# A Model-Assisted Combined Machine Learning Method for Ionospheric TEC Prediction
###### Abstract  
In order to improve the prediction accuracy of ionospheric total electron content (TEC), a combined intelligent prediction model (MMAdapGA-BP-NN) based on a multi-mutation, multi-cross adaptive genetic algorithm (MMAdapGA) and a back propagation neural network (BP-NN) was proposed. The model combines the international reference ionosphere (IRI), statistical machine learning (SML), BP-NN, and MMAdapGA. Compared with the IRI, SML-based, and other neural network models, MMAdapGA-BP-NN has higher accuracy and a more stable prediction effect. Taking the Athens station in Greece as an example, the root mean square errors (RMSEs) of MMAdapGA-BP-NN in 2015 and 2020 are 2.84 TECU and 0.85 TECU, respectively, 52.27% and 72.13% lower than the IRI model. Compared with the single neural network model, the MMAdapGA-BP-NN model reduced RMSE by 28.82% and 24.11% in 2015 and 2020, respectively. Furthermore, compared with the neural network optimized by a single mutation genetic algorithm, MMAdapGA-BP-NN has fewer iterations ranging from 10 to 30. The results show that the prediction effect and stability of the proposed model have obvious advantages. As a result, the model could be extended to an alternative prediction scheme for more ionospheric parameters. TEC; prediction; machine learning; neural network; genetic algorithm 20231529531033  
observation data to solve TEC will cause TEC data to lag relatively. TEC can be estimated in near-real-time using a certain ionospheric model [4]. Accurately predicting TEC is not only very important to ensure the stability of the radio system but also very significant in pre-earthquake identification and other fields. These predictions are also essential for many aerospace and astronomical observation applications. Due to the complexity of the ionosphere, many methods have been used for TEC modeling [5; 6; 7]. One of the models is the TEC prediction model established based on statistical experience. The most representative model is the International Reference Ionosphere (IRI) model. It is a well-known empirical model and is a recommended international standard [8; 9; 10]. The other is the empirical model of parameter prediction established by the ionosphere parameter observation data. This type of model is widely used in the forecast of ionosphere parameters due to its simple model structure and easy calculation. In order to improve the prediction accuracy of ionospheric parameters, the artificial intelligence method was introduced [11] to predict the critical frequency of the F2 layer (foF2) [12], the 3000 km transmission factor of the F2 layer (M(3000) F2) [13], TEC [14], peak height [15], and other parameters [16]. In particular, the rapid development of machine learning [17] and intelligent computing technology provides more abundant prediction methods for nonlinear and nonstationary ionospheric parameter data. For example, the regional long-term prediction method based on statistical machine learning using the principal component method [14] and the long-term prediction method using the autocorrelation prediction method [18] are both intelligent prediction algorithms. In addition, through the extrapolation method based on physical observation without the input of prediction interval, a new TEC prediction method for the Arctic region is proposed using data from the past 14 years [19]. A deep learning algorithm, such as a neural network (NN), is a very important ionospheric parameter prediction method and has been widely used in recent years [17; 20; 21; 22]. It often requires a large amount of data for training, so it has a good effect when dealing with large samples of data for a long time. It is very important to improve the prediction accuracy of ionospheric parameters, which is also a very popular research content [6; 7]. The improvement and optimization of deep learning algorithms are significant means to improve the prediction accuracy of ionospheric parameters.