# Forecasting Ionospheric foF2 Based on Deep Learning Method
## 1 Introduction  
The ionosphere of the Earth is an extremely complicated and non-linear system changing with time and space, and an important part of the near-Earth space environment. The F2 layer contains the highest electron density, and it mainly determines the characteristics of the ionosphere. Due to the highest level of conductivity in the propagation path, the propagation of high frequency (HF) waves going through the Earth's ionosphere are greatly influenced by the F2 layer's maximum electron density. It is mainly related to the critical frequency of ionosphere F2 layer foF2, which is one of the most important parameters for quantifying the plasma density variability and describing the characteristics of the ionosphere. Because of the time-varying and dispersive characteristics of the ionosphere, the working parameters for the HF communication systems and satellite communications must be adaptively adjusted according to the current state of the ionosphere [1]. During the ionospheric disturbance, the variations of the foF2 play a significant impact on wireless communication [2, 3], which may lead to the degradation or interruption of the information quality such as communication, navigation, measurement, and remote sensing [4, 5]. Therefore, forecasting foF2 has become an important concern in ionosphericstudies and applications to provide effective support and decision for high-frequency radars and shortwave communication systems. The largest ionospheric variability takes place in the F2-layer and is thus of fundamental significance in ionospheric modeling [6]. Much work so far has been done to predict the foF2 with different forecasting models for the short-term ionosphere prediction. The most complete and widely used predicting model is the International Reference Ionosphere (IRI) model [7], which has been established with global ionospheric observations. IRI provides empirically estimated values for a given time and location based on the monthly averages. Besides, many classical methods have been developed including the multi-linear-regression method [8], autocorrelation analysis [9], and data assimilation [10; 11] that use past foF2 values as an input to predict current foF2. With the development of machine learning, due to good non-linear mapping ability, self-learning adaptability, and parallel information processing ability, artificial neural networks are very encouraging in the prediction of foF2 which can approximate and simulate the complex non-linear system of the ionosphere very well [12]. The technique of neural networks has been successfully employed to build suitable forecasting models to predict foF2 [13; 14; 15; 16]. Meanwhile, various ionosphere models with different algorithms have been built to improve the performance and accuracy of neuron networks prediction, including the error backward propagation neural network method based on gradient descent [17], the improved particle swarm optimization neural network method [18], and the improved back-propagation (BP) neural network based on genetic algorithm method [19; 20; 21; 22]. In recent years, due to the computing capacity growth, deep learning has been widely used in the field of ionosphere with the advantage of learning time-series data. The observations of ionospheric critical frequency foF2 are time sequences, too. By the addition of connections with the past data, the deep learning method uses the result at the previous step as an input at the current step to learn time-series data. Based on deep learning, many forecasting methods are developed for ionospheric parameters prediction, such as a recurrent neural network (RNN) method [23; 24], a long-short-term memory LSTM method [25; 26], and an improved gated recurrent unit (GRU) method [27]. Unlike traditional neural networks models [28], deep learning models can infer the relationships between the previous time node and the latter time node of time-series data.