26560

Lederer J. 2021. Activation functions in artificial neural networks: A systematic overview. arXiv: 2101.09957

Lee N, Ajanthan T, Torr P H S, et al. 2021. Understanding the effects of data parallelism and sparsity on neural network training. In: Proceedings of the 9th International Conference on Learning Representations. Washington, DC, USA: ICLR, 11316

Leiteritz R, Pflüger D. 2021. How to avoid trivial solutions in physics-informed neural networks. arXiv: 2112.05620, doi: 10.48550/ARXIV.2112.05620

Li Xuyang, Bolandi H, Salem T, et al. 2022. NeuralSI: structural parameter identification in nonlinear dynamical systems. In: Proceedings of European Conference on Computer Vision. Tel Aviv, Israel: Springer, 332–348

Li Ming, Garrett C, Skyllingstad E. 2005. A regime diagram for classifying turbulent large eddies in the upper ocean. Deep-Sea Research Part I: Oceanographic Research Papers, 52(2): 259–278, doi: 10.1016/j.dsr.2004.09.004

Li Qing, Reichl B G, Fox-Kemper B, et al. 2019. Comparing ocean surface boundary vertical mixing schemes including langmuir turbulence. Journal of Advances in Modeling Earth Systems, 11(11): 3545–3592, doi: 10.1029/2019MS001810

Lou Qin, Meng Xuhui, Karniadakis G E. 2021. Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation. Journal of Computational Physics, 447: 110676, doi: 10.1016/j.jcp.2021.110676

Luo Shirui, Vellakal M, Koric S, et al. 2020. Parameter identification of RANS turbulence model using physics-embedded neural network. In: Proceedings of ISC High Performance 2020 International Conference on High Performance Computing. Frankfurt, Germany: Springer, 137–149

Martin P J, Savelyev I B. 2017. Tests of parameterized Langmuir circulation mixing in the ocean’s surface mixed layer II. NRL/MR/7320-17-9738, Naval Research Lab

McWilliams J C, Sullivan P P. 2000. Vertical mixing by langmuir circulations. Spill Science & Technology Bulletin, 6(3/4): 225–237, doi: 10.1016/S1353-2561(01)00041-X

McWilliams J C, Sullivan P P, Moeng C H. 1997. Langmuir turbulence in the ocean. Journal of Fluid Mechanics, 334: 1–30, doi: 10.1017/S0022112096004375

Mellor G L, Yamada T. 1974. A hierarchy of turbulence closure models for planetary boundary layers. Journal of the Atmospheric Sciences, 31(7): 1791–1806, doi: 10.1175/1520-0469(1974)031<1791:AHOTCM>2.0.CO;2

Mellor G L, Yamada T. 1982. Development of a turbulence closure model for geophysical fluid problems. Reviews of Geophysics, 20(4): 851–875, doi: 10.1029/RG020i004p00851

Moseley B, Markham A, Nissen-Meyer T. 2023. Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations. Advances in Computational Mathematics, 49(4): 62, doi: 10.1007/s10444-023-10065-9

Parascandolo G, Huttunen H, Virtanen T. 2017. Taming the waves: sine as activation function in deep neural networks. In: Proceedings of the 5th International Conference on Learning Representations, Washington DC, USA: ICLR

Paszke A, Gross S, Chintala S, et al. 2017. Automatic differentiation in PyTorch. In: Proceedings of the 31st Conference on Neural Information Processing Systems. Long Beach, USA: NIPS

Raissi M, Karniadakis G E. 2018. Hidden physics models: machine learning of nonlinear partial differential equations. Journal of Computational Physics, 357: 125–141, doi: 10.1016/j.jcp.2017.11.039

Raissi M, Perdikaris P, Karniadakis G E. 2019. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378: 686–707, doi: 10.1016/j.jcp.2018.10.045

Ramachandran P, Zoph B, Le Q V. 2018. Searching for activation functions. In: Proceedings of the 6th International Conference on Learning Representations. Vancouver, Canada: OpenReview. net

Repp A C, Roberts D M, Slack D J, et al. 1976. A comparison of frequency, interval, and time-sampling methods of data collection. Journal of Applied Behavior Analysis, 9(4): 501–508, doi: 10.1901/jaba.1976.9-501

Sharma R, Shankar V. 2022. Accelerated training of physics-informed neural networks (PINNs) using meshless discretizations. In: Proceedings of the 36th Conference on Neural Information Processing Systems. New Orleans, USA: Curran Associates Inc. , 1034–1046

Sun Jian, Li Xungui, Yang Qiyong, et al. 2023. Hydrodynamic numerical simulations based on residual cooperative neural network. Advances in Water Resources, 180: 104523, doi: 10.1016/j.advwatres.2023.104523

Suzuki N, Fox-Kemper B. 2016. Understanding stokes forces in the wave-averaged equations. Journal of Geophysical Research: Oceans, 121(5): 3579–3596, doi: 10.1002/2015JC011566

Świrszcz G, Czarnecki W M, Pascanu R. 2017. Local minima in training of neural networks. arXiv: 1611.06310

Tartakovsky A M, Marrero C O, Perdikaris P, et al. 2020. Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems. Water Resources Research, 56(5): e2019WR026731, doi: 10.1029/2019WR026731

Umlauf L, Burchard H. 2005. Second-order turbulence closure models for geophysical boundary layers. a review of recent work. Continental Shelf Research, 25(7/8): 795–827, doi: 10.1016/j.csr.2004.08.004

Umlauf L, Burchard H, Bolding K. 2006. GOTM sourcecode and test case documentation (version 4.0), http://gotm.net/manual/stable/pdf/letter.pdf [2024-01-11]

Waheed U B. 2022. Kronecker neural networks overcome spectral bias for PINN-based wavefield computation. IEEE Geoscience and Remote Sensing Letters, 19: 8029805, doi: 10.1109/LGRS.2022.3209901

Wengert R E. 1964. A simple automatic derivative evaluation program. Communications of the ACM, 7(8): 463–464, doi: 10.1145/355586.364791

Wight C L, Zhao Jia. 2020. Solving allen-cahn and cahn-hilliard equations using the adaptive physics informed neural networks. arXiv: 2007.04542

Wu Chenxi, Zhu Min, Tan Qinyang, et al. 2023. A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 403: 115671, doi: 10.1016/j.cma.2022.115671

Xiao Heng, Cinnella P. 2018. Quantification of model uncertainty in RANS simulations: a review. Progress in Aerospace Sciences, 108: 1–31, doi: 10.1016/j.paerosci.2018.10.001

Xu Chen, Cao Ba Trung, Yuan Yong, et al. 2023. Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios. Computer Methods in Applied Mechanics and Engineering, 405: 115852, doi: 10.1016/j.cma.2022.115852

Yuan Lei, Ni Yiqing, Deng Xiangyun, et al. 2022. A-PINN: auxiliary physics informed neural networks for forward and inverse problems of nonlinear integro-differential equations. Journal of Computational Physics, 462: 111260, doi: 10.1016/j.jcp.2022.111260

Zhang Xiaoping, Cheng Tao, Ju Lili. 2022. Implicit form neural network for learning scalar hyperbolic conservation laws. In: Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference. Lausanne, Switzerland: PMLR, 1082–1098

Zhang Zhiyong, Zhang Hui, Zhang Lisheng, et al. 2023. Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations. Journal of Computational Physics, 492: 112415, doi: 10.1016/j.jcp.2023.112415

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