论文｜Yang, Qihong, Deng, Yangtao, Yang, Yu, He, Qiaolin, Zhang, Shiquan：Neural networks based on power method and inverse power method for solving linear eigenvalue problems

本文（Neural networks based on power method and inverse power method for solving linear eigenvalue problems）原载 Computers and Mathematics with Applications，由四川大学贺巧琳教授等科研人员创作，系四川大学智慧法治超前部署学科系列学术成果。后续会持续分享四川大学智慧法治超前部署学科系列学术成果，欢迎大家阅读。

Abstract: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 dimension and higher dimensions. Numerical results show that accurate eigenvalue and eigenfunction approximations can be obtained by our methods.  

Yang, Qihong, Deng, Yangtao, Yang, Yu, He, Qiaolin, Zhang, Shiquan. “Neural networks based on power method and inverse power method for solving linear eigenvalue problems”， Computers and Mathematics with Applications, 2023, Vol.147, pp.14-24.（论文下载）