Lagged backward-compatible physics-informed neural networks for unsaturated soil consolidation analysis

This study develops a Lagged Backward-Compatible Physics-Informed Neural Network (LBC-PINN) for simulating and inverting one-dimensional unsaturated soil consolidation under long-term loading. To address the challenges of coupled air–water pressure dissipation across multi-scale time domains, the framework integrates logarithmic time segmentation, lagged compatibility loss enforcement, and segment-wise transfer learning. In forward analysis, the LBC-PINN with recommended segmentation schemes accurately predicts pore-air and pore-water pressure evolutions, which are validated against finite element method (FEM) results with mean absolute errors below 10-2 across time up to 1010seconds. A simplified segmentation strategy based on the characteristic air-phase dissipation time improves the computational efficiency while preserving the predictive accuracy. Sensitivity analyses confirm the framework’s robustness across air-to-water permeability ratios ka/kw from 10-3 to 103. In inverse analysis, the LBC-PINN recovers air- and water-phase consolidation coefficients, cva and cvw using both single-stage and two-stage strategies, with the two-stage approach remaining reliable under moderate noise levels. These results demonstrate the potential of LBC-PINN as a stable, mesh-free, and noise-resilient tool for modeling and parameter identification in unsaturated soil consolidation analysis.