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arxiv: 2605.23754 · v1 · pith:TUJTUSBRnew · submitted 2026-05-22 · 💻 cs.LG

LLM-driven design of physics-constrained constitutive models: two agents are better than one

Marius Tacke , Matthias Busch , Kian Abdolazizi , Jonas Eichinger , Kevin Linka , Roland Aydin , Christian Cyron This is my paper

Pith reviewed 2026-05-25 04:49 UTC · model grok-4.3

classification 💻 cs.LG
keywords constitutive modelsLLM agentsphysics constraintsmulti-agent systemsmaterial modelingCANNmodel generationphysics-informed AI
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The pith

A Creator-Inspector pair of LLM agents generates constitutive models that meet all nine physical constraints in up to 100 percent of cases.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates that single LLM pipelines for creating constitutive models from data frequently output expressions that break basic physical rules such as energy conservation or material symmetry. Adding a second Inspector agent that reviews each proposal against a fixed list of nine constraints and sends violations back for revision raises the fraction of fully compliant exported models from 91 percent to 100 percent with one backbone and from 37 percent to 56 percent with another. The resulting models retain accuracy on training data for brain tissue, rubber, and synthetic rubber while also generalizing to loading paths not seen during generation. The separation of proposal and audit therefore converts an otherwise unreliable generation process into one that produces models ready for direct engineering use.

Core claim

Separating model generation from constraint inspection in an LLM pipeline produces constitutive artificial neural networks that satisfy every one of nine physical constraints, match data accuracy, and extrapolate reliably to unseen deformation paths across multiple materials and LLM backbones.

What carries the argument

The Inspector agent, which audits each Creator-proposed constitutive model against nine explicit physical constraints and returns it for refinement on any detected violation.

If this is right

  • Exported models become physically valid in 100 percent of runs for the stronger backbone while accuracy on held-out data stays near baseline levels.
  • The same models generalize to loading paths outside the training distribution without additional tuning.
  • The two-agent structure works across different base LLMs and across brain tissue, experimental rubber, and synthetic rubber data.
  • The pipeline remains usable as LLM capabilities advance because it does not depend on any single model architecture.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The reported validity gains rest on the Inspector's detection reliability, so an external audit of the Inspector itself would be a direct next measurement.
  • The same Creator-Inspector split could be applied to other physics-constrained modeling tasks such as fluid constitutive relations or damage evolution laws.
  • If the nine constraints are incomplete for a new material class, the Inspector loop would need an expanded checklist rather than a change in architecture.

Load-bearing premise

The Inspector LLM can correctly and exhaustively detect every violation of the nine physical constraints in any model the Creator proposes.

What would settle it

A controlled test in which a model known to violate one specific constraint is fed to the Inspector and the Inspector either misses the violation or fails to request a fix.

Figures

Figures reproduced from arXiv: 2605.23754 by Christian Cyron, Jonas Eichinger, Kevin Linka, Kian Abdolazizi, Marius Tacke, Matthias Busch, Roland Aydin.

Figure 1
Figure 1. Figure 1: Previous LLM-based approaches to constitutive modeling rely on a single Creator agent that proposes [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Spectrum of constitutive models for hyperelastic materials. Hand-crafted symbolic equations (right) [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Detailed workflow of the Creator-Inspector pipeline. The Creator is prompted to implement a [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Adherence of generated models to physical constraints, split by Inspector verdict. For each [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Tool usage of the Inspector per inspection. Distribution of the number of tools called by the Inspector [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: State transitions between Creator and Inspector across refinement rounds. Relative frequencies of [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of physical constraint violations by type, separated into actual vs. flagged and correct [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Predictions of models generated with Claude Opus 4.7. For each case we show the best-out-of-ten [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Predictions of models generated with Kimi K2.5. For each case we show the best-out-of-ten adherent [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Predictions of models designed by human experts that serve as baselines. For brain tissue, we [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Reliability of the achieved accuracy across runs. Mean [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Effect of the iterative refinement loop. Mean [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Adherence of generated models to physical constraints in absolute counts. Same layout as Figure 4, [PITH_FULL_IMAGE:figures/full_fig_p034_13.png] view at source ↗
read the original abstract

Developing constitutive models that capture how materials deform under load traditionally requires years of specialized expertise in continuum mechanics, machine learning, and scientific programming. Large language models (LLMs) have recently been shown to lower this barrier by generating constitutive models on demand, but existing single-agent pipelines lack systematic checks that the resulting models respect fundamental physical laws. To close this gap, we introduce the first multi-agent LLM-driven approach for constitutive model generation: a Creator agent proposes a model tailored to the data, while an Inspector agent critically audits each proposal against nine physical constraints and returns it for refinement whenever a violation is detected. We demonstrate this concept with constitutive artificial neural networks (CANNs) and benchmark it on brain tissue, experimental rubber, and synthetic rubber, using two different LLM backbones (Claude Opus 4.7 and Kimi K2.5). Adding the Inspector raises the share of exported models that truly satisfy all physical constraints from 91% to a perfect 100% for Opus and from 37% to 56% for Kimi, while preserving near-baseline accuracy and remarkable generalization to unseen loading paths. In combination, the generated models are physically valid, highly accurate, and extrapolate reliably beyond the training data - properties that together make them directly usable in practice. Separating generation from inspection thus turns LLM-driven constitutive modeling into a genuinely trustworthy process. The paradigm is deliberately technique-agnostic and scales automatically with advances in LLM capability, opening a promising path toward automated, physics-aware model discovery.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper proposes a two-agent LLM system for generating constitutive artificial neural networks (CANNs): a Creator agent proposes models from data, and an Inspector agent audits proposals against nine physical constraints, iterating until compliance. Experiments on brain tissue, experimental rubber, and synthetic rubber using Claude Opus and Kimi backbones show that the Inspector raises the fraction of exported models satisfying all constraints from 91% to 100% (Opus) and 37% to 56% (Kimi), while preserving accuracy and generalization to unseen loading paths.

Significance. If the Inspector's constraint checks prove reliable, the multi-agent separation of generation from verification offers a scalable, technique-agnostic route to trustworthy LLM-generated constitutive models that could reduce reliance on manual expert oversight in continuum mechanics. The reported preservation of accuracy alongside perfect or improved validity rates would be a notable practical advance.

major comments (1)
  1. [Abstract] Abstract: The central claim that the Inspector produces models that 'truly satisfy all physical constraints' (raising validity to 100% for Opus and 56% for Kimi) rests exclusively on the Inspector LLM's pass/fail decisions. No independent verification step—such as symbolic differentiation of the exported CANN expressions, automated theorem checking, or expert audit of a sample—is described to confirm that the Inspector neither misses violations nor falsely accepts invalid models.
minor comments (1)
  1. The nine physical constraints are referenced repeatedly but never enumerated or derived in the provided text; adding an explicit list or table would improve reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive comment regarding independent verification of the Inspector's constraint checks. We agree that this is an important point for strengthening the manuscript's claims and will revise accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the Inspector produces models that 'truly satisfy all physical constraints' (raising validity to 100% for Opus and 56% for Kimi) rests exclusively on the Inspector LLM's pass/fail decisions. No independent verification step—such as symbolic differentiation of the exported CANN expressions, automated theorem checking, or expert audit of a sample—is described to confirm that the Inspector neither misses violations nor falsely accepts invalid models.

    Authors: We acknowledge that the reported validity rates (100% for Opus, 56% for Kimi) are based solely on the Inspector agent's LLM-driven pass/fail evaluations against the nine constraints. No post-hoc independent verification (e.g., symbolic differentiation of the exported model expressions or external expert review) is currently described in the manuscript. To address this, we will revise the manuscript by adding an independent verification procedure: for a representative sample of exported CANNs from each backbone, we will perform symbolic differentiation to explicitly confirm satisfaction of the physical constraints (e.g., objectivity, material symmetry, and thermodynamic consistency). These results will be reported in a new subsection of the Methods or Results, with the abstract updated to reflect that validity is Inspector-determined but corroborated by independent checks on a sample. This revision will be marked clearly in the resubmission. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical results measured against external constraints

full rationale

The manuscript presents an empirical multi-agent LLM workflow for generating CANN constitutive models, with reported validity rates (91% to 100% for Opus; 37% to 56% for Kimi) obtained by applying the Inspector agent to nine listed physical constraints. These constraints are independent physical requirements (e.g., thermodynamic consistency, material symmetry) rather than quantities defined inside the method itself. No equations, fitted parameters, or derivation steps appear in the provided text that would reduce the validity metric to a self-referential input by construction. No self-citation chains or uniqueness theorems are invoked as load-bearing premises. The central claim therefore remains an experimental observation rather than a tautological re-expression of its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption that the nine physical constraints are both necessary and sufficient for constitutive models of the tested materials; no free parameters or invented entities are described in the abstract.

axioms (1)
  • domain assumption Nine physical constraints (energy conservation, stress symmetry, etc.) are both necessary and sufficient to guarantee physical validity of constitutive models for brain tissue and rubber.
    The Inspector's role is defined solely by auditing against these nine constraints; their completeness is presupposed.

pith-pipeline@v0.9.0 · 5826 in / 1302 out tokens · 18194 ms · 2026-05-25T04:49:38.033344+00:00 · methodology

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Reference graph

Works this paper leans on

125 extracted references · 125 canonical work pages · 4 internal anchors

  1. [1]

    Journal of applied physics , volume=

    A theory of large elastic deformation , author=. Journal of applied physics , volume=. 1940 , doi=

    work page 1940

  2. [2]

    Large elastic deformations of isotropic materials. I. Fundamental concepts , author=. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences , volume=. 1948 , publisher=

    work page 1948

  3. [3]

    Further developments of the general theory , author=

    Large elastic deformations of isotropic materials IV. Further developments of the general theory , author=. Philosophical transactions of the royal society of London. Series A, Mathematical and physical sciences , volume=. 1948 , publisher=

    work page 1948

  4. [4]

    Proceedings of the Royal Society of London

    Large deformation isotropic elasticity--on the correlation of theory and experiment for incompressible rubberlike solids , author=. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences , volume=. 1972 , publisher=

    work page 1972

  5. [5]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Data-driven computational mechanics , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2016 , publisher=

    work page 2016

  6. [6]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Data-driven fracture mechanics , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2020 , publisher=

    work page 2020

  7. [7]

    Journal of engineering mechanics , volume=

    Knowledge-based modeling of material behavior with neural networks , author=. Journal of engineering mechanics , volume=. 1991 , publisher=

    work page 1991

  8. [8]

    International Journal for numerical methods in engineering , volume=

    Numerical implementation of a neural network based material model in finite element analysis , author=. International Journal for numerical methods in engineering , volume=. 2004 , publisher=

    work page 2004

  9. [9]

    Journal of the Mechanics and Physics of Solids , volume=

    A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials , author=. Journal of the Mechanics and Physics of Solids , volume=. 1993 , publisher=

    work page 1993

  10. [10]

    ACM Transactions on Graphics (TOG) , volume=

    Nonlinear material design using principal stretches , author=. ACM Transactions on Graphics (TOG) , volume=. 2015 , publisher=

    work page 2015

  11. [11]

    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences , volume=

    Variations on Ogden’s model: close and distant relatives , author=. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences , volume=. 2022 , publisher=

    work page 2022

  12. [12]

    Communications in numerical methods in engineering , volume=

    A model of incompressible isotropic hyperelastic material behavior using spline interpolations of tension--compression test data , author=. Communications in numerical methods in engineering , volume=. 2009 , publisher=

    work page 2009

  13. [13]

    Neural Networks , pages=

    MonoKAN: Certified Monotonic Kolmogorov-Arnold Network , author=. Neural Networks , pages=. 2025 , publisher=

    work page 2025

  14. [14]

    Computers & Structures , volume=

    Extension of the Sussman--Bathe spline-based hyperelastic model to incompressible transversely isotropic materials , author=. Computers & Structures , volume=. 2013 , publisher=

    work page 2013

  15. [15]

    Computational Mechanics , volume=

    What-you-prescribe-is-what-you-get orthotropic hyperelasticity , author=. Computational Mechanics , volume=. 2014 , publisher=

    work page 2014

  16. [16]

    Journal of the Mechanics and Physics of Solids , volume=

    Data-driven hyperelasticity, Part I: A canonical isotropic formulation for rubberlike materials , author=. Journal of the Mechanics and Physics of Solids , volume=. 2023 , publisher=

    work page 2023

  17. [17]

    Archives of Computational Methods in Engineering , year=

    A Review on Data-Driven Constitutive Laws for Solids , author=. Archives of Computational Methods in Engineering , year=

    work page

  18. [18]

    arXiv preprint arXiv:2211.08064 , year=

    Physics-informed machine learning: A survey on problems, methods and applications , author=. arXiv preprint arXiv:2211.08064 , year=

    work page arXiv

  19. [19]

    International Journal for Numerical Methods in Engineering , volume=

    A mechanics-informed artificial neural network approach in data-driven constitutive modeling , author=. International Journal for Numerical Methods in Engineering , volume=. 2022 , publisher=

    work page 2022

  20. [20]

    Journal of the Mechanics and Physics of Solids , volume=

    Neural networks meet hyperelasticity: A guide to enforcing physics , author=. Journal of the Mechanics and Physics of Solids , volume=. 2023 , publisher=

    work page 2023

  21. [21]

    Journal of Computational Physics , volume=

    Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning , author=. Journal of Computational Physics , volume=. 2021 , publisher=

    work page 2021

  22. [22]

    Proceedings of the national academy of sciences , volume=

    Discovering governing equations from data by sparse identification of nonlinear dynamical systems , author=. Proceedings of the national academy of sciences , volume=. 2016 , publisher=

    work page 2016

  23. [23]

    Acta Biomaterialia , volume=

    Automated model discovery for human brain using constitutive artificial neural networks , author=. Acta Biomaterialia , volume=. 2023 , publisher=

    work page 2023

  24. [24]

    International Journal for Numerical Methods in Engineering , volume=

    On sparse regression, Lp-regularization, and automated model discovery , author=. International Journal for Numerical Methods in Engineering , volume=. 2024 , publisher=

    work page 2024

  25. [25]

    Computers in biology and medicine , volume=

    Automated model discovery for tensional homeostasis: Constitutive machine learning in growth and remodeling , author=. Computers in biology and medicine , volume=. 2025 , publisher=

    work page 2025

  26. [26]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Discovering the mechanics of artificial and real meat , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2023 , publisher=

    work page 2023

  27. [27]

    Journal of computational physics , volume=

    Viscoelastic constitutive artificial neural networks (vCANNs)--A framework for data-driven anisotropic nonlinear finite viscoelasticity , author=. Journal of computational physics , volume=. 2024 , publisher=

    work page 2024

  28. [28]

    International Journal of Mechanical System Dynamics , volume=

    Fusion-Based Constitutive Model (FuCe): Toward Model-Data Augmentation in Constitutive Modeling , author=. International Journal of Mechanical System Dynamics , volume=. 2025 , publisher=

    work page 2025

  29. [29]

    Computer methods in applied mechanics and engineering , volume=

    Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations , author=. Computer methods in applied mechanics and engineering , volume=. 2023 , publisher=

    work page 2023

  30. [30]

    A Bradford Book , volume=

    Genetic programming: On the programming of computers by means of natural selection (complex adaptive systems) , author=. A Bradford Book , volume=

    work page

  31. [31]

    International Journal for Numerical Methods in Engineering , volume=

    Automatic generation of interpretable hyperelastic material models by symbolic regression , author=. International Journal for Numerical Methods in Engineering , volume=. 2023 , publisher=

    work page 2023

  32. [32]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Unsupervised discovery of interpretable hyperelastic constitutive laws , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2021 , publisher=

    work page 2021

  33. [33]

    npj Computational Materials , volume=

    Discovering plasticity models without stress data , author=. npj Computational Materials , volume=. 2022 , publisher=

    work page 2022

  34. [34]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Bayesian-EUCLID: Discovering hyperelastic material laws with uncertainties , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2022 , publisher=

    work page 2022

  35. [35]

    Journal of the Mechanics and Physics of Solids , volume=

    NN-EUCLID: Deep-learning hyperelasticity without stress data , author=. Journal of the Mechanics and Physics of Solids , volume=. 2022 , publisher=

    work page 2022

  36. [36]

    Kolmogorov, A. N. , title=. Dokl. Akad. Nauk SSSR , volume=

    work page

  37. [37]

    KAN: Kolmogorov-Arnold Networks

    Kan: Kolmogorov-arnold networks , author=. arXiv preprint arXiv:2404.19756 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  38. [38]

    arXiv preprint arXiv:2408.10205 , year=

    Kan 2.0: Kolmogorov-arnold networks meet science , author=. arXiv preprint arXiv:2408.10205 , year=

    work page arXiv

  39. [39]

    Journal of the Mechanics and Physics of Solids , pages=

    Constitutive Kolmogorov--Arnold Networks (CKANs): Combining accuracy and interpretability in data-driven material modeling , author=. Journal of the Mechanics and Physics of Solids , pages=. 2025 , publisher=

    work page 2025

  40. [40]

    2024 IEEE Conference on Artificial Intelligence (CAI) , pages=

    Large language model-assisted surrogate modelling for engineering optimization , author=. 2024 IEEE Conference on Artificial Intelligence (CAI) , pages=. 2024 , organization=

    work page 2024

  41. [41]

    Swarm and Evolutionary Computation , volume=

    Large language models as surrogate models in evolutionary algorithms: A preliminary study , author=. Swarm and Evolutionary Computation , volume=. 2024 , publisher=

    work page 2024

  42. [42]

    2025 , url=

    Qingpo Wuwu and Chonghan Gao and Tianyu Chen and Yihang Huang and Yuekai Zhang and Jianing Wang and Jianxin Li and Haoyi Zhou and Shanghang Zhang , booktitle=. 2025 , url=

    work page 2025

  43. [43]

    arXiv preprint arXiv:2505.08783 , year=

    CodePDE: An Inference Framework for LLM-driven PDE Solver Generation , author=. arXiv preprint arXiv:2505.08783 , year=

    work page arXiv

  44. [44]

    arXiv preprint arXiv:2505.02124 , year=

    GRAIL: Graph edit distance and node alignment using llm-generated code , author=. arXiv preprint arXiv:2505.02124 , year=

    work page arXiv

  45. [45]

    Code-Generated Graph Representations Using Multiple

    Jiao Huang and Qianli Xing and Jinglong Ji and Bo Yang , booktitle=. Code-Generated Graph Representations Using Multiple. 2025 , url=

    work page 2025

  46. [46]

    ChemRxiv preprint , year=

    Automated Generation of Mechanistic Models for Chemical Process Digital Twins using Reinforcement Learning-Part I: Conceptual Framework and Equation Generation , author=. ChemRxiv preprint , year=

    work page

  47. [47]

    Frey , booktitle=

    Angelica Chen and Samuel Don Stanton and Robert G Alberstein and Andrew Martin Watkins and Richard Bonneau and Vladimir Gligorijevic and Kyunghyun Cho and Nathan C. Frey , booktitle=. 2024 , url=

    work page 2024

  48. [48]

    arXiv preprint arXiv:2501.06327 , year=

    Openfoamgpt: a rag-augmented llm agent for openfoam-based computational fluid dynamics , author=. arXiv preprint arXiv:2501.06327 , year=

    work page arXiv

  49. [49]

    Tenenbaum and Daniela Rus and Chuang Gan and Wojciech Matusik , booktitle=

    Pingchuan Ma and Tsun-Hsuan Wang and Minghao Guo and Zhiqing Sun and Joshua B. Tenenbaum and Daniela Rus and Chuang Gan and Wojciech Matusik , booktitle=. 2024 , url=

    work page 2024

  50. [50]

    Machine Learning for Computational Science and Engineering , volume=

    Constitutive scientific generative agent (CSGA): Leveraging large language models for automated constitutive model discovery , author=. Machine Learning for Computational Science and Engineering , volume=. 2025 , publisher=

    work page 2025

  51. [51]

    Extreme Mechanics Letters , volume=

    MechAgents: Large language model multi-agent collaborations can solve mechanics problems, generate new data, and integrate knowledge , author=. Extreme Mechanics Letters , volume=. 2024 , publisher=

    work page 2024

  52. [52]

    Scientific Reports , volume=

    A fine-tuned large language model based molecular dynamics agent for code generation to obtain material thermodynamic parameters , author=. Scientific Reports , volume=. 2025 , publisher=

    work page 2025

  53. [53]

    Neural Networks , volume=

    Tdag: A multi-agent framework based on dynamic task decomposition and agent generation , author=. Neural Networks , volume=. 2025 , publisher=

    work page 2025

  54. [54]

    Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence , pages=

    AutoAgents: a framework for automatic agent generation , author=. Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence , pages=. 2024 , doi=

    work page 2024

  55. [55]

    arXiv preprint arXiv:2502.05957 , year=

    AutoAgent: A Fully-Automated and Zero-Code Framework for LLM Agents , author=. arXiv preprint arXiv:2502.05957 , year=

    work page arXiv

  56. [56]

    A Dynamic

    Zijun Liu and Yanzhe Zhang and Peng Li and Yang Liu and Diyi Yang , booktitle=. A Dynamic. 2024 , url=

    work page 2024

  57. [57]

    Proceedings of the 17th International Conference on Agents and Artificial Intelligence , pages=

    AgentFlow: A Context Aware Multi-Agent Framework for Dynamic Agent Collaboration , author=. Proceedings of the 17th International Conference on Agents and Artificial Intelligence , pages=. 2025 , doi=

    work page 2025

  58. [58]

    Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies , pages=

    EVOAGENT: Towards Automatic Multi-Agent Generation via Evolutionary Algorithms , author=. Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies , pages=. 2025 , doi=

    work page 2025

  59. [59]

    A Continuum Approach for Engineering , author=

    NONLINEAR SOLID MECHANICS. A Continuum Approach for Engineering , author=. 2001 , publisher=

    work page 2001

  60. [60]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Neural networks meet anisotropic hyperelasticity: A framework based on generalized structure tensors and isotropic tensor functions , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2025 , publisher=

    work page 2025

  61. [61]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Precise, efficient and flexible modeling of crystallizing elastomers based on physics-augmented neural networks , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2026 , publisher=

    work page 2026

  62. [62]

    SIAM Journal on Numerical Analysis , volume=

    Monotone piecewise cubic interpolation , author=. SIAM Journal on Numerical Analysis , volume=. 1980 , publisher=

    work page 1980

  63. [63]

    Journal of the Mechanics and Physics of Solids , volume=

    Polyconvex anisotropic hyperelasticity with neural networks , author=. Journal of the Mechanics and Physics of Solids , volume=. 2022 , publisher=

    work page 2022

  64. [64]

    arXiv preprint arXiv:2602.17750 , year=

    Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models , author=. arXiv preprint arXiv:2602.17750 , year=

    work page arXiv

  65. [65]

    Computational mechanics , volume=

    Democratizing biomedical simulation through automated model discovery and a universal material subroutine , author=. Computational mechanics , volume=. 2025 , publisher=

    work page 2025

  66. [66]

    Journal of the Mechanics and Physics of Solids , pages=

    A generalized dual potential for inelastic Constitutive Artificial Neural Networks: A JAX implementation at finite strains , author=. Journal of the Mechanics and Physics of Solids , pages=. 2025 , publisher=

    work page 2025

  67. [67]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Theory and implementation of inelastic constitutive artificial neural networks , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2024 , publisher=

    work page 2024

  68. [68]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Neural networks meet phase-field: A hybrid fracture model , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2025 , publisher=

    work page 2025

  69. [69]

    Brain Multiphysics , volume=

    Principal-stretch-based constitutive neural networks autonomously discover a subclass of Ogden models for human brain tissue , author=. Brain Multiphysics , volume=. 2023 , publisher=

    work page 2023

  70. [70]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Automated model discovery for skin: Discovering the best model, data, and experiment , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2023 , publisher=

    work page 2023

  71. [71]

    Acta biomaterialia , volume=

    Mechanical characterization of human brain tissue , author=. Acta biomaterialia , volume=. 2017 , publisher=

    work page 2017

  72. [72]

    Acta biomaterialia , volume=

    Rheological characterization of human brain tissue , author=. Acta biomaterialia , volume=. 2017 , publisher=

    work page 2017

  73. [73]

    Archives of Computational Methods in Engineering , year=

    Fifty shades of brain: a review on the mechanical testing and modeling of brain tissue , author=. Archives of Computational Methods in Engineering , year=

    work page

  74. [74]

    Transactions of the Faraday Society , volume=

    Stress-strain data for vulcanised rubber under various types of deformation , author=. Transactions of the Faraday Society , volume=. 1944 , publisher=

    work page 1944

  75. [75]

    2005 , month=

    Treloar, LRG , title=. 2005 , month=

    work page 2005

  76. [76]

    Engineering with Computers , volume=

    Data-driven modeling of the mechanical behavior of anisotropic soft biological tissue , author=. Engineering with Computers , volume=. 2022 , publisher=

    work page 2022

  77. [77]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Data-driven tissue mechanics with polyconvex neural ordinary differential equations , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2022 , publisher=

    work page 2022

  78. [78]

    Part I: Constitutive issues and rank-one convexity , author=

    The exponentiated Hencky-logarithmic strain energy. Part I: Constitutive issues and rank-one convexity , author=. Journal of Elasticity , volume=. 2015 , publisher=

    work page 2015

  79. [79]

    Archive for Rational Mechanics and Analysis , volume=

    Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids , author=. Archive for Rational Mechanics and Analysis , volume=. 1983 , publisher=

    work page 1983

  80. [80]

    Computer Methods in Applied Mechanics and Engineering , volume=

    Versatile data-adaptive hyperelastic energy functions for soft materials , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2024 , publisher=

    work page 2024

Showing first 80 references.