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This paper is the first attempt to use geometric deep learning and Sobolev training to incorporate non-Euclidean microstructural data such that anisotropic hyperelastic material machine learning models can be trained in the finite deformation range.
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The graph neural network model
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C. Miehe, M. Hofacker, and F. Welschinger · 2010
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A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality
MA Bessa, R Bostanabad, Z Liu, A Hu, Daniel W Apley, C Brinson, Wei Chen, and Wing Kam Liu · 2017
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Sobolev training for neural networks
Wojciech M Czarnecki, Simon Osindero, Max Jaderberg, Grzegorz Swirszcz, and Razvan Pascanu · 2017
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Semi-Supervised Classification with Graph Convolutional Networks
Thomas N. Kipf and Max Welling · 2017
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Inferring low-dimensional microstructure representations using convolutional neural networks
Nicholas Lubbers, Turab Lookman, and Kipton Barros · 2017
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graph2vec: Learning Distributed Representations of Graphs
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Spektral
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So(3)-invariance of graph-based deep neural network for anisotropic elastoplastic materials
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Predictive Modeling with Learned Constitutive Laws from Indirect Observations
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