mlsanityData to 14 Oct 2026

Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models

arXiv 2602.17750 ↗First posted 19 Feb 2026cond-mat.mtrl-sci cs.AI physics.comp-phcited by 6

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Abstract (arXiv)

A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain history and stress. Machine learning has lead to considerable advances in this field lately. Here we introduce inelastic Constitutive Kolmogorov-Arnold Networks (iCKANs). This novel artificial neural network architecture can discover in an automated manner symbolic constitutive laws describing both the elastic and inelastic behavior of materials. That is, it can translate data from material testing into corresponding elastic and inelastic potential functions in closed mathematical form. We demonstrate the advantages of iCKANs using both synthetic data and experimental data of the viscoelastic polymer materials VHB 4910 and VHB 4905. The results demonstrate that iCKANs accurately capture complex viscoelastic behavior while preserving physical interpretability. It is a particular strength of iCKANs that they can process not only mechanical data but also arbitrary additional information available about a material (e.g., about temperature-dependent behavior). This makes iCKANs a powerful tool to discover in the future also how specific processing or service conditions affect the properties of materials.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 34 of its 70 references that are in the map. First posted on arXiv 19 Feb 2026.

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34 of 70 references.

References · 34

  1. 2020Meta-Learning in Neural Networks: A Surveycited by 950
  2. 2019On the Convergence of Adam and Beyondcited by 841
  3. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  4. 2015Cyclical Learning Rates for Training Neural Networkscited by 629
  5. 2016Input Convex Neural Networkscited by 414
  6. 2020Liquid Time-constant Networkscited by 161
  7. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 84
  8. 2024Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networkscited by 67
  9. 2020Unsupervised discovery of interpretable hyperelastic constitutive lawscited by 51
  10. 2022A new family of Constitutive Artificial Neural Networks towards automated model discoverycited by 49
  11. 2023Neural networks meet hyperelasticity: A guide to enforcing physicscited by 46
  12. 2025Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networkscited by 42
22 more
  1. 2024A review on data-driven constitutive laws for solidscited by 35
  2. 2022Automated discovery of generalized standard material models with EUCLIDcited by 31
  3. 2021Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equationscited by 29
  4. 2024Smooth Kolmogorov Arnold networks enabling structural knowledge representationcited by 22
  5. 2022A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurementscited by 20
  6. 2024Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal variablescited by 17
  7. 2023Data-driven anisotropic finite viscoelasticity using neural ordinary differential equationscited by 16
  8. 2023Viscoelastic Constitutive Artificial Neural Networks (vCANNs) - a framework for data-driven anisotropic nonlinear finite viscoelasticitycited by 13
  9. 2025Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)cited by 13
  10. 2022Automatic generation of interpretable hyperelastic material models by symbolic regressioncited by 12
  11. 2023Theory and implementation of inelastic Constitutive Artificial Neural Networkscited by 12
  12. 2024Neural networks meet anisotropic hyperelasticity: A framework based on generalized structure tensors and isotropic tensor functionscited by 10
  13. 2024Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networkscited by 6
  14. 2024Automated model discovery of finite strain elastoplasticity from uniaxial experimentscited by 6
  15. 2024Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodelingcited by 6
  16. 2025A generalized dual potential for inelastic Constitutive Artificial Neural Networks: A JAX implementation at finite strainscited by 6
  17. 2025Input Convex Kolmogorov Arnold Networkscited by 5
  18. 2025History-Aware Neural Operator: Robust Data-Driven Constitutive Modeling of Path-Dependent Materialscited by 5
  19. 2025A physics-augmented neural network framework for finite strain incompressible viscoelasticitycited by 5
  20. 2024MonoKAN: Certified Monotonic Kolmogorov-Arnold Networkcited by 4
  21. 2025A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strainscited by 4
  22. 2025Unsupervised Constitutive Model Discovery from Sparse and Noisy Datacited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 6.

6 papers.

  1. 2026A Convex Route to Thermoelasticity: Learning Internal Energy and Dissipationcited by 1
  2. 2026LLM-driven design of physics-constrained constitutive models: two agents are better than onecited by 0
  3. 2026Discovering Thermodynamically Admissible Dissipation Potentials via Grammar-Based Symbolic Regressioncited by 0
  4. 2026Automatic-Differentiation-Enabled Finite Element Model Updating: Learning Constitutive Neural Networks from Structural Deformation Datacited by 0
  5. 2026Data-Driven Discovery of Composition-Dependent Constitutive Models for Hyperelasticity and Viscoelasticity of Digital Materialscited by 0
  6. 2026On architectural choices for interpretability and thermodynamic consistency in Physically Recurrent Neural Networks in the low-data regimecited by 0