Overview
Traditional machine learning models excel at pattern recognition but often ignore fundamental physical laws. Conversely, physics-based models require extensive parameterization and precise initial/boundary conditions. Our research bridges these approaches through physics-informed neural networks (PINNs) that embed physical equations directly into the machine learning framework.
This hybrid approach leverages the strengths of both paradigms: the flexibility and data-driven nature of machine learning combined with the reliability and interpretability of physics-based models. The result is a powerful tool for solving complex soil physics problems that are difficult or impossible to address with traditional methods alone.
Key Research Areas
1. Modeling Water Flow with PINNs
We develop neural network solutions to the Richardson-Richards equation (RRE), which describes water movement in unsaturated soils. Unlike traditional numerical methods, PINNs can:
- Handle sparse data: Work with limited soil moisture measurements without requiring complete initial and boundary conditions
- Solve inverse problems: Estimate hydraulic properties from field observations without repeatedly solving the forward problem
- Manage discontinuities: Use domain decomposition to accurately simulate layered soils with contrasting properties
2. Hydraulic Property Estimation
A major challenge in soil physics is the scale mismatch between laboratory measurements and field-scale processes. We use PINNs with monotonicity constraints to:
- Estimate field-scale hydraulic conductivity functions from volumetric water content data alone
- Calculate soil water flux density across the entire flow domain
- Avoid assumptions about specific hydraulic property models
3. Remote Sensing & Machine Learning Integration
Combining multispectral imagery from unoccupied aircraft systems (UAS) with machine learning to predict soil moisture across heterogeneous terrain. Our models incorporate:
- Terrain attributes from digital elevation models
- Hydrological variables (precipitation, evapotranspiration)
- Multispectral reflectance data
Why This Matters
Practical Applications
- Water management: Better predictions of irrigation needs and drainage patterns
- Climate modeling: Improved representation of soil processes in Earth System Models
- Contaminant transport: More accurate forecasting of pollutant movement through soils
- Agricultural decision-making: Spatial maps of soil moisture for precision agriculture
Technical Innovations
Adaptive Activation Functions
Traditional neural networks use fixed activation functions (e.g., ReLU, tanh). We implement adaptive activation functions that adjust during training, significantly improving PINN performance for solving partial differential equations.
Monotonicity Constraints
Hydraulic properties must be monotonic functions (e.g., hydraulic conductivity decreases as soil dries). We constrain neural networks to respect these physical requirements, ensuring physically realistic solutions.
Domain Decomposition
Soils are naturally layered with abrupt changes in properties. We use separate neural networks for each layer, accurately capturing discontinuities at layer boundaries that traditional methods struggle to handle.
Current Challenges & Future Directions
Computational efficiency: PINNs are currently slower than traditional numerical methods. We're exploring network architecture improvements and training strategies to reduce computation time.
Initialization sensitivity: PINN performance depends on network initialization. We're developing robust initialization schemes and ensemble approaches.
Scaling to 3D: Most PINN applications are 1D or 2D. We're extending these methods to fully 3D soil systems.
Recent Publications
- Soil Science-Informed Machine Learning.Minasny, B., Bandai, T., Ghezzehei, T. A., Huang, Y.-C., Ma, Y., McBratney, A. B., … Widyastuti, M.Geoderma, 452, 117094. Retrieved from https://www.sciencedirect.com/science/article/pii/S0016706124003239 2024.
Abstract
Machine learning (ML) applications in soil science have significantly increased over the past two decades, reflecting a growing trend towards data-driven research addressing soil security. This extensive application has mainly focused on enhancing predictions of soil properties, particularly soil organic carbon, and improving the accuracy of digital soil mapping (DSM). Despite these advancements, the application of ML in soil science faces challenges related to data scarcity and the interpretability of ML models. There is a need for a shift towards Soil Science-Informed ML (SoilML) models that use the power of ML but also incorporate soil science knowledge in the training process to make predictions more reliable and generalisable. This paper proposes methodologies for embedding ML models with soil science knowledge to overcome current limitations. Incorporating soil science knowledge into ML models involves using observational priors to enhance training datasets, designing model structures which reflect soil science principles, and supervising model training with soil science-informed loss functions. The informed loss functions include observational constraints, coherency rules such as regularisation to avoid overfitting, and prior or soil-knowledge constraints that incorporate existing information about the parameters or outputs. By way of illustration, we present examples from four fields: digital soil mapping, soil spectroscopy, pedotransfer functions, and dynamic soil property models. We discuss the potential to integrate process-based models for improved prediction, the use of physics-informed neural networks, limitations, and the issue of overparametrisation. These approaches improve the relevance of ML predictions in soil science and enhance the models’ ability to generalise across different scenarios while maintaining soil science principles, transparency and reliability.BibTeX
@article{MINASNY2024117094, title = {Soil Science-Informed Machine Learning}, journal = {Geoderma}, volume = {452}, pages = {117094}, year = {2024}, issn = {0016-7061}, doi = {https://doi.org/10.1016/j.geoderma.2024.117094}, url = {https://www.sciencedirect.com/science/article/pii/S0016706124003239}, author = {Minasny, Budiman and Bandai, Toshiyuki and Ghezzehei, Teamrat A. and Huang, Yin-Chung and Ma, Yuxin and McBratney, Alex B. and Ng, Wartini and Norouzi, Sarem and Padarian, Jose and Rudiyanto and Sharififar, Amin and Styc, Quentin and Widyastuti, Marliana}, keywords = {Artificial Intelligence, Process-based models, Physics Informed Neural Networks, Informed Machine Learning, Mechanistic models, Pedology}, research-theme = {machine-learning} } - Learning Constitutive Relations From Soil Moisture Data via Physically Constrained Neural Networks.Bandai, T., Ghezzehei, T. A., Jiang, P., Kidger, P., Chen, X., & Steefel, C. I.Water Resources Research, 60(7), e2024WR037318. 2024.
Abstract
Abstract The constitutive relations of the Richardson-Richards equation encode the macroscopic properties of soil water retention and conductivity. These soil hydraulic functions are commonly represented by models with a handful of parameters. The limited degrees of freedom of such soil hydraulic models constrain our ability to extract soil hydraulic properties from soil moisture data via inverse modeling. We present a new free-form approach to learning the constitutive relations using physically constrained neural networks. We implemented the inverse modeling framework in a differentiable modeling framework, JAX, to ensure scalability and extensibility. For efficient gradient computations, we implemented implicit differentiation through a nonlinear solver for the Richardson-Richards equation. We tested the framework against synthetic noisy data and demonstrated its robustness against varying magnitudes of noise and degrees of freedom of the neural networks. We applied the framework to soil moisture data from an upward infiltration experiment and demonstrated that the neural network-based approach was better fitted to the experimental data than a parametric model and that the framework can learn the constitutive relations.BibTeX
@article{p2024_bandai-b, author = {Bandai, Toshiyuki and Ghezzehei, Teamrat A. and Jiang, Peishi and Kidger, Patrick and Chen, Xingyuan and Steefel, Carl I.}, title = {Learning Constitutive Relations From Soil Moisture Data via Physically Constrained Neural Networks}, journal = {Water Resources Research}, volume = {60}, number = {7}, pages = {e2024WR037318}, keywords = {inverse modeling, soil hydraulic functions, physics-informed machine learning, neural networks, soil moisture}, doi = {10.1029/2024WR037318}, pdf = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2024WR037318}, note = {e2024WR037318 2024WR037318}, year = {2024}, research-theme = {machine-learning, water-flow} } - Estimating soil hydraulic properties from oven-dry to full saturation using shortwave infrared imaging and inverse modeling.Bandai, T., Sadeghi, M., Babaeian, E., Jones, S. B., Tuller, M., & Ghezzehei, T. A.Journal of Hydrology, 635, 131132. 2024.
Abstract
To minimize uncertainty related to soil processes in extreme events, we need accurate soil hydraulic properties across the entire range of soil water content. However, conventional methods are time-consuming and limited to specific ranges. To estimate soil hydraulic properties throughout the entire range, we conducted inverse modeling using upward infiltration experiments, where a shortwave infrared imaging camera was used to obtain high-resolution soil moisture data in space and time. Because the commonly used van Genuchten–Mualemmodel is unsuitable for describing soil hydraulic properties for dry conditions, we tested an alternative model, the Peters-Durner-Iden model, which considers both capillary and film water. The inverse modeling successfully estimated soil hydraulic properties for sandy loam and loam soils, and we demonstrated that the Peters-Durner-Iden model captured soil moisture dynamics better than the van Genuchten–Mualemmodel for dry conditions. However, both models could not adequately describe the soil moisture data for the other soils. The direct observation of the water flow via shortwave infrared images clarified that the reduced success was because of violating the one-dimensional flow assumption for coarse-textured soils and the micro-heterogeneity in soil hydraulic properties for soils with fine silt and clay materials.BibTeX
@article{p2024-Bandai-et-al, title = {Estimating soil hydraulic properties from oven-dry to full saturation using shortwave infrared imaging and inverse modeling}, journal = {Journal of Hydrology}, volume = {635}, pages = {131132}, year = {2024}, issn = {0022-1694}, doi = {https://doi.org/10.1016/j.jhydrol.2024.131132}, pdf = {https://pdf.sciencedirectassets.com/271842/1-s2.0-S0022169424X00050/1-s2.0-S0022169424005274/main.pdf}, author = {Bandai, Toshiyuki and Sadeghi, Morteza and Babaeian, Ebrahim and Jones, Scott B. and Tuller, Markus and Ghezzehei, Teamrat A.}, keywords = {Inverse modeling, Shortwave infrared imaging, Soil moisture, Soil hydraulic functions}, research-theme = {machine-learning, water-flow} }
- Interpretable Soil Water Retention Prediction Using Hierarchical Attention Networks with Uncertainty Quantificatio.Ghezzehei, T. A.Water Resources Research (under Review).
Abstract
Understanding which soil properties control water retention at different moisture states remains a critical challenge for predicting how soils respond to management and environmental change. Traditional pedotransfer functions predict parameters of equations like van Genuchten’s model, but parameter correlations create ill-posed inverse problems that propagate errors and reduce prediction accuracy. Fundamentally, these parameter-based approaches cannot reveal which properties matter most at different water potentials or how texture-structure interactions vary across the moisture spectrum—knowledge essential for mechanistic understanding and management applications. We present Hierarchical Attention-Based Pedotransfer Function (HABIT) to address these limitations through two objectives: (1) achieve superior prediction accuracy through direct moisture prediction that circumvents parameter correlation errors, and (2) quantify property importance and interactions across moisture regimes through interpretable attention mechanisms. The model employs neural network attention architectures that dynamically weight soil properties based on water potential, enforces physical constraints including monotonicity, and accommodates incomplete soil characterization through hierarchical training. We evaluate HABIT against traditional parameter-based approaches using comprehensive international soil databases spanning global textural and structural variability. Attention weight analysis reveals moisture-dependent property interactions, including asymmetric texture-structure information flow, organic carbon’s dual structural and sorptive roles, and saturated hydraulic conductivity’s diagnostic function in integrating pore network information. These patterns generate testable predictions while explaining how direct prediction with adaptive property weighting captures soil-specific retention behaviors that parametric forms miss. HABIT demonstrates that properly designed machine learning architectures serve as prediction tools and scientific discovery platforms, providing frameworks for understanding texture-structure interactions that remain qualitatively understood but quantitatively elusive.BibTeX
@article{2025-Ghezzehei, title = {Interpretable Soil Water Retention Prediction Using Hierarchical Attention Networks with Uncertainty Quantificatio}, language = {en}, journal = {Water Resources Research (under review)}, author = {Ghezzehei, Teamrat Afewerki}, pages = {}, research-theme = {machine-learning, water-flow} }
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