## 2 Related Studies  
Dst index prediction is usually achieved using different mathematical modeling approaches. [PERSON] et al. [8] developed an empirical model for predicting the occurrence of geomagnetic storms based on the Dst index of the Coronal Mass Ejection (CME) parameter, and the results showed that this parameter predicts both the occurrence of geomagnetic storms and the Dst index. [PERSON] et al. [9] proposed a solution for Dst index forecasting using an autoregressive model and solar wind parameter measurements, called the minimax approach, to identify the parameters of forecast models. [PERSON] et al. [10] proposed a data-driven deterministic algorithm, the Anemomilos algorithm, which can predict the Dst up to 6 days based on the arrival time of large, medium, or small magnetic storms to the Earth. [PERSON] et al. [11] used the direction and magnitude of the B\({}_{Z}\) component of the real-time solar wind and real-time interplanetary magnetic field (IMF) as input parameters to model the magnetosphere based on a metric automaton, and the simulation of the Dst met expectations. [PERSON] et al. [12] developed Gaussian Process Autoregressive (GP-AR) and Gaussian Process Autoregressive with external inputs (GP-ARX) models, whose Root Mean Square Errors (RMSEs) were only 14.04 nT and 11.88 nT and CCs (correlation coefficients) were 0.963 and 0.972, respectively. [PERSON] et al. [13] introduced a new probabilistic model based on adaptive incremental modulation and the concept of optimal state space, with the CC exceeding 0.90 and very small CCs between the mean absolute error and RMSE (3.54 and 5.15 nT). [PERSON] et al. [14] used a new Ensemble Kalman Filter (EnKF) method based on the dynamics of the circulating flow to forecast the Dst index in real-time; the resulting RMSE and CC values were 4.3 nT and 0.99. Compared with traditional mathematical methods, machine learning based on deep learning models can train different models based on different training data with better pertinence, scalability, and trainability. Much progress has been made in researching Dst index prediction using deep learning techniques. [PERSON] et al. [15] used a BP (Back-propagation) neural network to establish a method to forecast the Dst index one hour in advance and found that it is feasible to forecast the Dst parameter in the short term, but there is still some bias. [PERSON] et al. [16] proposed a method based on an Artificial Neural Network (ANN) combined with an analytical model of solar wind-magnetosphere interaction, and the predicted values were more accurate than others. [PERSON] et al. [17] combined the Support Vector Machine (SVM) with Distance Correlation (DC) coefficients to build a model, and the results showed more minor errors than the neural network (NN) and Linear Machine (LM). [PERSON] et al. [18] used Multivariate Relevance Vector Machines (MVRVMs) to predict various indices, among which the Dst index was predicted with an accuracy of 82.62%. [PERSON] et al. [19] proposed an ANN technique to forecast the Dst index using 24 past hourly solar wind parameter values, and the results showed that for forecasting 2 h in advance, the CC can reach 0.876. [PERSON] et al. [20] used the Bagging integrated learning algorithm, which combines three algorithms, ANN, SVM, and LSTM, to forecast the Dst index 1-6 hours in advance. They used solar wind parameters (including total interplanetary magnetic field, total IMF\({}_{\text{B}}\) field and IMF\({}_{\text{Z}}\) component, total electric field, solar wind speed, plasma temperature, and proton pressure) as inputs, and the RMSE of the forecast was always lower than 8.09 nT, the CC was always higher than 0.86, and the accuracy of the interval forecast was always higher than 90%. [PERSON] et al. [21] combined an empirical model and an ANN model to build a Dst index prediction model, which showed an excellent performance compared with the model using only ANN, predicting the Dst index 6 hours ahead with a CC of 0.8 and RMSE not greater than 24 nT. [PERSON] et al.