Towards physics-consistent machine learning models: A geomechanics-based artificial neural network for high-cyclic soil response

Physics-informed neural networks for predicting ultimate bearing capacity of layered soils under complex loading conditions

Integrating deep neural network with elastoplastic analysis: a hybrid approach for slope stability analysis

Conventional data-driven methods for slope stability analysis often exhibit an over-reliance on data while neglecting underlying physical principles. To address this limitation, this study proposes a physics-informed neural network (PINN) framework that integrates a neural network surrogate with the elastoplastic deformation mechanism of soil slopes. The governing equations incorporating the elastoplastic constitutive model based on the Mohr–Coulomb yield criterion, along with the boundary conditions, are embedded into the training framework of the PINN. The PINN functions as a surrogate model that requires no pre-constructed training dataset and automatically satisfies both the governing equations and the boundary conditions. Consequently, the developed PINN can directly predict the displacement field of a slope and automatically derive the associated stress–strain fields that comply with the deformation mechanism. These outputs are coupled with the multi-initial point sequential quadratic programming (MSQP) algorithm and the slip surface stress analysis (SSSA) method, enabling the efficient identification of the critical slip surface and the calculation of the corresponding factor of safety (FOS). The proposed method is validated through two illustrative examples. Comparisons of the results with those from commercial software confirm the high accuracy of the proposed method in predicting the stress–strain response and the FOS. This study provides a data-driven and physics-informed paradigm for slope stability analysis grounded in clear physical mechanisms.

Geotechnical Evaluation of Gradient-Based Neural Networks for Factor of Safety Prediction in Homogeneous Soil Slopes Under Hydraulic Variability

Slope stability assessment remains a fundamental challenge in geotechnical engineering because of the complex nonlinear interactions among soil properties, slope geometry, and hydraulic conditions, particularly variations in pore-water pressure. This study investigates the reliability of Artificial Neural Network–Multi-Layer Perceptron (ANN–MLP) models for predicting the Factor of Safety (FoS) of homogeneous soil slopes through a systematic comparison of three gradient-based optimization algorithms: Adam, Mini-Batch Gradient Descent (MBGD), and Nesterov Accelerated Gradient (NAG). A database comprising 2014 slope cases, compiled from published studies and numerically generated using Limit Equilibrium Method (LEM) and Finite Element Method (FEM) analyses, was used for model development and k-fold cross-validation. Beyond statistical evaluation, the developed models were validated using two classical dry-slope benchmark frameworks based on the Taylor stability charts and Bishop–Morgenstern stability coefficients, followed by two documented engineering case studies from Hulu Kelang and Pahang, Malaysia, to assess predictive performance under both dry and variable hydraulic conditions. Adam achieved the highest cross-validated predictive accuracy (R2 = 0.988; RMSE = 0.212), whereas MBGD demonstrated the closest overall agreement with the reference LEM solutions across the validation cases and under increasing pore-water pressure ratios. NAG generally produced more conservative predictions while exhibiting greater sensitivity to hyperparameter selection. All models successfully reproduced the expected nonlinear reduction in FoS with increasing pore-water pressure, consistent with established geotechnical behaviour. The results demonstrate that optimizer selection significantly influences ANN–MLP prediction behaviour and that properly validated gradient-based ANN models can serve as efficient decision-support tools for rapid slope stability assessment under hydraulic variability.

Reinforcement Loads Prediction of Geosynthetic-Reinforced Soil Structures Using Explainable and Nonexplainable Machine Learning Approaches

This study presents three advanced machine learning models: the evolutionary Gaussian process inference model, the artificial satellite search algorithm–moment balance machine (ASSA-MBM), and the Operation Rain Forest (ORF), which are designed to predict the maximum reinforcement load in geosynthetic-reinforced soil structures. These models were developed to enhance both predictive accuracy and model interpretability by incorporating state-of-the-art optimization algorithms and explainable machine learning frameworks. A comprehensive evaluation was conducted using 10-fold cross-validation, and the proposed models were benchmarked against previously developed AI models from literature, as well as traditional and semiempirical approaches such as Rankine, Coulomb, and K -stiffness. Among the proposed models, ASSA-MBM consistently achieved the best performance, recording the lowest testing root mean squared error (0.617), the highest correlation coefficient ( R = 0.918 ), and the highest reference index ( RI = 0.951 ). Additionally, the ORF model offers transparency by generating mathematical regression equations, which are crucial in geotechnical engineering.

Development of a Long-term Ground Settlement Prediction Model Using Physics-Informed Neural Networks

This study proposes a physics-informed neural network framework considering creep settlement (Creep-PINN) to accurately predict the long-term settlement behavior of soft clay deposits using only limited field measurements acquired during the early stage of embankment construction, thereby enabling efficient construction process management. Conventional empirical approaches and RNN-based time-series deep learning models generally require long-term field measurements obtained near the completion of consolidation to yield reliable predictions, while existing PINN-based settlement models remain limited in directly utilizing soil property information and in representing creep settlement associated with secondary consolidation. In contrast, the proposed model enforces the consolidation governing equation and staged embankment loading history as physics-based constraints during training and numerically incorporates the secondary compression (creep) mechanism to ensure physical consistency. In particular, an axisymmetric unit-cell u-PINN is employed to approximate the excess pore-water pressure field, and a CoeffNet is coupled to estimate consolidation parameters from site-specific soil properties, thereby accounting for spatial heterogeneity. Scenario-based validation using field monitoring data from OO Port demonstrates that, even within early prediction windows corresponding to initial degrees of consolidation of 10% and 30%, the proposed Creep-PINN achieves lower prediction errors ( = 10%, MAPE = 5.44%) than the Asaoka and hyperbolic methods. These results demonstrate that the proposed framework enables accurate prediction of long-term settlement immediately after embankment placement, supporting more informed decision-making regarding the timing of subsequent construction activities and reducing construction-related risks.

Physics-informed multi-task learning for permeability prediction and probabilistic HFU modeling: a case study from the Lower Bahariya Reservoir, Shahd SE field Egypt

Accurate permeability prediction is essential for reliable reservoir characterization and simulation, yet remains challenging due to complex nonlinear relationships and subsurface heterogeneity. Conventional hydraulic flow unit (HFU) methods rely on discrete rock typing and fixed porosity–permeability relationships, limiting their ability to capture continuous variations. Physics-informed neural networks (PINNs) offer a data-driven alternative with embedded physical constraints, but their effectiveness is often limited by weak enforcement of physics during inference. In this study, a physics-guided multi-task neural network (MT-PINN) is proposed to simultaneously predict permeability and hydraulic flow units within a unified framework. The model integrates data-driven learning with physics-based relationships and probabilistic rock typing, enabling permeability to be estimated as a weighted combination of multiple flow units and allowing smoother transitions between facies. The proposed approach was evaluated using core and well log data and compared against conventional HFU and standard PINN methods. Within the studied dataset, the MT-PINN demonstrated improved predictive performance, with a higher correlation coefficient (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:R\:=\:0.936$$\end{document}) compared to HFU (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:R\:=\:0.89$$\end{document}) and PINN (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:R\:=\:0.90$$\end{document}), along with a reduction in log-scale error. The model also provides more continuous and stable permeability predictions along depth. In addition to permeability estimation, the MT-PINN outputs both discrete HFU classifications and associated class probabilities, which can be incorporated into 3D stochastic reservoir modeling workflows for uncertainty-aware multi-realization analysis. The proposed framework demonstrates the potential to integrate traditional petrophysical methods with modern machine learning techniques, providing a promising workflow for permeability prediction and reservoir characterization within the studied reservoir.