Physic-informed Neural Network Approach for solving the 1D Steady Shallow Water Equations in Riverine Systems

Shallow water equations (SWE) are the governing equations in open channel flows. The numerical solution is widely considered the most effective approach for solving the SWE in the past few decades. However, numerical solutions are inefficient and need to compromise many aspects, such as order of scheme accuracy, Courant numbers, boundness, etc. In recent years, deep learning (DL) has been one of the rapidly rising techniques that has been widely used in the engineering field. DL models can bridge approximation relations between inputs and outputs variables by conducting multiple elementary operations constructed by artificial neural networks. Many researchers achieved success in hydrology and hydraulic problems by using DL models. However, there are still some drawbacks to the previous DL models. Most DL models are purely empirical and not physics-based, which may lead to larger prediction errors especially when test ranges are not included in the training dataset. Besides, training this model requires big data, which is mostly expensive in hydrology and hydraulic problems. This paper will introduce a novel and data-free neural network framework for solving the SWE. The architecture of the framework will be demonstrated through various case studies. The widely-used HEC-RAS model is used as the reference model for evaluating the performance of the proposed neural network framework.