Physics informed neural networks with self guided mutual distillation between Kolmogorov Arnold networks and multilayer perceptrons for multidimensional forward and inverse Biot consolidation analysis

Many geotechnical and underground engineering problems involve coupled fluid solid interactions in saturated porous media. Drainage boundaries, material interfaces, nonmonotonic pressure responses, and long time dissipation remain challenging for conventional physics informed neural networks (PINNs). Existing studies on Kolmogorov-Arnold networks (KANs) mainly compare standalone architectures with multilayer perceptrons (MLPs), while their complementary representation characteristics are rarely coordinated for coupled multiphysics problems. This study proposes a novel SGMD-PINN, a physics informed neural network with self guided mutual distillation that couples a globally smooth MLP peer with a locally expressive higher order ReLU Kolmogorov Arnold network (HRKAN). Normalized Biot residuals evaluate local physical reliability and guide bidirectional transfer in both solution and residual spaces, enabling adaptive coordination of the two heterogeneous peers. The method is validated for one dimensional Terzaghi, two dimensional Mandel, three dimensional Cryer, layered consolidation, and inverse identification problems in Biot poromechanics. A multi window temporal training strategy is introduced in the three dimensional consolidation analysis to further improve the resolution of post peak and long time pressure evolution. Results show consistent prediction of pressure dissipation, settlement, nonmonotonic pressure amplification, and interface gradient transitions, with balanced accuracy and physical consistency across the tested regimes. Parameter perturbation results are interpreted as evidence of robustness within classical linear Biot problems rather than unrestricted out of distribution generalization. Overall, SGMD-PINN provides a physics consistent framework that exploits complementary neural representations through residual guided mutual learning.