# MoCoformer: Quantifying Temporal Irregularities in Solar Wind for Long-Term Sequence Prediction
###### Abstract
The development of machine learning techniques has led to further optimization of solar wind predictions. Machine learning models can adaptively learn and make inferences about new or future data and play a role in long-term prediction. Machine learning algorithms such as regression algorithms, Support Vector Machines (SVM) [18], Random Forest (RF) [19], Bayesian Additive Regression Trees (BART) [20], and K-Nearest Neighbor(KNN) [21] are widely used in the solar wind output forecasting and wind speed prediction fields. Support vector machines are widely used in solar wind speed [22] prediction, and researchers have improved them to adapt to the characteristics of solar wind data. Parallel SVM (PSVM) [23] and Least Square SVM (LSSVM) [24] is a model that improves the robustness of SVM and the accuracy of solar wind output prediction. [PERSON] et al. [25] used RF for hour-ahead solar wind output prediction, which does not require a lot of tuning, and has the advantage of being able to do so. [PERSON] et al. [26] proposed a two-stage feature selection and decision tree restructuring method to improve the prediction accuracy, efficiency, and robustness of the RF model. Comparisons were made with the decision tree [27]. [PERSON] et al. [28] used the RF algorithm for wind speed input feature selection, which simplified the model structure, reduced the training time, and improved the accuracy and generalization ability. Common deep learning prediction models include autoregressive (AR) [29], moving average (MA) [30], autoregressive moving average (ARMA) [31], and autoregressive integrated moving average (ARIMA) [32]. [PERSON] et al. [33] used the AR model in wind speed prediction. The study by [PERSON] et al. [34] used ARMA for wind speed prediction, while [PERSON] et al. [35] used a calibrated ARMA model to improve the accuracy of short- and medium-term wind power prediction. However, these methods are mainly applicable to linear and smooth time series, making it difficult to deal with non-linear and non-smooth series. To overcome this problem, recurrent neural networks (RNNs) [36], especially popular ones such as long short-term memory (LSTM) [37] and gated recurrent unit (GRU) [38], have been introduced in deep learning variants, performing excellently in time series forecasting, [PERSON] et al. [39] predicted the power output of different wind turbine data, which were calculated using techniques such as LSTM. Additionally, RNN models based on attention mechanisms are widely used in time series forecasting tasks. As a classic deep learning model, Transformer plays an indispensable role in long-term sequence prediction. Self-attention blocks, a cornerstone in Transformer [40], hold substantial innovative significance in natural language processing. Recent models, including Sparseformer [41] for sparse attention, Switchformer [42] for multimodal data, Compressive Transformer [43] based on Hadamard transform [44], and Linformer [45] with low-rank approximation, contribute to handling diverse data efficiently. These models advance natural language processing and broaden practical applications. Self-attention mechanisms [46] play a crucial role in time series forecasting. Transformer excels in various prediction tasks. However, its limitations in handling long sequences led to the development of enhanced models. LogSparse Transformer [47] employs sparse attention mechanisms, Pyraformer [48] reduces complexity with a pyramid attention approach, Informer [49] uses a hierarchical structure and masking mechanism, Autoformer [50] introduces adaptive feed-forward mechanisms and reversible embeddings, FEDformer [51] innovates with a federated learning framework, and InParformer [52] incorporates interactive attention for enhanced temporal pattern extraction. These models advance time series forecasting, offering diverse solutions for practical applications.