A deep energy method for finite deformation hyperelasticity

verfasst von: Vien Minh Nguyen-Thanh, Xiaoying Zhuang, Timon Rabczuk
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.
Organisationseinheit(en): Institut für Kontinuumsmechanik
Externe Organisation(en): Ton Duc Thang University
Typ: Artikel
Journal: European Journal of Mechanics, A/Solids
Band: 80
ISSN: 0997-7538
Publikationsdatum: 03.2020
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Werkstoffwissenschaften (insg.), Werkstoffmechanik, Maschinenbau, Physik und Astronomie (insg.)
Elektronische Version(en): https://doi.org/10.1016/j.euromechsol.2019.103874 (Zugang: Geschlossen)
: Details im Forschungsportal „Research@Leibniz University“

BibTeX

@article{738164dd6fa74b1a9f77656ff46ba804,
title = "A deep energy method for finite deformation hyperelasticity",
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.",
keywords = "Artificial neural networks (ANNs), Deep energy method, Hyperelasticity, Machine learning, Partial differential equations (PDEs)",
author = "Nguyen-Thanh, {Vien Minh} and Xiaoying Zhuang and Timon Rabczuk",
note = "Funding Information: The first and second authors owe the gratitude to the sponsorship from Sofja Kovalevskaja Programme of Alexander von Humboldt Foundation. The first author also would like to thank MSc. Somdatta Goswami and especially Dr. Cosmin Anitescu, Dr. Simon Hoell for the first code and the fruitful discussions during his research stay at Bauhaus Universit{\"a}t Weimar.",
year = "2020",
month = mar,
doi = "10.1016/j.euromechsol.2019.103874",
language = "English",
volume = "80",
journal = "European Journal of Mechanics, A/Solids",
issn = "0997-7538",
publisher = "Elsevier BV",
}