  In this paper, we propose a type of tensor-neural-network-based machine
learning method to compute multi-eigenpairs of high dimensional eigenvalue
problems without Monte-Carlo procedure. Solving multi-eigenvalues and their
corresponding eigenfunctions is one of the basic tasks in mathematical and
computational physics. With the help of tensor neural network and deep Ritz
method, the high dimensional integrations included in the loss functions of the
machine learning process can be computed with high accuracy. The high accuracy
of high dimensional integrations can improve the accuracy of the machine
learning method for computing multi-eigenpairs of high dimensional eigenvalue
problems. Here, we introduce the tensor neural network and design the machine
learning method for computing multi-eigenpairs of the high dimensional
eigenvalue problems. The proposed numerical method is validated with plenty of
numerical examples.
