【摘要】 近年来，使用机器学习方法求解微分方程在不同领域受到越来越多的关注，然而机器学习方法在求解时间发展方程上遇到许多问题。本文从数据驱动的深度学习方法和基于方程学习的深度学习方法两个方面对现阶段针对时间发展方程的机器学习求解方法进行总结，并介绍在不同神经网络架构下针对性的求解算法。总结了使用物理信息引入的神经网络方法求解时间发展方程的训练特点与最新工作，并对未来工作进行展望。更多还原

【Abstract】 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.更多还原