{
  "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.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Geosciences, The Pennsylvania State University , University Park, Pennsylvania, 16802 ,",
    "Lamont Doherty Earth Observatory, Columbia University , Palisades, New York, 10964 ,",
    "Earth Resources Laboratory, Massachusetts Institute of Technology , Cambridge, MA, 02139 ,",
    "Department of Earth and Atmospheric Sciences, Cornell University , Ithaca, New York, 14850 ,",
    "GFZ Helmholtz Center for Geosciences , Telegrafenberg, 14473 Potsdam ,",
    "Laboratoire de Mécanique et Génie Civil, Université de Montpellier ,"
  ],
  "article_type": "research article",
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  "author_total": 6,
  "authors": [
    {
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        0
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      "name": "Kangan Li",
      "orcid": "0009-0004-8751-2814"
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    {
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        0
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      "name": "Tushar Mittal",
      "orcid": "0000-0002-8026-0018"
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    {
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        2
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      "name": "Benjamin Holtzman",
      "orcid": "0000-0002-6226-7689"
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    {
      "affs": [
        3
      ],
      "name": "Seth Saltiel",
      "orcid": "0000-0002-8058-6894"
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    {
      "affs": [
        0,
        4
      ],
      "name": "Raphael Affinito",
      "orcid": "0000-0002-5799-8620"
    },
    {
      "affs": [
        5
      ],
      "name": "Loic Daridon",
      "orcid": "0000-0003-1056-0100"
    }
  ],
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  "doi": "10.1093/pnasnexus/pgag349",
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      "openalex",
      "2211|Rock Mechanics and Modeling"
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  "pdf_url": "https://academic.oup.com/pnasnexus/advance-article-pdf/doi/10.1093/pnasnexus/pgag349/71787212/pgag349.pdf",
  "pmcid": "PMC13721771",
  "pmid": "42965089",
  "published": "2026-10-09",
  "publisher": "Oxford University Press (OUP)",
  "ris": "https://research.draconitic.com/paper/0n205d5htbspm.ris",
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  "subjects": [],
  "title": "TIP-INN: A thermodynamics-informed machine learning framework for the mechanical behavior of rocks",
  "title_text": "TIP-INN: A thermodynamics-informed machine learning framework for the mechanical behavior of rocks",
  "type": "peer-reviewed",
  "updated_at": "2026-11-03T12:22:24Z",
  "url": "https://research.draconitic.com/paper/0n205d5htbspm",
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