This study develops a dimensionless multi-domain physics-informed neural network (PINN) framework for electro-osmotic radial consolidation considering smear effects and combined vacuum and surcharge loading. Three PINN-based models are investigated: a standard soft-constrained PINN (Std-PINN), a modified gated PINN (Mod-PINN), and a modified gated PINN with hard-constraint boundary encoding (Mod-HC-PINN). The models are evaluated against FEM reference solutions under four loading cases, including constant vacuum, exponential vacuum, exponential vacuum with ramp surcharge, and exponential vacuum with cyclic haversine surcharge. The results indicate that the gated architecture applied in Mod-PINN improves the resolution of steep pressure gradients near the cathode and smear-zone interface under constant vacuum loading. Under time-dependent loading, the soft-constrained Mod-PINN shows reduced accuracy because it must learn multiple competing objectives simultaneously. The Mod-HC-PINN mitigates this issue by embedding the cathode boundary and initial conditions into the output structure, thereby reducing the optimization burden and improving physical consistency. The Mod-HC-PINN achieves MAE values of 0.43, 0.41, and 0.27 kPa for the exponential vacuum, ramp surcharge, and cyclic surcharge cases, respectively. Sensitivity analyses further demonstrate that the proposed framework remains robust across practical ranges of network architecture, collocation density, and permeability contrast.

翻译：本研究开发了一个无量纲多域物理信息神经网络（PINN）框架，用于考虑涂抹效应及真空-堆载联合加载条件下的电渗径向固结问题。研究探讨了三种基于PINN的模型：标准软约束PINN（Std-PINN）、改进门控PINN（Mod-PINN）以及采用硬约束边界编码的改进门控PINN（Mod-HC-PINN）。通过四种加载工况（包括恒定真空、指数真空、指数真空+斜坡堆载、指数真空+循环半正弦堆载）下的有限元参考解对模型进行验证。结果表明：在恒定真空加载条件下，Mod-PINN中的门控架构提高了阴极与涂抹区界面附近陡峭压力梯度的解析能力；而在时变加载条件下，软约束Mod-PINN因需同时学习多个竞争目标导致精度下降。Mod-HC-PINN通过将阴极边界条件和初始条件嵌入输出结构缓解此问题，从而降低优化负担并提升物理一致性。该模型在指数真空、斜坡堆载及循环堆载工况下的平均绝对误差（MAE）分别为0.43、0.41和0.27 kPa。敏感性分析进一步表明，在网络架构、配置点密度及渗透性对比度等实际参数范围内，所提框架保持稳健性。