Abstract
Solar flares can strongly disturb the ionosphere and significantly affect radio communication and satellite navigation systems. In this paper, the Ionospheric responses to four X-class solar flare events that occurred during the 25th solar cycle were investigated through the prediction of Total Electron Content (TEC). A Kolmogorov-Arnold Network (KAN) algorithm-based deep learning approach, combined both with the Adaptive Gradient Algorithm (Adagrad) optimiser and without an optimiser, was implemented to forecast TEC variations. A Deep Belief Network with Adagrad optimiser (DBN-Adagrad) is a deep learning model used to provide a clear comparison with the proposed KAN-based approach. The proposed models were analysed with three sets of dataset split strategies, and also the models were validated with Leave future out cross-validation. A geomagnetically quiet day on 28 April 2025, with Kp < 3, is also considered as a reference for evaluating model performance under undisturbed ionospheric conditions. These KAN-based TEC predictions were compared with TEC predictions based on the DBN-Adagrad, IRI-2020 model and with GNSS-derived TEC observations at the HYDE (Hyderabad, India) and CPN (Chumphon, Thailand) stations. The proposed KAN and DBN models used the important solar and geomagnetic parameters, such as Ap, Kp indices, SSN, and the 10.7 cm solar radio flux, as input parameters during quiet and disturbed conditions. Four major solar flares (SF) events on 26th October 2024 (X1.86 SF), 13th May 2025 (X1.21 SF), 14th May 2025 (X2.7 SF), and 25th May 2025 (X1.1 SF), were analysed orderly in this study. Moreover, model performance was evaluated using standard statistical measures, including Willmott's Index of Agreement (WIA), Kling-Gupta Efficiency (KGE) and Spearman's Correlation Coefficient (SCC). As for the X1.86 SF event (first SF) observed over HYDE and CPN stations, the KAN with Adagrad optimiser and DBN with Adagrad optimiser models achieved KGE values of 0.8586,0.7885 and 0.8573,0.8248, respectively, demonstrating their good performance as compared to other models (KAN without optimiser and IRI-2020 models). Overall, the results showed that the KAN model with Adagrad optimiser and DBN with Adagrad optimiser generally provided TEC predictions with improved accuracy at both stations as compared to other models, except on May 13th, 2025, over the HYDE station, where the KAN without optimiser performed better. As for the X1.1 SF event on 25th May 2025 (fourth SF) over HYDE station, two KAN models with Adagrad optimiser and without optimiser exhibited nearly equal performance. This study demonstrated that AI-driven deep learning models can effectively capture TEC variations during strong SF events and play a valuable role in improving the reliability of global navigation satellite systems (GNSS) under disturbed space weather conditions.