mlsanityData to 7 Oct 2026

Unsupervised discovery of interpretable hyperelastic constitutive laws

arXiv 2010.13496 ↗First posted 26 Oct 2020cs.CEcited by 51

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Abstract (arXiv)

We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing and digital image correlation techniques; it delivers interpretable models, i.e., models that are embodied by parsimonious mathematical expressions discovered through sparse regression of a large catalogue of candidate functions; it is one-shot, i.e., discovery only needs one experiment - but can use more if available. The problem of unsupervised discovery is solved by enforcing equilibrium constraints in the bulk and at the loaded boundary of the domain. Sparsity of the solution is achieved by l_p regularization combined with thresholding, which calls for a non-linear optimization scheme. The ensuing fully automated algorithm leverages physics-based constraints for the automatic determination of the penalty parameter in the regularization term. Using numerically generated data including artificial noise, we demonstrate the ability of the approach to accurately discover five hyperelastic models of different complexity. We also show that, if a "true" feature is missing in the function library, the proposed approach is able to surrogate it in such a way that the actual response is still accurately predicted.

Key facts. Cited by 51 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Oct 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 8; 2023: 10; 2024: 8; 2025: 11; 2026: 11.

51 papers.

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  1. 2021Polyconvex anisotropic hyperelasticity with neural networkscited by 54
  2. 2024A review on data-driven constitutive laws for solidscited by 35
  3. 2022NN-EUCLID: deep-learning hyperelasticity without stress datacited by 30
  4. 2022Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problemscited by 21
  5. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  6. 2022A deep learning energy method for hyperelasticity and viscoelasticitycited by 20
  7. 2022Constitutive model characterization and discovery using physics-informed deep learningcited by 17
  8. 2023Data-driven anisotropic finite viscoelasticity using neural ordinary differential equationscited by 16
  9. 2023Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanicscited by 16
  10. 2023On sparse regression, Lp-regularization, and automated model discoverycited by 15
  11. 2022A physics-informed deep neural network for surrogate modeling in classical elasto-plasticitycited by 14
  12. 2022Calibrating constitutive models with full-field data via physics informed neural networkscited by 12
38 more
  1. 2023Theory and implementation of inelastic Constitutive Artificial Neural Networkscited by 12
  2. 2025Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)cited by 12
  3. 2021CENN: Conservative energy method based on neural networks with subdomains for solving variational problems involving heterogeneous and complex geometriescited by 10
  4. 2023Interpreting and generalizing deep learning in physics-based problems with functional linear modelscited by 9
  5. 2023A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimescited by 8
  6. 2022G2Phinet: Relating Genotype and Biomechanical Phenotype of Tissues with Deep Learningcited by 6
  7. 2023Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applicationscited by 6
  8. 2024Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networkscited by 6
  9. 2024Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodelingcited by 6
  10. 2022Convolution, aggregation and attention based deep neural networks for accelerating simulations in mechanicscited by 5
  11. 2023DCEM: A deep complementary energy method for solid mechanicscited by 5
  12. 2025On the definition and importance of interpretability in scientific machine learningcited by 5
  13. 2026Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material modelscited by 5
  14. 2025A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strainscited by 4
  15. 2024Neural Networks for Generating Better Local Optima in Topology Optimizationcited by 3
  16. 2025Generalized invariants meet constitutive neural networks: A novel framework for hyperelastic materialscited by 3
  17. 2025Automated Constitutive Model Discovery by Pairing Sparse Regression Algorithms with Model Selection Criteriacited by 3
  18. 2024Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networkscited by 2
  19. 2025Input Specific Neural Networkscited by 2
  20. 2025COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updatescited by 2
  21. 2025Beyond empirical models: Discovering new constitutive laws in solids with graph-based equation discoverycited by 2
  22. 2025Automating modeling in mechanics: LLMs as designers of physics-constrained neural networks for constitutive modeling of materialscited by 2
  23. 2026Hyperelastic constitutive model discovery with differentiable finite elements and structure-preserving neural networkscited by 2
  24. 2021Explainable artificial intelligence for mechanics: physics-informing neural networks for constitutive modelscited by 1
  25. 2023Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variablescited by 1
  26. 2024Data-driven discovery of mechanical models directly from MRI spectral datacited by 1
  27. 2025Robust Physics-Informed Neural Network Approach for Estimating Heterogeneous Elastic Properties from Noisy Displacement Datacited by 1
  28. 2025Unsupervised full-field Bayesian inference of orthotropic hyperelasticity from a single biaxial test: a myocardial case studycited by 1
  29. 2024Learning Physics-Consistent Material Behavior from Dynamic Displacementscited by 0
  30. 2024Finding the Underlying Viscoelastic Constitutive Equation via Universal Differential Equations and Differentiable Physicscited by 0
  31. 2026Data-efficient Bayesian-guided design selection from large candidate sets: Application to hyperelastic stochastic metamaterialscited by 0
  32. 2026LLM-driven design of physics-constrained constitutive models: two agents are better than onecited by 0
  33. 2026Finite Element-Based Material Learning via Automatic Differentiation: Learning constitutive neural network models from full-field deformation datacited by 0
  34. 2026CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field datacited by 0
  35. 2026Physics-Informed Discovery of Yield Functions in Plasticity via Convex Neural Representationscited by 0
  36. 2026Probabilistic Physics-Informed Neural Networks for Estimating Heterogeneous Elastic Properties from Low-Resolution and Noisy Displacement Datacited by 0
  37. 2026Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modelingcited by 0
  38. 2026pyALDIC: A Python Implementation of Augmented Lagrangian Digital Image Correlation with a GUI, Adaptive Meshing, and Mask-Aware Subset Splittingcited by 0

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