Deep Learning Identification of the Governing Equation for Water Flow in Heterogeneous Soils From Data
Abstract Despite the remarkable advances in using deep learning for describing and predicting soil water flow, these models inherently cannot deepen our understanding of its underlying physical mechanisms as they are black‐box approaches. To address this issue, a novel data‐driven equation discovery...
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2025-03-01
|
| Series: | Water Resources Research |
| Subjects: | |
| Online Access: | https://doi.org/10.1029/2024WR037786 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850211945859252224 |
|---|---|
| author | Wenxiang Song Liangsheng Shi Leilei He Yuanyuan Zha Xiaolong Hu Mehdi Rahmati Harry Vereecken |
| author_facet | Wenxiang Song Liangsheng Shi Leilei He Yuanyuan Zha Xiaolong Hu Mehdi Rahmati Harry Vereecken |
| author_sort | Wenxiang Song |
| collection | DOAJ |
| description | Abstract Despite the remarkable advances in using deep learning for describing and predicting soil water flow, these models inherently cannot deepen our understanding of its underlying physical mechanisms as they are black‐box approaches. To address this issue, a novel data‐driven equation discovery approach has recently been widely used to facilitate scientific discovery in geoscience disciplines, including soil hydrology. However, due to the inherent complexity of soils, current data‐driven discovery approaches cannot deal with heterogeneous soil scenarios. In this study, we present a new group sparse regression theory and a deep learning framework to extend previous studies to be able to identify the governing equations for soil water flow in heterogeneous soils from observational data. Specifically, we focus on discovering equations from only time series of volumetric soil water content data, which are easily accessible. To accommodate it, the underlying assumption of the generalized soil‐water content‐based governing equation is utilized, and a coarse‐grained group sparsity theory is developed. Furthermore, we incorporate the proposed group sparse regression into a new deep‐learning framework: Extended‐DeepGS (Extended Deep‐learning‐based Group Sparsity). Through deep‐learning identification, it realizes simultaneous reconstructions of soil moisture dynamics and governing equations. A series of comprehensive numerical experiments are designed and conducted to test the performance of the theory and framework, and the results show its robustness. We also summarize the potential effects of soil heterogeneity on the discovery of equations. Finally, we discuss the limitations of the approach, which may inform future developments. |
| format | Article |
| id | doaj-art-1eabe232bd7f4dde8d476001bea7be48 |
| institution | OA Journals |
| issn | 0043-1397 1944-7973 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Wiley |
| record_format | Article |
| series | Water Resources Research |
| spelling | doaj-art-1eabe232bd7f4dde8d476001bea7be482025-08-20T02:09:27ZengWileyWater Resources Research0043-13971944-79732025-03-01613n/an/a10.1029/2024WR037786Deep Learning Identification of the Governing Equation for Water Flow in Heterogeneous Soils From DataWenxiang Song0Liangsheng Shi1Leilei He2Yuanyuan Zha3Xiaolong Hu4Mehdi Rahmati5Harry Vereecken6State Key Laboratory of Water Resources Engineering and Management Wuhan University Wuhan ChinaState Key Laboratory of Water Resources Engineering and Management Wuhan University Wuhan ChinaState Key Laboratory of Water Resources Engineering and Management Wuhan University Wuhan ChinaState Key Laboratory of Water Resources Engineering and Management Wuhan University Wuhan ChinaState Key Laboratory of Water Resources Engineering and Management Wuhan University Wuhan ChinaInstitute of Bio‐ and Geosciences: Agrosphere (IBG‐3) Forschungszentrum Jülich Jülich GermanyInstitute of Bio‐ and Geosciences: Agrosphere (IBG‐3) Forschungszentrum Jülich Jülich GermanyAbstract Despite the remarkable advances in using deep learning for describing and predicting soil water flow, these models inherently cannot deepen our understanding of its underlying physical mechanisms as they are black‐box approaches. To address this issue, a novel data‐driven equation discovery approach has recently been widely used to facilitate scientific discovery in geoscience disciplines, including soil hydrology. However, due to the inherent complexity of soils, current data‐driven discovery approaches cannot deal with heterogeneous soil scenarios. In this study, we present a new group sparse regression theory and a deep learning framework to extend previous studies to be able to identify the governing equations for soil water flow in heterogeneous soils from observational data. Specifically, we focus on discovering equations from only time series of volumetric soil water content data, which are easily accessible. To accommodate it, the underlying assumption of the generalized soil‐water content‐based governing equation is utilized, and a coarse‐grained group sparsity theory is developed. Furthermore, we incorporate the proposed group sparse regression into a new deep‐learning framework: Extended‐DeepGS (Extended Deep‐learning‐based Group Sparsity). Through deep‐learning identification, it realizes simultaneous reconstructions of soil moisture dynamics and governing equations. A series of comprehensive numerical experiments are designed and conducted to test the performance of the theory and framework, and the results show its robustness. We also summarize the potential effects of soil heterogeneity on the discovery of equations. Finally, we discuss the limitations of the approach, which may inform future developments.https://doi.org/10.1029/2024WR037786soil moisturedata‐driven discoverydeep learning |
| spellingShingle | Wenxiang Song Liangsheng Shi Leilei He Yuanyuan Zha Xiaolong Hu Mehdi Rahmati Harry Vereecken Deep Learning Identification of the Governing Equation for Water Flow in Heterogeneous Soils From Data Water Resources Research soil moisture data‐driven discovery deep learning |
| title | Deep Learning Identification of the Governing Equation for Water Flow in Heterogeneous Soils From Data |
| title_full | Deep Learning Identification of the Governing Equation for Water Flow in Heterogeneous Soils From Data |
| title_fullStr | Deep Learning Identification of the Governing Equation for Water Flow in Heterogeneous Soils From Data |
| title_full_unstemmed | Deep Learning Identification of the Governing Equation for Water Flow in Heterogeneous Soils From Data |
| title_short | Deep Learning Identification of the Governing Equation for Water Flow in Heterogeneous Soils From Data |
| title_sort | deep learning identification of the governing equation for water flow in heterogeneous soils from data |
| topic | soil moisture data‐driven discovery deep learning |
| url | https://doi.org/10.1029/2024WR037786 |
| work_keys_str_mv | AT wenxiangsong deeplearningidentificationofthegoverningequationforwaterflowinheterogeneoussoilsfromdata AT liangshengshi deeplearningidentificationofthegoverningequationforwaterflowinheterogeneoussoilsfromdata AT leileihe deeplearningidentificationofthegoverningequationforwaterflowinheterogeneoussoilsfromdata AT yuanyuanzha deeplearningidentificationofthegoverningequationforwaterflowinheterogeneoussoilsfromdata AT xiaolonghu deeplearningidentificationofthegoverningequationforwaterflowinheterogeneoussoilsfromdata AT mehdirahmati deeplearningidentificationofthegoverningequationforwaterflowinheterogeneoussoilsfromdata AT harryvereecken deeplearningidentificationofthegoverningequationforwaterflowinheterogeneoussoilsfromdata |