A neural-symbolic thermodynamic framework for explicit constitutive modeling of geomaterials

Accurate characterization and simulation of the constitutive behavior of geomaterials remain a central challenge in soil mechanics. Classical plasticity-based models often rely on phenomenological assumptions that lead to complex formulations with limited generalizability, while purely data-driven approaches suffer from poor extrapolation capability and interpretability. To address these limitations, this study proposes a novel neural-symbolic thermodynamic modeler (NSTM) that integrates thermodynamics-informed neural networks (TINN) with physics-guided symbolic regression (phgSR). The framework cyclically refines the expressions for Helmholtz free energy and dissipation rate by combining numerical approximation with symbolic discovery, thereby incorporating first-order thermodynamic constraints that are typically absent in conventional TINNs. Validated through cyclic triaxial and cyclic simple shear tests conducted under varying drainage conditions, the NSTM demonstrates superior prediction accuracy and exceptional extrapolation capability compared to baseline models, offering a robust and physically consistent approach to constitutive modeling of geomaterials.