# Ionospheric Electron Density Model by Electron Density Grid Deep Neural Network (EDG-DNN)
## 1 Introduction
Later, many scholars established several GNSS ionospheric tomography models on this basis. These models can be divided into function-based ionospheric tomography models and pixel-based ionospheric tomography models. Both function-based and pixel-based models have their advantages and disadvantages. The potential improvements of GNSS-based ionospheric tomography at a global scale by combining the upcoming LEO constellations are investigated in [PERSON] et al. 's paper [10]. In terms of function basis, [PERSON] et al. used two-dimensional Hale wavelet and empirical orthogonal function as basis functions, respectively, to simulate the horizontal and vertical structures of the electron density and propose the solution using the truncated singular value decomposition (TSVD) method [11]. In terms of pixel basis, [PERSON] has proposed a tomography method that integrates GPS observation data and altimeter data [12]. [PERSON] et al. have presented the main results of GPS/GLONASS radio sounding of ionospheric disturbances of natural and anthropogenic origin [13]. The observation of the ionosphere has never stopped, and the means are becoming more and more abundant. Today, a variety of observations of ionospheric data provide a wealth of useful data for studying the ionosphere and electron density. The four-dimensional fine modelling of ionospheric electron density based on a variety of observational data has gradually become a new development direction of ionospheric electron density research. With its powerful computational and data-learning capabilities, deep learning can effectively process large amounts of data, and therefore has significant advantages in dealing with data-heavy electron density profiles. Many studies are now using deep learning to study various features of the ionosphere; using deep-learning neural networks, high-accuracy ionospheric electron density modelling can be achieved. [PERSON] et al. proposed a residual minimisation-based training neural network method to reconstruct the three-dimensional ionospheric electron density distribution in local areas, using ionospheric sounding data to improve the vertical resolution [14]. [PERSON] et al. (2011) proposed a neural network-based predictive model for ionospheric TEC modelling in South Africa and developed a global 3-D electron density reconstruction based on COSMIC 2006-2019 data and neural networks [15; 16]. They found that the model based only on the COSMIC dataset was able to reproduce different ionospheric features. [PERSON] et al. used statistical and machine-learning methods to simultaneously study the relationship between earthquakes, radon gas (Rn), and total electron content (TEC) [17]. [PERSON], et al. proposed a data-driven machine-learning approach for the total ionospheric electron content and compared it with a conventional linear regression model: the machine learning achieved \(RMSE\)\(\sim\)2 TECU, while the linear regression model based on significant features resulted in \(\sim\)4 TECU [18]. [PERSON] et al. proposed an improved neural network based on a genetic algorithm to predict TEC in China [19]. It overcomes the problem that traditional neural networks tend to fall into in local optimization and establishes a TEC model to control the error within a certain range. [PERSON] et al. applied deep convolutional generative adversarial networks (DCGAN) to complement TEC pictures and constructed four LSTM-based algorithms to predict the global TEC map from 2011 to 2019 [20; 21]. [PERSON] et al. used the neural network method to predict the TEC of stations in different geographical locations in the world and established the global TEC model [22]. Because electron density just adds height to latitude, longitude, and time, deep learning can potentially process electron density data. At present, deep learning is mainly used in the modelling of TEC, but it is relatively less used in the modelling of electron density.