期刊
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
卷 80, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.euromechsol.2019.103874
关键词
Machine learning; Artificial neural networks (ANNs); Partial differential equations (PDEs); Hyperelasticity; Deep energy method
类别
资金
- Sofja Kovalevskaja Programme of Alexander von Humboldt Foundation
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.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据