Physics-informed neural networks for predicting velocity and pressure fields from wave elevation based on Boussinesq model

The task of achieving high-accuracy full-field reconstruction in the realm of water waves is widely acknowledged as a challenge, primarily due to the sparsity and incompleteness of data measurement in both temporal and spatial dimensions. We develop a full-field velocity and pressure reconstruction approach for non-linear water waves based on physics-informed neural networks from the free surface measurement. The fully non-linear highly dispersive Boussinesq model is integrated to reduce the training cost by representing the three dimensional water wave problems in the horizontal two-dimensional plane with the inherent velocity distribution along water depth. A series of test cases, including the solitary waves, fifth-order Stokes waves, standing waves, and superimposed waves, are employed to evaluate the performance of the algorithm. The proposed novel neural networks are capable of accurately reconstructing the flow fields even when assimilating the limited and sparse free surface deformation data, which facilitates the development of detecting the flow characteristics in real ocean waves.