## 1 Introduction  
As an essential physical field of the Earth, the geomagnetic field is an integral part of space weather, which has a complex spatial structure and temporal evolution characteristics. A deep understanding of the spatial and temporal characteristics, origin, and relationship between the geomagnetic field and other geophysical phenomena provides excellent help for studying the magnetic field of the Earth and other planets. The Dst index, an important index reflecting perturbation of the geomagnetic field, was first proposed by [PERSON] in 1964. It is also known as the geomagnetic hourly geomagnetic index, which describes the process of magnetic storms and reflects changes in equatorial westerly ring current [1]. This index is calculated using the horizontal component \(H\) of the geomagnetic field at four middle- and low-latitude observatories after removing the secular variation and the ring current latitudinal correction [2]. The Dst index is one of the most widely used indices in geomagnetism and space physics because it can monitor the occurrence and change of magnetic storms succinctly and continuously. The modeling and prediction of the Dst index have significant scientific and applicated meanings for studying changes in geomagnetic external fields, magnetic storms, and even solar activity.  
Numerical methods, such as least squares estimation and spline interpolation [3], are generally used to predict geomagnetic indices. These traditional methods mainly carry out numerical processes like iteration from the data itself, error approximation, seeking extremum, and so on, to obtain the best-approximated value that satisfies the accuracy requirement. However, they cannot highlight the characteristics of the data based on in-depth learning and mining of the existing and constantly emerging new data. In recent years, with the continuous improvement in computing power and the rapid development of artificial intelligence (AI), deep learning, a type of multi-layer neural network learning algorithm, has become an essential part of the machine learning field. Deep learning is usually used to process images, sounds, text signals, etc. It is mainly applied to multi-modal classification problems, data processing, and simulation, as well as artificial intelligence [4]. The Long-Short Time Memory (LSTM) network method [5] is the most widely used simulation and forecasting algorithm model. This method has a complex hidden unit, which can selectively increase or decrease information. It, therefore, can accurately model data with short-term or long-term dependencies in the data for accurate modeling [6]. So far, LSTM has shown excellent forecasting ability in long-term time series data processing [7]. We believe that it is very suitable for forecasting the Dst index. Therefore, in this study, we use LSTM and its mixed model--EMD-LSTM--for Dst index prediction and try to optimize the prediction results.  
The rest of this study is organized as follows. Section 2 describes related studies. Section 3 gives the data sources and selection conditions for this paper. Section 4 describes the rationale of the methodology used. Section 5 explains the results of the different methods. The conclusions and discussion are given in Sections 6 and 7, respectively.