论文标题
部分可观测时空混沌系统的无模型预测
Neural Networks Based on Power Method and Inverse Power Method for Solving Linear Eigenvalue Problems
论文作者
论文摘要
在本文中，我们提出了两种灵感启发的神经网络和逆力方法，以解决线性特征值问题。这些神经网络与传统方法共享相似的想法，在这种方法中，通过自动差异来实现差异操作员。特征值问题的本征函数是通过优化特殊定义的损失函数来实现的。可以有效地解决最大的正征值，最小的特征值和内部特征值。我们在数值实验中检查了在一个维度，二维和更高维度的数值实验中的适用性和准确性。数值结果表明，可以通过我们的方法获得准确的特征值和特征功能近似值。
In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential operator is realized by automatic differentiation. The eigenfunction of the eigenvalue problem is learned by the neural network and the iterative algorithms are implemented by optimizing the specially defined loss function. The largest positive eigenvalue, smallest eigenvalue and interior eigenvalues with the given prior knowledge can be solved efficiently. We examine the applicability and accuracy of our methods in the numerical experiments in one dimension, two dimensions and higher dimensions. Numerical results show that accurate eigenvalue and eigenfunction approximations can be obtained by our methods.
