Identification of physical processes and unknown parameters of 3D groundwater contaminant problems via theory-guided U-net

He, Tianhao1; Chang, Haibin2; Zhang, Dongxiao3,4

2023-11-01

10.1007/s00477-023-02604-z

STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT   影响因子和分区

1436-3240

1436-3259

Identification of unknown physical processes and parameters of groundwater contaminant problems is a challenging task due to their ill-posed and non-unique nature. Numerous works have focused on determining nonlinear physical processes through model selection methods. However, identifying corresponding nonlinear systems for different physical phenomena using numerical methods can be computationally prohibitive. With the advent of machine learning (ML) algorithms, more efficient surrogate models based on neural networks (NNs) have been developed in various disciplines. In this work, a theory-guided U-net (TgU-net) framework is proposed for surrogate modeling of three-dimensional (3D) groundwater contaminant problems in order to efficiently elucidate their involved processes and unknown parameters. In TgU-net, the underlying governing equations are embedded into the loss function of U-net as soft constraints. Herein, sorption is considered to be a potential process of an uncertain type, and three equilibrium sorption isotherm types (i.e., linear, Freundlich, and Langmuir) are considered. Different from traditional approaches in which one model corresponds to one equation (Schoeniger et al. in Water Resour Res 50(12):9484-9513, 2014; Cao et al. in Hydrogeol J 27(8):2907-2918, 2019), these three sorption types are modeled through only one TgU-net surrogate. Accurate predictions illustrate the satisfactory generalizability and extrapolability of the constructed TgU-net. Furthermore, based on the constructed TgU-net surrogate, a data assimilation method is employed to identify the physical process and parameters simultaneously. The convergence of indicators demonstrates the validity of the proposed method. The influence of sparsity-promoting techniques, data noise, and quantity of observation information is also explored. Results demonstrate the feasibility of neural network learning a cluster of equations that have similar behaviors. This work shows the possibility of governing equation discovery of physical problems that contain multiple and even uncertain processes by using deep learning and data assimilation methods.

SCI ; EI

英语

通讯

This work is partially funded by the National Natural Science Foundation of China (Grant No. 52288101), the Shenzhen Key Laboratory of Natural Gas Hydrates (Grant No. ZDSYS20200421111201738), and the SUSTech-Qingdao New Energy Technology Research Institute[52288101] ; National Natural Science Foundation of China[ZDSYS20200421111201738]

Engineering ; Environmental Sciences & Ecology ; Mathematics ; Water Resources

Engineering, Environmental ; Engineering, Civil ; Environmental Sciences ; Statistics & Probability ; Water Resources

WOS:001103786000002

SPRINGER

20234715077513

Deep learning ; Groundwater ; Groundwater pollution ; Learning systems ; Numerical methods ; Parameter estimation

Groundwater:444.2 ; Water Pollution Sources:453.1 ; Ergonomics and Human Factors Engineering:461.4 ; Chemical Operations:802.3 ; Numerical Methods:921.6

ENGINEERING

Web of Science

1.Peking Univ, Coll Engn, Beijing 100871, Peoples R China
2.China Univ Min & Technol Beijing, Sch Energy & Min Engn, Beijing 100083, Peoples R China
3.Eastern Inst Technol, Eastern Inst Adv Study, Ningbo 315200, Peoples R China
4.Southern Univ Sci & Technol, Sch Environm Sci & Engn, Shenzhen 518055, Peoples R China

He, Tianhao,Chang, Haibin,Zhang, Dongxiao. Identification of physical processes and unknown parameters of 3D groundwater contaminant problems via theory-guided U-net[J]. STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT,2023.

He, Tianhao,Chang, Haibin,&Zhang, Dongxiao.(2023).Identification of physical processes and unknown parameters of 3D groundwater contaminant problems via theory-guided U-net.STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT.

He, Tianhao,et al."Identification of physical processes and unknown parameters of 3D groundwater contaminant problems via theory-guided U-net".STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT (2023).