Analysis and prediction of TEC values during geomagnetic storm periods across low-, mid-, and high-latitude regions using Autoformer with AdamW optimiser

In this paper, an enhanced Autoformer-based model for Total Electron Content (TEC) forecasting during geomagnetic storms is proposed using the Autoformer (AF) model with AdamW (AW) optimiser. The AF(AW) model introduces an optimised Autoformer-based TEC forecasting framework by integrating progressive time-series decomposition and auto-correlation learning with the AdamW optimiser to effectively capture long-term time dependencies and the changing characteristics of the ionospheric TEC during intense geomagnetic storms. The model was tested during six intense geomagnetic storms that occurred between 2004 and 2025 using the IONOLAB GPS-TEC data covering low, mid, and high-latitude regions. Solar and geomagnetic parameters such as Kp, Ap, Dst, F10.7, and Sunspot Number from OMNIWeb are also used as exogenous variables to improve the forecasting results. The efficiency of the model is assessed using standard statistical and regression metrics such as RMSE, MAE, Willmott’s Index of Agreement, Spearman’s and Pearson’s Correlation Coefficients, R², and cross-correlation analysis. The results of the AF(AW) model outperformed the IRI-2020 model in terms of lower prediction error across all three latitudes during the six geomagnetic storms. The average RMSE values for the AF(AW) model were 7.79 TECU, 4.44 TECU and 3.41 TECU for low, mid and high-latitudes, while the average RMSE values for the IRI-2020 model were 14.03 TECU, 6.37 TECU, and 6.29 TECU, respectively. These results correspond to RMSE enhancements of 44.5%, 30.3%, and 45.8% across the three latitude regions. Statistical validation, the Wilcoxon signed-rank test yielded a p-value of 7.63 × 10⁻⁶, proving the statistical significance of the enhancement achieved by the AF(AW). In addition, the predicted TEC values were compared with those from previously reported COKSM and RNN-based models at low- and mid-latitude locations. The results obtained in this work clearly indicate that the proposed framework based on the AF(AW) approach is reliable and robust for the prediction of TEC values during geomagnetic storms.