TIP-INN: A Thermodynamics-informed Machine Learning Framework for the Mechanical Behavior of Rocks

Modeling the mechanical deformation of geological materials across the vast range of relevant thermodynamic conditions and dynamic processes remains a fundamental challenge in Earth sciences. Conventional rheological models often rely on isolated disciplinary approaches and hard-coded iterative solvers that struggle with strongly coupled, non-linear constitutive laws. Furthermore, inverting macroscopic laboratory data to infer sub-grid micro-physics is fundamentally ill-posed, leading to structural non-uniqueness and models that may violate thermodynamic laws during transient loading. To address these limitations, we present TIP-INN (Thermodynamics of Irreversible Processes Informed Neural Network), a thermodynamically consistent machine learning framework grounded in the Generalized Standard Materials (GSM) formalism. TIP-INN discovers constitutive laws directly from time-series stress-strain data by learning two strictly convex scalar thermodynamic potentials-the Helmholtz free energy and the dual dissipation potential-architecturally guaranteeing non-negative mechanical dissipation. By utilizing a continuous, differentiable neural integrator to solve internal state variable (ISV) evolution as an initial-value problem, TIP-INN enables stable rapid training across complex rheologies. We resolve the inherent non-uniqueness of the constitutive inverse problem through two regularizing strategies: (1) utilizing diverse loading protocols (e.g., cyclic and stress-relaxation paths) to map the full topological state space of the potentials, and (2) a multi-modal loss formulation that directly assimilates auxiliary seismo-acoustic data. Thus, TIP-INN provides a mathematically rigorous bridge between continuum damage mechanics and laboratory seismology. Finally, to ensure physical interpretability, the learned potentials are distilled via a Sparse Identification of Nonlinear Potentials (SINP) procedure into closed-form analytical expressions enabling efficient implementation in geodynamic codes.