1-D coupled surface flow and transport equations revisited via the physics-informed neural network approach

•Applied physics-informed neural network (PINN) to solve solve coupled shallow water and transport equations.•PINN outperforms the traditional numerical finite difference method.•PINN is suitable for solving inverse problems with sparse and noisy data.•The accuracy of PINN is correlated with the num...

Full description

Saved in:
Bibliographic Details
Published inJournal of hydrology (Amsterdam) Vol. 625; no. Part B; p. 130048
Main Authors Niu, Jie, Xu, Wei, Qiu, Han, Li, Shan, Dong, Feifei
Format Journal Article
LanguageEnglish
Published United States Elsevier B.V 01.10.2023
Elsevier
Subjects
Online AccessGet full text

Cover

Loading…
More Information
Summary:•Applied physics-informed neural network (PINN) to solve solve coupled shallow water and transport equations.•PINN outperforms the traditional numerical finite difference method.•PINN is suitable for solving inverse problems with sparse and noisy data.•The accuracy of PINN is correlated with the number of hidden parameters and layers. The de Saint-Venant equation (SVE) and advection–diffusion equation (ADE) are commonly employed to solve solute transport problems in surface water. In this work, we propose a mesh-free method based on the physics-informed neural network (PINN) to solve the one dimensional (1-D) SVE, ADE, and the coupled SVE and ADE (SVE-ADE) under various initial and boundary conditions. The PINN model extends the architecture of deep neural networks (DNNs) with implementation of loss function, which are additionally subject to constraints imposed by the physical laws of SVE and ADE, along with their initial and boundary conditions. In such a manner, PINNs can be quickly steered to the true solution while obeying the physical laws. The results of PINN model are compared with the analytical and/or numerical solutions under various conditions to investigate its accuracy and efficiency in solving the SVE, ADE, and SVE-ADE. Our results indicate PINN can accurately simulate the shock wave morphology and avoid numerical dissipation in unsteady flow condition. The PINN method outweighed traditional numerical methods in several aspects, including its ability to function with small amounts of data, no grid discretization, and random selection of sampling points, etc. Additionally, the PINN method is also suitable for solving inverse problems with sparse and noisy data. With 1% noise and 2000 initial and boundary condition points (Nu), the errors of the estimated flow rate (v) and diffusion coefficient (D) are 0.003% and 0.105%, respectively, which indicate the accuracy and robustness of the proposed method. Our results indicate the capability and robustness of the proposed PINN methodology for solving multi-physics problems, irrespective of the presence of sparse and noisy data in the training dataset.
Bibliography:PNNL-SA-190227
USDOE
National Natural Science Foundation of China (NSFC)
AC05-76RL01830; 41972244
ISSN:0022-1694
1879-2707
DOI:10.1016/j.jhydrol.2023.130048