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

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.