Articles | Volume 26, issue 16
https://doi.org/10.5194/hess-26-4469-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-26-4469-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
30 Aug 2022
Research article |
| 30 Aug 2022
| 30 Aug 2022
Forward and inverse modeling of water flow in unsaturated soils with discontinuous hydraulic conductivities using physics-informed neural networks with domain decomposition
Life and Environmental Science Department, University of California, Merced, CA, USA
Teamrat A. Ghezzehei
Life and Environmental Science Department, University of California, Merced, CA, USA
Viewed
Total article views: 8,879 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 25 Feb 2022)
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 6,427 | 2,325 | 127 | 8,879 | 700 | 158 | 180 |
- HTML: 6,427
- PDF: 2,325
- XML: 127
- Total: 8,879
- Supplement: 700
- BibTeX: 158
- EndNote: 180
Total article views: 7,113 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 30 Aug 2022)
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 5,357 | 1,660 | 96 | 7,113 | 236 | 140 | 160 |
- HTML: 5,357
- PDF: 1,660
- XML: 96
- Total: 7,113
- Supplement: 236
- BibTeX: 140
- EndNote: 160
Total article views: 1,766 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 25 Feb 2022)
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 1,070 | 665 | 31 | 1,766 | 464 | 18 | 20 |
- HTML: 1,070
- PDF: 665
- XML: 31
- Total: 1,766
- Supplement: 464
- BibTeX: 18
- EndNote: 20
Viewed (geographical distribution)
Total article views: 8,879 (including HTML, PDF, and XML)
Thereof 8,510 with geography defined
and 369 with unknown origin.
Total article views: 7,113 (including HTML, PDF, and XML)
Thereof 6,843 with geography defined
and 270 with unknown origin.
Total article views: 1,766 (including HTML, PDF, and XML)
Thereof 1,667 with geography defined
and 99 with unknown origin.
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
Cited
66 citations as recorded by crossref.
- Physics-informed Kolmogorov–Arnold networks to model flow in heterogeneous porous media with a mixed pressure-velocity formulation X. Rao et al.
- Soil Science-Informed Machine Learning B. Minasny et al.
- APPLICATION OF AN ADAPTIVE NEURAL NETWORK FOR THE IDENTIFICATION OF FRACTIONAL PARAMETERS OF HEAT AND MOISTURE TRANSFER PROCESSES IN FRACTAL MEDIA Y. Sokolovskyy & T. Samotii
- Enhancing inverse modeling in groundwater systems through machine learning: a comprehensive comparative study J. Chen et al.
- Physics-informed neural networks for modeling two-phase steady state flow with capillary heterogeneity at varying flow conditions A. Chakraborty et al.
- Predicting water movement in unsaturated soil using physics-informed deep operator networks Q. Ye et al.
- Advancing Sub-Seasonal to Seasonal Streamflow Forecasting in Canada: A Review of Conventional and Emerging Approaches for Operational Applications D. Nguyen et al.
- A finite-volume based physics-informed Fourier neural operator network for parametric learning of subsurface flow X. Yan et al.
- A survey of physics-informed AI for complex urban systems E. Xu et al.
- Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems A. Sarma et al.
- Simultaneous Estimation of Soil Hydraulic and Thermal Properties Based on Multiobjective Optimization Algorithms J. Zhang & N. Li
- Analysis Model of Load Transfer Method Based on Domain Decomposition Physics-Informed Neural Networks X. Jia et al.
- Bayesian back analysis of unsaturated hydraulic parameters for rainfall-induced slope failure: A review H. Yang & L. Zhang
- A multifactorial study of mass movement in the hilly and gully Loess Plateau based on intensive field surveys and remote sensing techniques L. Yan et al.
- Development of a modified Green–Ampt model considering the unsaturated zone Y. Li et al.
- A forward progressive physics informed neural network with Taylor series expansion for solving evolution partial differential equations W. Liu & Y. Liu
- A physics-informed neural network workflow for forward and inverse modeling of unsaturated flow and root water uptake from hydrogeophysical data C. Sakar et al.
- Combining physical models and machine learning for enhanced soil moisture estimation M. Li et al.
- A generalized physics-driven neural network for micromechanical and microstructural evolution of heterogeneous materials Z. Xiong & P. Zhao
- Time series predictions in unmonitored sites: a survey of machine learning techniques in water resources J. Willard et al.
- A comparative study of physics-informed neural network strategies for modeling water and nitrogen transport in unsaturated soils H. Kamil et al.
- Applications of physics-informed neural networks in fluid flow in porous media - A review study O. Samarkanov et al.
- Physics informed neural networks for an inverse problem in peridynamic models F. Difonzo et al.
- Inverse modeling of layered soil water flow under hydrothermal coupling using a multi-physics informed Neural Network Y. Gao et al.
- A data-driven physics-informed deep learning approach for estimating sub-core permeability from coreflooding saturation measurements A. Chakraborty et al.
- Application of PINNs to Define Roughness Coefficients for Channel Flow Problems S. Strijhak et al.
- Diverse methods of incorporating physics into neural networks: A comprehensive review M. Rajabi et al.
- Progressive Domain Decomposition for Efficient Training of Physics-Informed Neural Network D. Luo et al.
- Application of physics-informed neural networks (PINNs) solution to coupled thermal and hydraulic processes in silty sands Y. Feng et al.
- Machine Learning and Artificial Intelligence Applications in Soil Science B. Minasny & A. McBratney
- Causal prior-embedded physics-informed neural networks and a case study on metformin transport in porous media Q. Kang et al.
- Enhancing the prediction of irrigation demand for open field vegetable crops in Germany through neural networks, transfer learning, and ensemble models S. Rubo & J. Zinkernagel
- Modeling fluid flow in heterogeneous porous media with physics-informed neural networks: Weighting strategies for the mixed pressure head-velocity formulation A. Alhubail et al.
- Reconstructing the Unsaturated Flow Equation From Sparse and Noisy Data: Leveraging the Synergy of Group Sparsity and Physics‐Informed Deep Learning W. Song et al.
- Physics-informed neural networks for martensitic transformation: Toward morphology-based material parameters estimation A. Khan & M. Mamivand
- A neighbour-aware LSTM-PINN model for simultaneous soil moisture forecasting and retention function estimation C. Jiang et al.
- A unified fractional-order model for soil infiltration X. Guo et al.
- Numerical modeling of one-dimensional variably saturated flow in a homogeneous and layered soil–water system via mixed form Richards equation with Picard iterative scheme S. Shah et al.
- High-Resolution Estimation of Soil Saturated Hydraulic Conductivity via Upscaling and Karhunen–Loève Expansion within DREAM(ZS) Y. Xia & N. Li
- Ensemble learning of soil–water characteristic curve for unsaturated seepage using physics-informed neural networks H. Yang et al.
- Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media S. Roy et al.
- Hybrid data-mechanism-driven model of the unsteady soil temperature field for long-buried crude oil pipelines with non-isothermal batch transportation W. Jiang et al.
- Inverse Physics-Informed Neural Networks for transport models in porous materials M. Berardi et al.
- Physics informed neural networks for learning the horizon size in bond-based peridynamic models F. Difonzo et al.
- Inverse analysis for estimating geotechnical parameters using physics-informed neural networks S. Ito et al.
- Applications of physics-informed neural networks in geosciences: From basic seismology to comprehensive environmental studies M. Habib et al.
- Domain-decomposed physics-informed neural network for one-dimensional soil consolidation under multi-step surcharge loading H. Zhang et al.
- Modeling Water Flow and Solute Transport in Unsaturated Soils Using Physics‐Informed Neural Networks Trained With Geoelectrical Data P. Haruzi & Z. Moreno
- A Physics-Informed Neural Network Based on the Separation of Variables for Solving the Distributed-Order Time-Fractional Advection–Diffusion Equation W. Liu & Y. Liu
- A mixed pressure-velocity formulation to model flow in heterogeneous porous media with physics-informed neural networks F. Lehmann et al.
- Differentiable Physical Modeling for Forest Above-Ground Biomass Retrieval by Unifying a Water Cloud Model and Deep Learning C. Zhao et al.
- Physics-informed neural operators for efficient modeling of infiltration in porous media H. Kamil et al.
- Scientific machine learning in hydrology: a unified perspective A. Adombi
- Groundwater inverse modeling: Physics-informed neural network with disentangled constraints and errors Y. Ji et al.
- Integrating the Grading Entropy Theory (GET) into a Physics-Informed Neural Network (PINN) to predict soil hydraulic properties R. Polo-Mendoza et al.
- Integrating multiple physical processes with deep learning for the prediction of coupled water-vapor-heat water flux in unsaturated zone Y. Wang et al.
- A transfer learning physics-informed deep learning framework for modeling multiple solute dynamics in unsaturated soils H. Kamil et al.
- A comprehensive review of advances in physics-informed neural networks and their applications in complex fluid dynamics C. Zhao et al.
- Interaction Modeling of Surface Water and Groundwater: An Evaluation of Current and Future Issues N. Khurshid et al.
- Some Remarks About Forward and Inverse Modelling in Hydrology, Within a General Conceptual Framework M. Giudici
- PINN enhanced extended multiscale finite element method for fast mechanical analysis of heterogeneous materials Z. Wu et al.
- Physics-informed machine learning in geotechnical engineering: a direction paper B. Yuan et al.
- A novel approach to estimate sand particle-size using convolutional neural network with acoustic sensing Y. Sung et al.
- Solving fluid flow in discontinuous heterogeneous porous media and multi-layer strata with interpretable physics-encoded finite element network X. Wang et al.
- Modeling One-Dimensional Nonlinear Consolidation Problems by Physics-Informed Neural Network with Layer-Wise Locally Adaptive Activation Functions J. Zhou et al.
- Physics-Informed Neural Networks for Fast 3D Consolidation Prediction: A Surrogate Modelling Application B. Yuan et al.
66 citations as recorded by crossref.
- Physics-informed Kolmogorov–Arnold networks to model flow in heterogeneous porous media with a mixed pressure-velocity formulation X. Rao et al.
- Soil Science-Informed Machine Learning B. Minasny et al.
- APPLICATION OF AN ADAPTIVE NEURAL NETWORK FOR THE IDENTIFICATION OF FRACTIONAL PARAMETERS OF HEAT AND MOISTURE TRANSFER PROCESSES IN FRACTAL MEDIA Y. Sokolovskyy & T. Samotii
- Enhancing inverse modeling in groundwater systems through machine learning: a comprehensive comparative study J. Chen et al.
- Physics-informed neural networks for modeling two-phase steady state flow with capillary heterogeneity at varying flow conditions A. Chakraborty et al.
- Predicting water movement in unsaturated soil using physics-informed deep operator networks Q. Ye et al.
- Advancing Sub-Seasonal to Seasonal Streamflow Forecasting in Canada: A Review of Conventional and Emerging Approaches for Operational Applications D. Nguyen et al.
- A finite-volume based physics-informed Fourier neural operator network for parametric learning of subsurface flow X. Yan et al.
- A survey of physics-informed AI for complex urban systems E. Xu et al.
- Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems A. Sarma et al.
- Simultaneous Estimation of Soil Hydraulic and Thermal Properties Based on Multiobjective Optimization Algorithms J. Zhang & N. Li
- Analysis Model of Load Transfer Method Based on Domain Decomposition Physics-Informed Neural Networks X. Jia et al.
- Bayesian back analysis of unsaturated hydraulic parameters for rainfall-induced slope failure: A review H. Yang & L. Zhang
- A multifactorial study of mass movement in the hilly and gully Loess Plateau based on intensive field surveys and remote sensing techniques L. Yan et al.
- Development of a modified Green–Ampt model considering the unsaturated zone Y. Li et al.
- A forward progressive physics informed neural network with Taylor series expansion for solving evolution partial differential equations W. Liu & Y. Liu
- A physics-informed neural network workflow for forward and inverse modeling of unsaturated flow and root water uptake from hydrogeophysical data C. Sakar et al.
- Combining physical models and machine learning for enhanced soil moisture estimation M. Li et al.
- A generalized physics-driven neural network for micromechanical and microstructural evolution of heterogeneous materials Z. Xiong & P. Zhao
- Time series predictions in unmonitored sites: a survey of machine learning techniques in water resources J. Willard et al.
- A comparative study of physics-informed neural network strategies for modeling water and nitrogen transport in unsaturated soils H. Kamil et al.
- Applications of physics-informed neural networks in fluid flow in porous media - A review study O. Samarkanov et al.
- Physics informed neural networks for an inverse problem in peridynamic models F. Difonzo et al.
- Inverse modeling of layered soil water flow under hydrothermal coupling using a multi-physics informed Neural Network Y. Gao et al.
- A data-driven physics-informed deep learning approach for estimating sub-core permeability from coreflooding saturation measurements A. Chakraborty et al.
- Application of PINNs to Define Roughness Coefficients for Channel Flow Problems S. Strijhak et al.
- Diverse methods of incorporating physics into neural networks: A comprehensive review M. Rajabi et al.
- Progressive Domain Decomposition for Efficient Training of Physics-Informed Neural Network D. Luo et al.
- Application of physics-informed neural networks (PINNs) solution to coupled thermal and hydraulic processes in silty sands Y. Feng et al.
- Machine Learning and Artificial Intelligence Applications in Soil Science B. Minasny & A. McBratney
- Causal prior-embedded physics-informed neural networks and a case study on metformin transport in porous media Q. Kang et al.
- Enhancing the prediction of irrigation demand for open field vegetable crops in Germany through neural networks, transfer learning, and ensemble models S. Rubo & J. Zinkernagel
- Modeling fluid flow in heterogeneous porous media with physics-informed neural networks: Weighting strategies for the mixed pressure head-velocity formulation A. Alhubail et al.
- Reconstructing the Unsaturated Flow Equation From Sparse and Noisy Data: Leveraging the Synergy of Group Sparsity and Physics‐Informed Deep Learning W. Song et al.
- Physics-informed neural networks for martensitic transformation: Toward morphology-based material parameters estimation A. Khan & M. Mamivand
- A neighbour-aware LSTM-PINN model for simultaneous soil moisture forecasting and retention function estimation C. Jiang et al.
- A unified fractional-order model for soil infiltration X. Guo et al.
- Numerical modeling of one-dimensional variably saturated flow in a homogeneous and layered soil–water system via mixed form Richards equation with Picard iterative scheme S. Shah et al.
- High-Resolution Estimation of Soil Saturated Hydraulic Conductivity via Upscaling and Karhunen–Loève Expansion within DREAM(ZS) Y. Xia & N. Li
- Ensemble learning of soil–water characteristic curve for unsaturated seepage using physics-informed neural networks H. Yang et al.
- Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media S. Roy et al.
- Hybrid data-mechanism-driven model of the unsteady soil temperature field for long-buried crude oil pipelines with non-isothermal batch transportation W. Jiang et al.
- Inverse Physics-Informed Neural Networks for transport models in porous materials M. Berardi et al.
- Physics informed neural networks for learning the horizon size in bond-based peridynamic models F. Difonzo et al.
- Inverse analysis for estimating geotechnical parameters using physics-informed neural networks S. Ito et al.
- Applications of physics-informed neural networks in geosciences: From basic seismology to comprehensive environmental studies M. Habib et al.
- Domain-decomposed physics-informed neural network for one-dimensional soil consolidation under multi-step surcharge loading H. Zhang et al.
- Modeling Water Flow and Solute Transport in Unsaturated Soils Using Physics‐Informed Neural Networks Trained With Geoelectrical Data P. Haruzi & Z. Moreno
- A Physics-Informed Neural Network Based on the Separation of Variables for Solving the Distributed-Order Time-Fractional Advection–Diffusion Equation W. Liu & Y. Liu
- A mixed pressure-velocity formulation to model flow in heterogeneous porous media with physics-informed neural networks F. Lehmann et al.
- Differentiable Physical Modeling for Forest Above-Ground Biomass Retrieval by Unifying a Water Cloud Model and Deep Learning C. Zhao et al.
- Physics-informed neural operators for efficient modeling of infiltration in porous media H. Kamil et al.
- Scientific machine learning in hydrology: a unified perspective A. Adombi
- Groundwater inverse modeling: Physics-informed neural network with disentangled constraints and errors Y. Ji et al.
- Integrating the Grading Entropy Theory (GET) into a Physics-Informed Neural Network (PINN) to predict soil hydraulic properties R. Polo-Mendoza et al.
- Integrating multiple physical processes with deep learning for the prediction of coupled water-vapor-heat water flux in unsaturated zone Y. Wang et al.
- A transfer learning physics-informed deep learning framework for modeling multiple solute dynamics in unsaturated soils H. Kamil et al.
- A comprehensive review of advances in physics-informed neural networks and their applications in complex fluid dynamics C. Zhao et al.
- Interaction Modeling of Surface Water and Groundwater: An Evaluation of Current and Future Issues N. Khurshid et al.
- Some Remarks About Forward and Inverse Modelling in Hydrology, Within a General Conceptual Framework M. Giudici
- PINN enhanced extended multiscale finite element method for fast mechanical analysis of heterogeneous materials Z. Wu et al.
- Physics-informed machine learning in geotechnical engineering: a direction paper B. Yuan et al.
- A novel approach to estimate sand particle-size using convolutional neural network with acoustic sensing Y. Sung et al.
- Solving fluid flow in discontinuous heterogeneous porous media and multi-layer strata with interpretable physics-encoded finite element network X. Wang et al.
- Modeling One-Dimensional Nonlinear Consolidation Problems by Physics-Informed Neural Network with Layer-Wise Locally Adaptive Activation Functions J. Zhou et al.
- Physics-Informed Neural Networks for Fast 3D Consolidation Prediction: A Surrogate Modelling Application B. Yuan et al.
Saved (final revised paper)
Latest update: 28 Apr 2026
Short summary
Scientists use a physics-based equation to simulate water dynamics that influence hydrological and ecological phenomena. We present hybrid physics-informed neural networks (PINNs) to leverage the growing availability of soil moisture data and advances in machine learning. We showed that PINNs perform comparably to traditional methods and enable the estimation of rainfall rates from soil moisture. However, PINNs are challenging to train and significantly slower than traditional methods.
Scientists use a physics-based equation to simulate water dynamics that influence hydrological...
