mlsanityData to 7 Oct 2026

Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations

arXiv 2302.03598 ↗First posted 11 Jan 2023cond-mat.soft cs.LGcited by 16

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Abstract (arXiv)

We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven functions that a priori satisfy physics-based constraints such as objectivity and the second law of thermodynamics. Our approach enables modeling viscoelastic behavior of materials under arbitrary loads in three-dimensions even with large deformations and large deviations from the thermodynamic equilibrium. The data-driven nature of the governing potentials endows the model with much needed flexibility in modeling the viscoelastic behavior of a wide class of materials. We train the model using stress-strain data from biological and synthetic materials including humain brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 13 of its 42 references that are in the map. First posted on arXiv 11 Jan 2023.

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13 of 42 references.

References · 13

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2021Convex optimizationcited by 2,479
  3. 2016Input Convex Neural Networkscited by 407
  4. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
  5. 2021Polyconvex anisotropic hyperelasticity with neural networkscited by 54
  6. 2020Unsupervised discovery of interpretable hyperelastic constitutive lawscited by 51
  7. 2020Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticitycited by 49
  8. 2022A new family of Constitutive Artificial Neural Networks towards automated model discoverycited by 48
  9. 2022Automated discovery of generalized standard material models with EUCLIDcited by 31
  10. 2022NN-EUCLID: deep-learning hyperelasticity without stress datacited by 30
  11. 2021Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equationscited by 28
  12. 2021Data-driven Modeling of the Mechanical Behavior of Anisotropic Soft Biological Tissuecited by 14
1 more
  1. 2021Predicting the Mechanical Properties of Biopolymer Gels Using Neural Networks Trained on Discrete Fiber Network Datacited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 3; 2025: 3; 2026: 5.

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  1. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  2. 2023Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanicscited by 16
  3. 2023On sparse regression, Lp-regularization, and automated model discoverycited by 15
  4. 2023Theory and implementation of inelastic Constitutive Artificial Neural Networkscited by 12
  5. 2023Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion Fieldscited by 7
  6. 2024Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networkscited by 6
  7. 2026Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material modelscited by 5
  8. 2025Automating modeling in mechanics: LLMs as designers of physics-constrained neural networks for constitutive modeling of materialscited by 2
  9. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  10. 2024A thermodynamically consistent physics-informed deep learning material model for short fiber/polymer nanocompositescited by 0
  11. 2024Finding the Underlying Viscoelastic Constitutive Equation via Universal Differential Equations and Differentiable Physicscited by 0
  12. 2025Physics-based machine learning for fatigue lifetime prediction under non-uniform loading scenarioscited by 0
4 more
  1. 2025Fully data-driven inverse hyperelasticity with hyper-network neural ODE fieldscited by 0
  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. 2026Data-Driven Discovery of Composition-Dependent Constitutive Models for Hyperelasticity and Viscoelasticity of Digital Materialscited by 0