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Equivariant graph convolutional neural networks for the representation of homogenized anisotropic microstructural mechanical response

arXiv 2404.17584 ↗First posted 5 Apr 2024cond-mat.mtrl-sci cs.LGcited by 0

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Abstract (arXiv)

Composite materials with different microstructural material symmetries are common in engineering applications where grain structure, alloying and particle/fiber packing are optimized via controlled manufacturing. In fact these microstructural tunings can be done throughout a part to achieve functional gradation and optimization at a structural level. To predict the performance of particular microstructural configuration and thereby overall performance, constitutive models of materials with microstructure are needed. In this work we provide neural network architectures that provide effective homogenization models of materials with anisotropic components. These models satisfy equivariance and material symmetry principles inherently through a combination of equivariant and tensor basis operations. We demonstrate them on datasets of stochastic volume elements with different textures and phases where the material undergoes elastic and plastic deformation, and show that the these network architectures provide significant performance improvements.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 36 of its 99 references that are in the map. First posted on arXiv 5 Apr 2024.

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References · 36

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  3. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,057
  4. 2018Neural Ordinary Differential Equationscited by 3,779
  5. 2016Group Equivariant Convolutional Networkscited by 1,165
  6. 2021E(n) Equivariant Graph Neural Networkscited by 965
  7. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  8. 2019Hamiltonian Neural Networkscited by 712
  9. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
  10. 2017Learning Sparse Neural Networks through L0 Regularizationcited by 583
  11. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  12. 2016Input Convex Neural Networkscited by 414
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  2. 2020Lagrangian Neural Networkscited by 398
  3. 2019Augmented Neural ODEscited by 397
  4. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 354
  5. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 300
  6. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 295
  7. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  8. 2016Exploiting Cyclic Symmetry in Convolutional Neural Networkscited by 91
  9. 2022Wavelet neural operator: a neural operator for parametric partial differential equationscited by 78
  10. 2021Polyconvex anisotropic hyperelasticity with neural networkscited by 55
  11. 2020Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticitycited by 49
  12. 2023Neural networks meet hyperelasticity: A guide to enforcing physicscited by 46
  13. 2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
  14. 2020Hamiltonian neural networks for solving equations of motioncited by 33
  15. 2021On physics-informed data-driven isotropic and anisotropic constitutive models through probabilistic machine learning and space-filling samplingcited by 24
  16. 2021Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)cited by 18
  17. 2023Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanicscited by 16
  18. 2018Rotation Equivariance and Invariance in Convolutional Neural Networkscited by 12
  19. 2022FEANN - An efficient data-driven multiscale approach based on physics-constrained neural networks and automated data miningcited by 12
  20. 2019Tensor Basis Gaussian Process Models of Hyperelastic Materialscited by 11
  21. 2021Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graphcited by 11
  22. 2023Stress representations for tensor basis neural networks: alternative formulations to Finger-Rivlin-Ericksencited by 9
  23. 2021Mesh-based graph convolutional neural networks for modeling materials with microstructurecited by 7
  24. 2022Deep learning and multi-level featurization of graph representations of microstructural datacited by 2

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