Three-branch adaptive physics-informed neural network for geotechnical stiffness inversion

Recovering spatially variable stiffness from displacement observations is fundamental to geotechnical model calibration, yet remains difficult when material interfaces are unknown. Conventional physics-informed neural networks commonly represent mechanical states that vary with loading and material fields that are shared across load cases within a single network, which can smear stiffness transitions in heterogeneous ground. This study develops a Three-Branch Adaptive Physics-Informed Neural Network (TBA-PINN) for distributed inversion of bulk and shear modulus fields. The method couples coordinated representations of mechanical states, material components, and interfaces with an adaptive grouped weighting strategy referenced to the material branch. Material region geometry and interface coordinates are not prescribed during inversion. The assessment combines analytic and finite element reference problems for layered deposits, localized stiffness anomalies, and weak interlayers with controls for observation sparsity, noise, and initialization. In the layered and localized anomaly benchmarks, TBA-PINN reduced modulus field errors from between 8.07% and 20.03% for a Standard PINN to between 2.00% and 4.25%. The resulting modulus fields also preserved markedly sharper stiffness transitions. Comparisons with controls that match parameter count, separate network roles, or alter weighting showed that neither additional network capacity nor loss balancing alone accounted for the improvement. The reconstruction advantage persisted under reduced observation density, discretized reference fields, and noisy displacement data. These results show that field representations that encode material topology can improve distributed geotechnical stiffness inversion when displacement boundaries are known but the subsurface material topology is unavailable.