Physic-Informed Neural Network Approach Coupled with Boundary Conditions for Solving 1D Steady Shallow Water Equations for Riverine System
Conference
Yin, Z, Bian, L, Hu, B et al. (2023). Physic-Informed Neural Network Approach Coupled with Boundary Conditions for Solving 1D Steady Shallow Water Equations for Riverine System
. 280-288. 10.1061/9780784484852.027
Yin, Z, Bian, L, Hu, B et al. (2023). Physic-Informed Neural Network Approach Coupled with Boundary Conditions for Solving 1D Steady Shallow Water Equations for Riverine System
. 280-288. 10.1061/9780784484852.027
Shallow water equations (SWE) are the governing equations for the open channel flow. 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 have been widely used in the engineering field. DL models can bridge approximation relations between input and output 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. These DL models are often purely empirical and not constrained by real physics, which may cause a larger prediction error when test conditions are not included in the training data set. Besides, training this model requires big data, which is mostly expensive in hydrology and hydraulic problems. In this paper, we will introduce a novel and data-free neural network framework that can solve the SWE. The architecture of the framework will be demonstrated in detail, and the framework can be applied to any SWE problems. Additionally, we employed a numerical solver, HEC-RAS, as reference to verify the solution accuracy. As a result, this framework shows great agreement with numerical solutions.
