A noise-aware physics-informed neural network method for nonlinear consolidation with non-Darcian flow and continuous drainage boundary

Accurate characterization of soft soil nonlinear consolidation with non-Darcian flow and complex boundary conditions is fundamental to assessing foundation stability. This study presents a Noise-Aware Physics-Informed Neural Network (NA-PINN) framework for one-dimensional nonlinear consolidation problems involving a continuous drainage boundary and non-Darcian flow. Multiple nonlinear couplings can cause gradient imbalance in standard PINNs. Furthermore, when measurement noise and sparse data are present, the inversion of the flow index is susceptible to ill-posedness. To address this problem, the PDE residual weight is prescribed based on the assumed noise level of the observation data, ensuring that the governing equation can provide stronger constraints during inverse training under noisy conditions. In addition, a differentiable variable transformation is used to keep the identified flow index within prescribed physical bounds. Benchmark comparisons with finite difference solutions show that, in eight repeated inverse runs under the nominal setting with 10 % measurement noise, the relative errors of the identified flow index remained below 0.1 %. The continuous excess pore water pressure field was also reconstructed from 15 noisy temporal observations of the average degree of consolidation. The proposed framework captures the nonlinear evolution of excess pore water pressure dissipation and average consolidation response under time-dependent loading, and provides a useful tool for consolidation analysis when monitoring data are sparse or noisy.