TIP-INN: A thermodynamics-informed machine learning framework for the mechanical behavior of rocks

Abstract

Abstract Modeling the mechanical deformation of geological materials across relevant thermodynamic conditions and dynamic processes remains a fundamental challenge in Earth sciences. Conventional rheological models rely on isolated disciplinary approaches and hard-coded iterative solvers that struggle with strongly coupled, non-linear constitutive laws. Inverting macroscopic laboratory data to infer sub-grid micro-physics is also ill-posed, producing 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 thermodynamic potentials-the Helmholtz free energy and the dual dissipation potential-architecturally guaranteeing non-negative mechanical dissipation. A continuous, differentiable neural integrator solves internal state variable (ISV) evolution as an initial-value problem, enabling stable, rapid training across complex rheologies. Benchmarked against existing thermodynamics-informed networks, TIP-INN trains 10 to 30 times faster than variational baselines and reduces extrapolation error by up to two orders of magnitude. We resolve the non-uniqueness of this inverse problem through two strategies: (1) diverse loading protocols (e.g., cyclic and stress-relaxation paths) that map the full geometry of the potential state space, and (2) a multi-modal loss assimilating auxiliary seismo-acoustic data. TIP-INN thus rigorously bridges continuum damage mechanics and laboratory seismology. Finally, to ensure physical interpretability, the learned potentials are distilled via Sparse Identification of Nonlinear Potentials (SINP) into closed-form expressions for efficient implementation in geodynamic codes.

The authors' abstract, as published at the source. PNAS Nexus, 2026 · DOI ↗