深度学习神经网络是近年来机器学习领域的重大技术性突破，它在无人驾驶汽车、机器翻译、图片识别与分类等相关领域都取得了很多的成果。本文主要综述了长短期记忆网络(LSTM)以及LSTM前身循环神经网络(RNN)的运行原理。并根据神经网络的历史发展脉络，简单介绍了几种基本的神经网络结构。

   在应用方面，本文以上证500指数1998年1月5日至2020年6月2日的基本参数为原始数据，使用Python代码编写程序，借助Pytorch提供的强大的深度学习库搭建LSTM神经网络，采用Adam梯度下降优化算法，对整体的网络训练过程进行优化，选取MSE作为损失函数标准。通过上述工作得出的实验结果可以看出，LSTM在预测股价方面具有一定的优势。同时，本文归纳了应用LSTM时可能会出现的问题，更具体的是将金融数据导入LSTM模型之后可能会出现的震荡以及过拟合问题，并针对这些问题的要点上给出了解决方案。

Deep learning neural network is a major technological breakthrough in the field of machine learning in recent years. It has achieved many results in related fields such as driverless cars, machine translation, image recognition and classification. This paper mainly reviews the operation principle of long short-term memory network (LSTM) and LSTM predecessor recurrent neural network (RNN). And according to the historical development of neural network, several basic neural network structures are briefly introduced.

In terms of application, this paper uses the basic parameters of the SSE 500 Index from January 5, 1998 to June 2, 2020 as the original data, writes programs using Python code, and builds LSTM neural networks with the help of the powerful deep learning library provided by Pytorch. The Adam gradient descent optimization algorithm optimizes the overall network training process, and MSE is selected as the loss function standard. From the results of the above work, it can be seen that LSTM has certain advantages in predicting stock prices. At the same time, this article summarizes the problems that may arise when applying LSTM, more specifically, the abnormal fluctuation and overfitting problems that may occur after importing financial data into the LSTM model, and gives solutions to these problems.