mlsanityData to 7 Oct 2026

What machine learning can do for computational solid mechanics

arXiv 2109.08419 ↗First posted 17 Sep 2021cs.CEcited by 12

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Abstract (arXiv)

Machine learning has found its way into almost every area of science and engineering, and we are only at the beginning of its exploration across fields. Being a popular, versatile and powerful framework, machine learning has proven most useful where classical techniques are computationally inefficient, which applies particularly to computational solid mechanics. Here, we dare to give a non-exhaustive overview of potential avenues for machine learning in the numerical modeling of solids and structures and offer our (subjective) perspective on what is yet to come.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Sep 2021.

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Citing papers per year: 2022: 4; 2023: 1; 2024: 4; 2025: 3.

12 papers.

  1. 2024A review on data-driven constitutive laws for solidscited by 35
  2. 2022NN-EUCLID: deep-learning hyperelasticity without stress datacited by 30
  3. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  4. 2023Data-Driven Design for Metamaterials and Multiscale Systems: A Reviewcited by 17
  5. 2024A review of graph neural network applications in mechanics-related domainscited by 14
  6. 2025Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)cited by 12
  7. 2022Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanicscited by 11
  8. 2022Spiking neural networks for nonlinear regressioncited by 10
  9. 2024A physics-encoded Fourier neural operator approach for surrogate modeling of divergence-free stress fields in solidscited by 4
  10. 2025Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energiescited by 3
  11. 2024ML-based identification of the interface regions for coupling local and nonlocal modelscited by 0
  12. 2025Graph Neural Network Surrogates for Contacting Deformable Bodies with Necessary and Sufficient Contact Detectioncited by 0