Optimizing BP and LSTM neural network model for long-term and short-term prediction of ionospheric TEC

The total electron content (TEC) of the ionosphere has a significant impact on fields such as radio communication and satellite navigation positioning, therefore, accurate prediction is crucial. In response to the problem of difficult effective prediction of ionospheric TEC, the research introduces deep learning methods and constructs ionospheric TEC prediction models based on back propagation (BP) neural network, K-fold cross validation (KCV)-BP neural network, genetic algorithm (GA)-BP neural network, and long short-term memory (LSTM) neural network using ionospheric TEC grid data (global ionospheric map (GIM)) provided by the Center for Orbit Determination in Europe (CODE). These models are used for 1 h short-term prediction and 7-15 d long-term prediction of ionospheric TEC in different latitude regions, different longitude regions and different solar activity period. Indicators such as root mean square error (RMSE), goodness of fit R², mean absolute percentage error (MAPE) are introduced to evaluate prediction applicability of different models. Research has shown that in short-term forecasting, among different models, the prediction performance from high to low is GA-BP, LSTM, KCV-BP, BP, and ordinary least squares (OLS), and the optimal prediction error is within 1 TECU. In long-term forecasting, OLS has the best prediction performance, especially with a significant advantage at 15 d, while GA-BP has the best long-term timeliness and good prediction stability. The MAPE indicators demonstrate significant differences in the predictive applicability of the model between the northern and southern hemispheres. Finally, when evaluating the applicability of the model to the region, using a single RMSE to measure it is one-sided and requires the comprehensive use of indicators such as R² and MAPE to measure it.