In recent years, the use of machine learning methods to solve differential equations has attracted increasing attention from researchers in different fields. However, with the deepening of the research, researchers have begun to identify numerous challenges associated with the use of machine learning methods for solving time development equations. This paper presents a summary of the machine learning methods for solving the evolution equation. First, we present a summary of data-driven methods and deep learning methods based on equation learning. Then we introduce targeted algorithms for solving the problem under different neural network architectures. Finally, this paper presents a summary of the training features and recent work on the use of PINN method for solving the evolution equation. It also provides an outlook for future work.