A comparative investigation of physics-driven machine learning architectures for consolidation analysis

Physics-driven machine learning has emerged as a powerful framework for forward and inverse modeling of partial differential equations (PDEs), with increasing applications in geotechnical engineering. However, the relative performance of different physics-driven learning strategies remains problem-dependent, and their suitability for typical geotechnical problems has not been systematically established. This study systematically compares four physics-driven machine learning paradigms for consolidation analysis by combining Multi‑Layer Perceptrons (MLPs) and Kolmogorov–Arnold Networks (KANs) with physics-informed neural networks (PINN) and the discrete-time deep energy method (DTDEM). The paradigms are evaluated for forward and inverse consolidation problems in one and three dimensions, with particular attention to convergence, computational cost, parameter inversion, accuracy, and robustness to noise. For forward problems governed by PDEs, although the energy-form DTDEM converges in fewer epochs than the strong-form PINN under both MLP and KAN architectures, its higher per-epoch cost results in a longer total wall-clock training time. A similar trade-off applies to KAN relative to MLP where the higher per-epoch cost can offset the benefit of faster convergence in terms of epochs. In terms of solution accuracy, replacing MLP with KAN improves both accuracy and training-loss convergence under the strong-form PINN framework, while under the DTDEM framework this advantage is not consistent. For parameter inversion, the DTDEM-based energy formulation is ineffective for parameter inversion because treating material parameters as additional optimization variables make the functional unbounded from below, resulting in divergent training. In contrast, within the strong-form framework, KAN substantially improves parameter-inversion accuracy and robustness to noisy data compared with MLPs.