TY - JOUR

T1 - A deep energy method for finite deformation hyperelasticity

AU - Nguyen-Thanh, Vien Minh

AU - Zhuang, Xiaoying

AU - Rabczuk, Timon

N1 - 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 Universität Weimar.

PY - 2020/3

Y1 - 2020/3

N2 - 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.

AB - 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.

KW - Artificial neural networks (ANNs)

KW - Deep energy method

KW - Hyperelasticity

KW - Machine learning

KW - Partial differential equations (PDEs)

UR - http://www.scopus.com/inward/record.url?scp=85076246280&partnerID=8YFLogxK

U2 - 10.1016/j.euromechsol.2019.103874

DO - 10.1016/j.euromechsol.2019.103874

M3 - Article

AN - SCOPUS:85076246280

VL - 80

JO - European Journal of Mechanics, A/Solids

JF - European Journal of Mechanics, A/Solids

SN - 0997-7538

M1 - 103874

ER -