Physics-Informed Neural Networks for Fast 3D Consolidation Prediction: A Surrogate Modelling Application

Abstract Physics-informed neural networks (PINNs) have recently gained traction in geotechnical engineering for solving partial differential equations (PDEs), particularly the one-dimensional Terzaghi consolidation equation. However, their application to fast three-dimensional (3D) consolidation prediction remains a significant challenge due to increased spatial complexity and computational demands across multiple directions. In 3D problems, convergence issues and overfitting often arise from inconsistencies in the loss functions across spatial dimensions. This paper proposes a novel PINN framework that explicitly accounts for directional variations in space, enhancing the monitoring and prediction of geotechnical displacements in three dimensions. To address 3D consolidation challenges, distinct regularisation penalty terms are introduced for different cases, emphasising the anisotropic characteristics of 3D behaviour. Moreover, a two-stage training strategy is introduced, combining importance-probability-based resampling with loss-driven dynamic weight adjustment, to further enhance model performance. The proposed framework effectively solves both forward and inverse consolidation problems in 3D settings. Model performance is evaluated and compared against traditional numerical methods for forward predictions, while the framework's ability to identify parameters and handle noisy data is tested in inverse problems. Results show that the proposed method achieves accuracy levels exceeding 98% compared to ground truth in both forward and inverse tasks. Furthermore, a well-trained surrogate model enables near-instantaneous (< 1s) prediction of geotechnical settlements under complex geological conditions, offering substantial practical value. These promising results highlight the potential of PINNs in developing real-time geotechnical response monitoring systems.