论文标题
通过使用机器学习，选择内部罚款不连续的盖勒金方法内部罚款系数
Choice of Interior Penalty Coefficient for Interior Penalty Discontinuous Galerkin Method for Biot's System by Employing Machine Learning
论文作者
论文摘要
在本文中，通过利用神经网络和机器学习，研究了不连续的Galerkin有限元方法的内部惩罚参数的最佳选择。选择最佳内部惩罚参数至关重要，该参数的稳定性，稳健性和效率不太大，或者不太大。线性回归和非线性人工神经网络方法均采用并使用多个数值实验进行比较，以说明我们提出的计算框架的能力。该框架是开发自动化数值仿真平台的组成部分，因为它可以自动识别最佳内部惩罚参数。还可以实现实时反馈，以更新和提高模型的准确性。
In this paper, the optimal choice of the interior penalty parameter of the discontinuous Galerkin finite element methods for both the elliptic problems and the Biot's systems are studied by utilizing the neural network and machine learning. It is crucial to choose the optimal interior penalty parameter, which is not too small or not too large for the stability, robustness, and efficiency of the numerical discretized solutions. Both linear regression and nonlinear artificial neural network methods are employed and compared using several numerical experiments to illustrate the capability of our proposed computational framework. This framework is an integral part of a developing automated numerical simulation platform because it can automatically identify the optimal interior penalty parameter. Real-time feedback could also be implemented to update and improve model accuracy on the fly.
