In this paper, physics-informed neural network (PINN) based on characteristic-based split (CBS) is proposed, which can be used to solve the time-dependent Navier-Stokes equations (N-S equations). In this method, The output parameters and corresponding losses are separated, so the weights between output parameters are not considered. Not all partial derivatives participate in gradient backpropagation, and the remaining terms will be reused.Therefore, compared with traditional PINN, this method is a rapid version. Here, labeled data, physical constraints and network outputs are regarded as priori information, and the residuals of the N-S equations are regarded as posteriori information. So this method can deal with both data-driven and data-free problems. As a result, it can solve the special form of compressible N-S equations -- -Shallow-Water equations, and incompressible N-S equations. As boundary conditions are known, this method only needs the flow field information at a certain time to restore the past and future flow field information. We solve the progress of a solitary wave onto a shelving beach and the dispersion of the hot water in the flow, which show this method's potential in the marine engineering. We also use incompressible equations with exact solutions to prove this method's correctness and universality. We find that PINN needs more strict boundary conditions to solve the N-S equation, because it has no computational boundary compared with the finite element method.

本文提出了一种基于特征分裂的物理知识神经网络(PINN)，用于解决时间依赖的Navier-Stokes方程，该方法既支持数据驱动的问题，也支持无数据的问题。该方法的应用于海洋工程领域表现出了很好的潜力。

物理启发式神经网络与基于特征的分裂法相结合求解Navier-Stokes方程组