Physics-Informed Neural Network Approach for Solving the One-Dimensional Unsteady Shallow-Water Equations in Riverine Systems

In recent years, many researchers have used machine learning approaches to bridge the relationship between big data and physics in the practical engineering field. However, the widely used machine learning models are highly dependent on the quality and quantity of data. These long-term monitoring data usually are expensive to obtain in water system. This paper presents a novel neural network structure, the physics-informed neural network (PINN), which can implement the shallow-water equations (SWEs) directly so that the training stage is based fully on physical laws. Similar to numerical models, our PINN model requires the same data as the numerical method, e.g., boundary conditions, the digital elevation of the terrain, and so forth. Because the SWEs are solved directly in our framework, this framework can be understood as a data-free method. The PINN was tested using two case studies: a flow spike in a hypothetical trapezoidal channel, and a historical scenario of downstream Cypress Creek, Houston. The results indicated great agreement with the widely used numerical solver, HEC-RAS.