Groundwater inverse modeling: Physics-informed neural network with disentangled constraints and errors
•A PINN method (KLE-PINN) is proposed for estimating hydraulic conductivity under different scenarios.•Analyzing water head fitting error improve understanding the results of our model.•KLE-PINN can easily investigate cases where BCs are unknown. This study combines a physics-informed neural network...
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| Published in | Journal of hydrology (Amsterdam) Vol. 640; p. 131703 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.08.2024
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| Subjects | |
| Online Access | Get full text |
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| Abstract | •A PINN method (KLE-PINN) is proposed for estimating hydraulic conductivity under different scenarios.•Analyzing water head fitting error improve understanding the results of our model.•KLE-PINN can easily investigate cases where BCs are unknown.
This study combines a physics-informed neural network (PINN) and Karhunen-Loeve expansion (KLE) (i.e., KLE-PINN) to solve the groundwater inverse problem. The hydraulic head (u) distribution is approximated by a deep neural network (DNN), while the hydraulic conductivity (K) field is constructed by KLE with given prior geostatistical information. KLE-PINN is applied to investigate the inversion using data from a single pumping test, natural gradient flow (NG), and hydraulic tomography (HT). The results from these cases demonstrate that our inverse method is robust. Our error analysis endeavors to quantify the sources of error by using two custom reference indicators, eforward and ecoupling. Moreover, the study finds that the inversion using data from multiple pumping tests (HT) yields more accurate estimates, leads to faster training convergence, and maintains higher stability. In addition, by investigating cases with different outer boundary conditions (BCs), we find that KLE-PINN is more flexible. Precisely, in scenarios with missing BCs, our network still fits well with the observed data, and the estimates capture the approximate spatial pattern in the region where the observation wells are distributed. Even with incorrect BCs, our network still performs well because the observational data constraints are strongly enforced during training. |
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| AbstractList | •A PINN method (KLE-PINN) is proposed for estimating hydraulic conductivity under different scenarios.•Analyzing water head fitting error improve understanding the results of our model.•KLE-PINN can easily investigate cases where BCs are unknown.
This study combines a physics-informed neural network (PINN) and Karhunen-Loeve expansion (KLE) (i.e., KLE-PINN) to solve the groundwater inverse problem. The hydraulic head (u) distribution is approximated by a deep neural network (DNN), while the hydraulic conductivity (K) field is constructed by KLE with given prior geostatistical information. KLE-PINN is applied to investigate the inversion using data from a single pumping test, natural gradient flow (NG), and hydraulic tomography (HT). The results from these cases demonstrate that our inverse method is robust. Our error analysis endeavors to quantify the sources of error by using two custom reference indicators, eforward and ecoupling. Moreover, the study finds that the inversion using data from multiple pumping tests (HT) yields more accurate estimates, leads to faster training convergence, and maintains higher stability. In addition, by investigating cases with different outer boundary conditions (BCs), we find that KLE-PINN is more flexible. Precisely, in scenarios with missing BCs, our network still fits well with the observed data, and the estimates capture the approximate spatial pattern in the region where the observation wells are distributed. Even with incorrect BCs, our network still performs well because the observational data constraints are strongly enforced during training. |
| ArticleNumber | 131703 |
| Author | Shi, Liangsheng Yeh, Tian-Chyi J. Ji, Yuzhe Zha, Yuanyuan Wang, Yanling |
| Author_xml | – sequence: 1 givenname: Yuzhe orcidid: 0009-0000-4975-8507 surname: Ji fullname: Ji, Yuzhe organization: State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan, China – sequence: 2 givenname: Yuanyuan orcidid: 0000-0003-4323-0730 surname: Zha fullname: Zha, Yuanyuan email: zhayuan87@whu.edu.cn organization: State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan, China – sequence: 3 givenname: Tian-Chyi J. orcidid: 0000-0003-0826-5268 surname: Yeh fullname: Yeh, Tian-Chyi J. organization: Department of Hydrology and Atmospheric Sciences, University of Arizona, Tucson, AZ, USA – sequence: 4 givenname: Liangsheng surname: Shi fullname: Shi, Liangsheng organization: State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan, China – sequence: 5 givenname: Yanling surname: Wang fullname: Wang, Yanling organization: State Key Laboratory of Water Resources Engineering and Management, Wuhan University, Wuhan, China |
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| Title | Groundwater inverse modeling: Physics-informed neural network with disentangled constraints and errors |
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