Solving fluid dynamics problems mainly rely on experimental methods and numerical simulation. However, in experimental methods it is difficult to simulate the physical problems in reality, and there is also a high-cost to the economy while numerical simulation methods are sensitive about meshing a complicated structure. It is also time-consuming due to the billion degrees of freedom in relevant spatial-temporal flow fields. Therefore, constructing a cost-effective model to settle fluid dynamics problems is of significant meaning. Deep learning (DL) has great abilities to handle strong nonlinearity and high dimensionality that attracts much attention for solving fluid problems. Unfortunately, the proposed surrogate models in DL are almost black-box models and lack interpretation. In this paper, the Physical Informed Neural Network (PINN) combined with Resnet blocks is proposed to solve fluid flows depending on the partial differential equations (i.e., Navier-Stokes equation) which are embedded into the loss function of the deep neural network to drive the model. In addition, the initial conditions and boundary conditions are also considered in the loss function. To validate the performance of the PINN with Resnet blocks, Burger’s equation with a discontinuous solution and Navier-Stokes (N-S) equation with continuous solution are selected. The results show that the PINN with Resnet blocks (Res-PINN) has stronger predictive ability than traditional deep learning methods. In addition, the Res-PINN can predict the whole velocity fields and pressure fields in spatial-temporal fluid flows, the magnitude of the mean square error of the fluid flow reaches to ${10}^{-5}$. The inverse problems of the fluid flows are also well conducted. The errors of the inverse parameters are 0.98% and 3.1% in clean data and 0.99% and 3.1% in noisy data.

Due to the strong nonlinear interaction with river discharge, tides in estuaries are characterised as nonstationary and their mechanisms are yet to be fully understood. It remains highly challenging to accurately predict estuarine water levels. Machine learning methods, which offer a unique ability to simulate the unknown relationships between variables, have been increasingly used in a large number of research areas. This study applies the LightGBM model to predicting the water levels along the lower reach of the Columbia River. The model inputs consist of the discharges from two upstream rivers (Columbia and Willamette Rivers) and the tide characteristics, including the tide range at the estuary mouth (Astoria) and tide constituents. The model is optimized with the selected parameters. The results show that the LightGBM model can achieve high prediction accuracy, with the root-mean-square-error values of water level being reduced to 0.14 m and the correlation coefficient and skill score being in the ranges of 0.975–0.987 and 0.941–0.972, respectively, which are statistically better than those obtained from physics-based models such as the nonstationary tidal harmonic analysis model (NS_TIDE). The importance of subtide constituents in interacting with the river discharge in the estuary is clearly revealed from the model results.

A three-degrees-of-freedom model, including surge, sway and yaw motion, with differential thrusters is proposed to describe unmanned surface vehicle (USV) dynamics in this study. The experiment is carried out in the Qing Huai River and the data obtained from different zigzag trajectories are filtered by a Gaussian filtering method. A physics-informed neural network (PINN) is proposed to identify the dynamic models of the USV. PINNs combine the advantages of data-driven machine learning and physical models. They can also embed the speed and steering models into the loss function, which can significantly retain all types of information. Compared with traditional neural networks, the results show that the PINN has better generalization ability in predicting the surge and sway velocities and rotation speed with only limited training data.