A global spatiotemporal ionospheric prediction model based on a time–frequency mixture-of-experts mechanism

Spatiotemporal Observer (ST-Observer) is a recently proposed spatiotemporal prediction framework grounded in dynamical system theory, which outperforms many spatiotemporal prediction models on three publicly available datasets. However, through careful analysis, we found that its structure weakens its ability to model temporal dependencies on data. Moreover, it lacks the ability to model frequency dependencies in the data. To address these issues, this paper first proposed a Time–Frequency Mixture-of-Experts (TFMoE) module that utilized a time branch to enhance temporal dependency modeling capabilities, a frequency branch composed of multiple experts to increase frequency dependency modeling capabilities, and cross-domain attention to mix temporal and frequency dependencies. TFMoE was then embedded into ST-Observer to form a Spatiotemporal Observer with Time–Frequency Mixture-of-Experts (ST-TFMoE-Observer), compensating for its weak temporal dependency modeling ability and lack of frequency dependency modeling ability. Finally, this article applied ST-TFMoE-Observer for Total Electron Content (TEC) spatiotemporal prediction. The ablation experiment showed that TFMoE can reduce the Root Mean Square Error ( R M S E ) and Mean Absolute Percentage Error ( M A P E ) by 6.72% and 9.80% respectively in high solar activity years, and by 9.69% and 13.22% in low activity years. The comparison results against six widely used models in Total Electron Content spatiotemporal prediction showed that the proposed model has obvious advantages, especially in predictions of complex spatial structures such as the hump structure in Equatorial Ionization Anomaly (EIA) region and the trough structure in mid-latitude regions. The code for this model can be obtained at http://github.com/myklbkl/ST-TFMoE-Observer .