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

Journal Article · 22 August 2023 · Journal of Hydrology

DOI: https://doi.org/10.1016/j.jhydrol.2023.130048 · OSTI ID:2202422

Niu, Jie ^[1]; Xu, Wei ^[2]; Qiu, Han  ^[3]; Li, Shan ^[4]; Dong, Feifei ^[4]

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1. Guizhou University (China)
2. Chinese Academy of Sciences (CAS), Beijing (China). Institute of Atmospheric Physics
3. Univ. of Wisconsin, Madison, WI (United States); Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
4. Jinan Univ., Guangzhou, Guangdong (China)

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 (N_u), 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. Finally, 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.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
• Sponsoring Organization: National Natural Science Foundation of China (NSFC); USDOE
• Grant/Contract Number: AC05-76RL01830
• OSTI ID: 2202422
• Report Number(s): PNNL-SA--190227
• Journal Information: Journal of Hydrology, Journal Name: Journal of Hydrology Journal Issue: Part B Vol. 625; ISSN 0022-1694
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English