# MoCoformer: Quantifying Temporal Irregularities in Solar Wind for Long-Term Sequence Prediction
###### Abstract  
Long-term solar wind sequence forecasting is essential for understanding the influence of the solar wind on celestial settings, predicting variations in solar wind parameters, and identifying patterns of solar activity. The intrinsic erratic temporal features of solar wind datasets present significant challenges to the development of solar wind factor estimate techniques. In response to these challenges, we present MoCoformer, a novel model based on the Transformer model in deep learning that integrates the Multi-Mode Decomp Block and Mode Independence Attention. The Multi-Mode Decomp Block employs an optimized version of variational mode decomposition technology to flexibly handle irregular features by adaptively decomposing and modeling the impact of sudden events on the temporal dynamics, enhancing its ability to manage non-stationary and irregular features effectively. Meanwhile, the Mode Independence Attention module computes attention independently for each mode, capturing the correlation between sequences and mitigating the negative impact of irregular features on time series prediction. The experimental results on solar wind datasets demonstrate that MoCoformer significantly outperforms current state-of-the-art methods in time series forecasting, showcasing superior predictive performance. This underscores the resilience of MoCoformer in handling the intricate, irregular temporal characteristics of solar wind data, rendering it a valuable instrument for enhancing the understanding and forecasting of solar wind dynamics. long-term prediction; solar wind forecasting; deep learning; machine learning +
Footnote †: journal: Medical  
interstellar shocks and solar wind events; The National Oceanic and Atmospheric Administration (NOAA) of the United States of America introduced the ENLIL model [4], while the Space Environment Modeling Centre (SEMC) released the Space Weather Modeling Framework (SWMF) [5]; [PERSON] et al. proposed the 3-D MHD model [6], while the Hybrid Heliospheric Modeling System (HAMS) combines the 3-D MHD model [7] with the Hakamada-Akasofu-Fry (HAF) model. The COrona-INplanetary (COIN) model developed by the SIGMA group at the Chinese Academy of Sciences (CAS) [8] represents an improvement on the Interplanetary Total Variation Diminishing (IN-TVD) model. (2) Empirical or semi-empirical modeling based on statistics, for example, [PERSON] et al. [9], established probability distribution functions linking the current solar wind and slope with the solar wind one solar rotation period in the future; The Wang-Sheeley-Arge (WSA) model proposed by [PERSON] et al. [10] is based on the negative correlation between the observed solar wind speed and the coronal magnetic field expansion factor at the source surface; [PERSON] et al. [11] improved the WSA model by introducing the correlation of the continuum function. [PERSON] et al. [12] further refined the model by introducing an angular distance from the coronal hole boundary. In addition, the Potential Field Source Surface (PFSS) model [13] is another semi-empirical model that can be used to compute the coronal magnetic field and derive the fs and b parameters. [PERSON] et al. [14] proposed a simple method based on the Sun's 27-day rotational period for solar wind parameter prediction. In addition, [PERSON] et al. [15] used a Kalman filter for data assimilation, which significantly improved the model performance compared to the baseline model, and [PERSON] et al. [16] used a support vector machine algorithm to predict solar wind speed. However, the irregular and intense solar wind features are shaped by irregular and vigorous solar activities and geomagnetic storms [17]. These pronounced irregularities lead to unpredictable oscillations and intermittent gaps, making the temporal structure complex and challenging to model using conventional methods. The introduction of deep learning models facilitates the identification of patterns in irregular solar wind properties and the production of precise forecasts.