Learning constitutive relations from indirect observations using deep neural networks
Learning constitutive relations from indirect observations using deep neural networks
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DOI：
10.1016/j.jcp.2020.109491
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发表时间：
2020-09-01
影响因子：
4.1
通讯作者：
Darve, Eric
中科院分区：
文献类型：
--
作者：
Huang, Daniel Z.;Xu, Kailai;Darve, Eric
我们提出了一种机械系统预测建模及其不确定性量化的新方法，其中本构关系等粗粒度模型直接从观测数据导出。我们探索使用神经网络来表示未知的本构关系，将神经网络与分段线性函数、径向基函数和径向基函数网络进行比较，并表明该神经网络在某些情况下优于其他网络。我们使用缩放参数来分析神经网络的近似误差。我们框架中的训练和预测过程结合了有限元方法、自动微分和神经网络（或其他函数逼近器）。我们的框架还允许以置信区间的形式量化不确定性。固体力学中的多尺度纤维增强板问题和非线性橡胶膜问题的数值例子证明了我们框架的有效性。
We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived directly from observation data. We explore the use of a neural network to represent the unknown constitutive relations, compare the neural networks with piecewise linear functions, radial basis functions, and radial basis function networks, and show that the neural network outperforms the others in certain cases. We analyze the approximation error of the neural networks using a scaling argument. The training and predicting processes in our framework combine the finite element method, automatic differentiation, and neural networks (or other function approximators). Our framework also allows uncertainty quantification in the form of confidence intervals. Numerical examples on a multiscale fiber-reinforced plate problem and a nonlinear rubbery membrane problem from solid mechanics demonstrate the effectiveness of our framework.