The DOI matches its Crossref record; 36 of the 36 references it cites were found in a registry or an index.
A deep energy method for finite deformation hyperelasticity
Abstract
Abstract We present a deep energy method for finite deformation hyperelasticitiy using deep neural networks (DNNs). The method avoids entirely a discretization such as FEM. Instead, the potential energy as a loss function of the system is directly minimized. To train the DNNs, a backpropagation dealing with the gradient loss is computed and then the minimization is performed by a standard optimizer. The learning process will yield the neural network's parameters (weights and biases). Once the network is trained, a numerical solution can be obtained much faster compared to a classical approach based on finite elements for instance. The presented approach is very simple to implement and requires only a few lines of code within the open-source machine learning framework such as Tensorflow or Pytorch. Finally, we demonstrate the performance of our DNNs based solution for several benchmark problems, which shows comparable computational efficiency such as FEM solutions.
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Cites
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Deep learning modelling techniques: Current progress, applications, advantages, and challenges
Ahmed, S. F., Alam, M. S. B., Hassan, M., Rozbu, M. R., Ishtiak, T., Rafa, N., Mofijur, M., Shawkat Ali, A. B. M., & Gandomi, A. H. (2023) · Artificial Intelligence Review · doi:10.1007/s10462-023-10466-8 · Cited by 1,079
Deep learning for topology optimization of 2D metamaterials
Kollmann, H. T., Abueidda, D. W., Koric, S., Guleryuz, E., & Sobh, N. A. (2020) · Materials & Design · doi:10.1016/j.matdes.2020.109098 · Cited by 361
Metadata
- Authors
- Nguyen-Thanh, V. M., Zhuang, X., & Rabczuk, T.
- Venue
- European Journal of Mechanics - A/Solids
- Publisher
- Elsevier BV
- Published
- 2020-03
- Volume
- 80
- Pages
- 103874
- ISSN
- 0997-7538 (ISSN-L)
- OpenAlex
- W2982123645
- Cited by
- 334
- References
- 36
- FWCI
- 9.26
- Type
- journal article
- Language
- en
- Open access
- closed
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