Pith Number

pith:UMXWL5UK

pith:2026:UMXWL5UKMC4EGOPF4IH3EOOVCD

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A Neural-Network Framework to Learn History-Dependent Constitutive Laws and Identifiability of Internal Variables

Andrew Stuart, Kaushik Bhattacharya, Lianghao Cao, Mayank Raj

Neural networks can learn history-dependent constitutive laws for materials while guaranteeing consistency with the second law of thermodynamics and stability under extreme strain.

arxiv:2605.14179 v1 · 2026-05-13 · cond-mat.mtrl-sci

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Claims

C1strongest claim

We show that the internal variables that are learned from the data are unique up to a linear transform. The framework is deployed to learn the Taylor-averaged response of a polycrystalline magnesium unit cell. We achieve 2% relative error in the prediction of the Taylor-averaged response.

C2weakest assumption

That a neural network can be formulated in a causal and energetic manner to guarantee consistency with the second law of thermodynamics, stability under extreme strain, and existence of solutions to the governing equations while retaining sufficient expressiveness for real material data.

C3one line summary

A causal energetic neural network framework learns thermodynamically consistent history-dependent constitutive laws, proving internal variables are unique up to linear transformation and achieving 2% error on polycrystalline magnesium data.

References

37 extracted · 37 resolved · 1 Pith anchors

[1] Brandon Amos, Lei Xu, and J. Zico Kolter. Input convex neural networks, 2017 2017

[2] A mechanics-informed artificial neural network approach in data-driven constitutive modeling.International Journal for Numerical Methods in Engineering, 123 20 (12):2738–2759, 2022 2022 · doi:10.1002/nme.6957

[3] A mechanics-informed deep learning framework for data-driven non- linear viscoelasticity.Computer Methods in Applied Mechanics and Engineering, 417:116463, 2023 2023 · doi:10.1016/j.cma.2023.116463

[4] Faisal As’ad and Charbel Farhat. A staggered training framework for mechanics-informed neu- ral networks in tractable multiscale homogenization with application to woven fabrics.Computer Methods in Ap 2026 · doi:10.1016/j.cma.2025.118666

[5] J. M. Ball. Constitutive inequalities and existence theorems in nonlinear elastostat- ics.Nonlinear Analysis and Mechanics, Heriot-Watt Symposium Vol. 1, 1977. URL https://people.maths.ox.ac.uk/~ball/ 1977

Receipt and verification

First computed	2026-05-17T23:39:11.264032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a32f65f68a60b84339e5e20fb239d510f06cbc6731411c6848022ff50778669a

Aliases

arxiv: 2605.14179 · arxiv_version: 2605.14179v1 · doi: 10.48550/arxiv.2605.14179 · pith_short_12: UMXWL5UKMC4E · pith_short_16: UMXWL5UKMC4EGOPF · pith_short_8: UMXWL5UK

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/UMXWL5UKMC4EGOPF4IH3EOOVCD \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a32f65f68a60b84339e5e20fb239d510f06cbc6731411c6848022ff50778669a

Canonical record JSON

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    "abstract_canon_sha256": "cefa29523992f05d29473f10c8194cf8c1d8b6ce0298dacec2a754ad0519e9b4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.mtrl-sci",
    "submitted_at": "2026-05-13T22:59:58Z",
    "title_canon_sha256": "b7db76b375000e11a50d96c35a9b77ace9447f20ae96eb4cda129fb1c6909548"
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