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

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, nonlinear constitutive laws. Inverting macroscopic laboratory data to infer subgrid microphysics is also ill-posed, producing structural nonuniqueness 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 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 nonuniqueness of this inverse problem through two strategies: (i) diverse loading protocols (e.g. cyclic and stress-relaxation paths) that map the full geometry of the potential state space and (ii) a multimodal 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 into closed-form expressions for efficient implementation in geodynamic codes.