Title: Physics-Informed Neural Networks for Radial Consolidation of Combined Electroosmotic, Vacuum and Surcharge Preloading Considering Smear Effects

Abstract

This research introduces a dimensionless, multi-domain physics-informed neural network (PINN) framework designed to model radial consolidation in electro-osmotic processes, specifically accounting for smear effects and the application of combined vacuum and surcharge loads. The study examines three distinct PINN architectures: a standard soft-constrained PINN (Std-PINN), a modified gated PINN (Mod-PINN), and a modified gated PINN featuring hard-constraint boundary encoding (Mod-HC-PINN). These models are benchmarked against Finite Element Method (FEM) reference solutions across four specific loading scenarios: constant vacuum, exponential vacuum, exponential vacuum paired with ramp surcharge, and exponential vacuum paired with cyclic haversine surcharge.

Findings reveal that the gated architecture utilized in the Mod-PINN enhances the resolution of steep pressure gradients, particularly near the cathode and the smear-zone interface, under constant vacuum conditions. However, under time-dependent loading regimes, the soft-constrained Mod-PINN experiences a decline in accuracy due to the challenge of simultaneously learning multiple competing objectives. The Mod-HC-PINN addresses this limitation by integrating cathode boundary and initial conditions directly into the output structure. This approach lessens the optimization burden and strengthens physical consistency. In terms of performance, the Mod-HC-PINN recorded Mean Absolute Error (MAE) values of 0.43 kPa, 0.41 kPa, and 0.27 kPa for the exponential vacuum, ramp surcharge, and cyclic surcharge cases, respectively. Furthermore, sensitivity analyses confirm that the proposed framework maintains robustness across varying practical ranges of network architecture, collocation density, and permeability contrast.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC