A new neurodynamic model with Adam optimization method for solving generalized eigenvalue problem

In this paper we proposed a new neurodynamic model with recurrent learning process for solving ill-condition Generalized eigenvalue problem (GEP) Ax = lambda Bx. our method is based on recurrent neural networks with customized energy function for finding smallest (largest) or all eigenpairs. We evaluate our method on collected structural engineering data from Harwell Boeing collection with high dimensional parameter space and ill-conditioned sparse matrices. The experiments demonstrate that our algorithm using Adam optimizer, in comparison with other stochastic optimization methods like gradient descent works well in practice and improves complexity and accuracy of convergence.

Keywords:

Recurrent Neural Network , eigenpairs , Adam Optimizer , positive definite matrix , ill-condition