Performance of Physical-informed Neural Network (PINN) for the key parameter inference in Langmuir turbulence parameterization scheme

Fangrui Xiu Zengan Deng

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. doi: 10.1007/s13131-024-2329-4
Citation: 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. doi: 10.1007/s13131-024-2329-4

doi: 10.1007/s13131-024-2329-4

Performance of Physical-informed Neural Network (PINN) for the key parameter inference in Langmuir turbulence parameterization scheme

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.
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  • Figure  1.  Architecture of PINN for key parameter E6 inference in KC04.

    Figure  2.  Illustration of spatiotemporal sampling interval combinations. a. Illustration for Exp1; b–e. Illustration for Exp2.

    Figure  3.  Response of TKE (a), l (b), and Kq (c) to variations in E6 values.

    Figure  4.  Inference curves (a–d) and loss curves (e–h) of the E6 inference process in the Exp1.

    Figure  5.  Results of the Temporal group: Inference curves (a) and loss curves (c) are the results of Model 2_1; Inference curves (b) and loss curves (d) are the results of Model 2_2.

    Figure  6.  Results of the Spatial group: inference curves (a) and loss curves (c) are the results of Model 2_3; inference curves (b) and loss curves (d) are the results of Model 2_4. The dashed lines of different colors in a represent the preset E6 values in the corresponding cases.

    Figure  7.  Average SEs of E6 inference from all PINN models in Set2.

    Figure  8.  Function curve (a) and first derivative curve (b) of the Tanh and Arctan.

    Table  1.   Experimental sets and experiment settings

    Experimental set (number) Experiment (number) Activation
    function
    Sampling intervals Preset E6 value (case number)/
    model number
    GOTM Sensitivity Experiment Set (Set1) / / / 5.0 (Case 1), 6.0 (Case 2),
    7.0 (Case 3), 8.0 (Case 4)
    PINN key hyperparameters
    sensitivity experiment set (Set2)
    Activation Functions sensitivity
    experiment (Exp1)
    Tanh Δt = 1s, Δz = 0.1 m Model 1_1
    Arctan Δt = 1s, Δz = 0.1 m Model 1_2
    Sine Δt = 1s, Δz = 0.1 m Model 1_3
    Sampling intervals sensitivity
    experiment (Exp2)
    the optimal
    one in Exp1
    Δt = 2s, Δz = 0.1 m Model 2_1
    Δt = 5s, Δz = 0.1 m Model 2_2
    Δt = 1s, Δz = 0.2 m Model 2_3
    Δt = 1s, Δz = 0.5 m Model 2_4
    Notes: / indicates that the item is not set or used in the experiment set.
    下载: 导出CSV

    Table  2.   Number of sampling points for each PINN model in Set2

    Model Spatial
    number
    Temporal
    number
    Total number
    Model 1_1, Model 1_2,
    Model 1_3
    300 300 90 000 (300 × 300)
    Model 2_1 300 150 45 000 (300 × 150)
    Model 2_2 300 60 18 000 (300 × 60)
    Model 2_3 150 300 45 000 (150 × 300)
    Model 2_4 60 300 18 000 (60 × 300)
    下载: 导出CSV

    Table  3.   Inference results and biases of the Exp1Case Activation function $ E_6^* $ SE

    Case 1 (E6 = 5.0) Sin / /
    Arctan / /
    Tanh 4.903 0.0094
    Case 2 (E6 = 6.0) Sin / /
    Arctan 4.062 3.7558
    Tanh 5.932 0.0046
    Case 3 (E6 = 7.0) Sin / /
    Arctan 5.952 1.0983
    Tanh 6.781 0.048
    Case 4 (E6 = 8.0) Sin / /
    Arctan 5.999 4.004
    Tanh 7.97 0.0009
    Note: / indicates that the model fails to reach a stable state in the corresponding case.
    下载: 导出CSV

    Table  4.   Inference results and biases of the temporal group in the Exp2

    Model Case $ E_6^* $ SE
    Model 2_1 Case 1 (E6 = 5.0) / /
    Case 2 (E6 = 6.0) 7.167 1.3619
    Case 3 (E6 = 7.0) 7.787 0.6194
    Case 4 (E6 = 8.0) / /
    Model 2_2 Case 1 (E6 = 5.0) 10.027 25.2707
    Case 2 (E6 = 6.0) / /
    Case 3 (E6 = 7.0) / /
    Case 4 (E6 = 8.0) 3.231 22.7434
    Note: “/” indicates that the PINN model fails to reach a stable state in the corresponding case.
    下载: 导出CSV

    Table  5.   Inference results and biases of the spatial group in the Exp2

    Model Case $ E_6^* $ SE
    Model 2_3 Case 1 (E6 = 5.0) 5.472 0.2228
    Case 2 (E6 = 6.0) 5.965 0.0012
    Case 3 (E6 = 7.0) 6.675 0.1056
    Case 4 (E6 = 8.0) 7.382 0.3819
    Model 2_4 Case 1 (E6 = 5.0) / /
    Case 2 (E6 = 6.0) 7.046 1.0941
    Case 3 (E6 = 7.0) 5.846 1.3317
    Case 4 (E6 = 8.0) 7.343 0.4316
    Note: / indicates that the PINN model fails to reach a stable state in the corresponding case.
    下载: 导出CSV
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  • 收稿日期:  2024-02-11
  • 录用日期:  2024-04-22
  • 网络出版日期:  2024-05-23

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