In this talk, we will consider the neural network-based machine learning method for solving eigenvalue problems of differential operators. Based on a new understanding of the error estimation for machine learning methods, we design a type of machine learning method with numerical integration to achieve high accuracy. As an example, we will design a tensor neural network-based machine learning method for solving high-dimensional eigenvalue problems, including the famous Schrodinger equations. Some numerical examples are provided to validate the high accuracy and efficiency of the proposed tensor neural network-based machine learning methods.