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<p>This study focuses on the application of physically informed neural networks (PINNs) in three-dimensional (3D) airfoil flow field computation. Given that PINNs face challenges such as high dimensionality, network architecture design, data requirements, numerical stability, and physical constraints formulation when dealing with this problem, the fluid dynamics PINN with DeepONet (FDPI-DeepONet) network is proposed. It combines the advantages of PINN physical constraint modeling and DeepONet data-driven learning, utilizes branch networks with different functions of the two to collaborate with the backbone network, represents the 3D flow field through Cartesian coordinates, and is trained based on the DeepONet framework and the loss function of physical information. The experiments are tested with M6 and NACA0012 airfoil data, and the results show that FDPI-DeepONet performs excellently in terms of prediction accuracy and computational resource consumption, e.g., it outperforms the comparative methods in terms of average <i>R</i><sup>2</sup> metrics, and the computation time is reduced significantly. The network effectively overcomes challenges and provides efficient solutions to complex fluid dynamics problems.</p>

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FDPI-DeepONet: A novel integration for 3D airfoil flow field computation

  • 期刊论文

  • 发表日期：

    2026年1月17日

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  • Pengyu Wang,
  • Bolin Pan,
  • Zhe Liu,
  • Liangjie Gao

摘要

This study focuses on the application of physically informed neural networks (PINNs) in three-dimensional (3D) airfoil flow field computation. Given that PINNs face challenges such as high dimensionality, network architecture design, data requirements, numerical stability, and physical constraints formulation when dealing with this problem, the fluid dynamics PINN with DeepONet (FDPI-DeepONet) network is proposed. It combines the advantages of PINN physical constraint modeling and DeepONet data-driven learning, utilizes branch networks with different functions of the two to collaborate with the backbone network, represents the 3D flow field through Cartesian coordinates, and is trained based on the DeepONet framework and the loss function of physical information. The experiments are tested with M6 and NACA0012 airfoil data, and the results show that FDPI-DeepONet performs excellently in terms of prediction accuracy and computational resource consumption, e.g., it outperforms the comparative methods in terms of average R2 metrics, and the computation time is reduced significantly. The network effectively overcomes challenges and provides efficient solutions to complex fluid dynamics problems.