Domain-decomposed physics-informed neural network for one-dimensional soil consolidation under multi-step surcharge loading

Abstract

Physics-Informed Neural Networks (PINNs) have become a powerful framework for solving both forward and inverse problems governed by partial differential equations, particularly when observational data are sparse or boundary conditions are complex. This study proposes a domain-decomposed PINN (DD-PINN) approach to model one-dimensional soil consolidation under multi-stage surcharge loading. By introducing a temporal subdomain partitioning strategy, separate neural networks are assigned to each loading interval, enabling the model to effectively capture discontinuities and improve training stability. The method is applied to both forward and inverse settings. In the forward problem, the model predicts the dissipation of excess pore water pressure under time-dependent surface loads and varying boundary drainage conditions. In the inverse problem, the coefficient of consolidation is identified from sparse observations by treating it as a trainable parameter within the neural network. Numerical experiments under different drainage conditions validate the accuracy and robustness of the proposed approach. The subdomain-based PINN demonstrates superior performance compared to conventional single-network architectures in terms of predictive accuracy and error convergence. This work highlights the potential of physics-informed deep learning in geotechnical modeling and provides a foundation for future applications involving nonlinear material behavior, multidimensional domains, or field-monitored datasets.