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1. Introduction

The ionosphere is a crucial component of the Sun–Earth space environment, located within the atmospheric layer at altitudes ranging from 60 to 1000 km above the Earth’s surface. It forms as a result of ionization processes, driven by solar radiation, cosmic rays, and high-energy particles from outer space, which cause gas molecules and atoms in the atmosphere to ionize, creating abundant free electrons and high concentrations of ions. As an essential part of the atmosphere, the ionosphere’s significant fluctuations can profoundly impact fields such as global satellite navigation, radio communications, space weather, and positioning, navigation, and timing (PNT) systems [1,2,3,4,5,6,7,8,9,10,11,12,13], such as reducing satellite navigation accuracy and communication quality [14,15,16,17,18]. In recent years, numerous studies have shown that natural disasters such as earthquakes, typhoons, and tsunamis can trigger significant ionospheric fluctuations, which may potentially serve as a new method for the early warning of major geological hazards [19,20,21,22,23,24,25,26,27,28,29,30,31]. Therefore, a deep understanding of the complex dynamics of the global ionosphere is crucial for the economic and social development of humanity, as well as for national defense and security.

The current ionospheric modeling mainly consists of empirical models and physics-based models. Traditional empirical ionospheric models, such as Klobuchar, NeQuick, Chapman, and International Reference Ionosphere (IRI), are computationally efficient and suitable for scenarios that demand high operational efficiency [32,33,34]. However, their accuracy does not meet the requirements of high-demand navigation and positioning services. Mathematical algorithms such as spherical cap harmonic analysis, semi-parametric estimation, low-order and high-order polynomial functions, trigonometric series, principal component analysis, support vector machines, and autoregressive moving average have been applied in ionospheric modeling [35,36,37,38,39]. Ionospheric models have been developed for regions such as China, Australia, Europe, and South America, offering higher accuracy than traditional empirical ionospheric models. However, function-based mathematical models tend to smooth ionospheric structures, losing local fine-scale characteristics and failing to accurately represent the ionosphere’s responses to extreme space weather and major natural disasters. In response, researchers have developed physics-based models based on the energy conservation equation, such as the Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM) [40], Ground-to-Atmosphere-Ionosphere for Aeronomy (GAIA [41], and Whole Atmosphere Community Climate Model (WACCM-X) [42]. These models are typically global in scale, which results in long computation times and relatively low spatiotemporal resolution. Additionally, physics-based models rely on initial state inputs, leading to an accumulation of simulation errors over time, which limits their ability to fully meet the demands of regional real-time services.

Deep learning technology simulates the structure and function of the human brain based on Artificial Neural Networks (ANNs). By constructing multi-layered networks (often referred to as deep neural networks), it learns complex patterns and representations [43,44,45]. In particular, the 2024 Nobel Prize in Physics was awarded to two pioneers in artificial intelligence, John J. Hopfield and Geoffrey E. Hinton. Likewise, deep learning technology has shown remarkable potential in the field of ionospheric modeling. Numerous high-precision models have been developed at single-station, regional, and global scales, targeting ionospheric parameters such as Total Electron Content (TEC), the critical frequency of the F2 layer (foF2), the height of the F2 peak electron density (hmF2), and electron density (Ne) [8,46,47,48,49,50]. For example, Xia et al. constructed a global TEC forecasting model using an encoder–decoder structure with convolutional long short-term memory (ED-ConLSTM) in deep learning. The results showed that the model’s root mean square error (RMSE) was reduced by 51.3% compared to IRI-2016 [51]. Weng et al. used a Multi-Model Adaptive Genetic Algorithm Backpropagation Neural Network (MMAdapGA-BP-NN) model to predict at the Athens station, and the results showed that the RMSE of this model was reduced by 72.13% compared to the IRI model [52]. The excellent performance of deep learning in ionospheric modeling has also been validated in various regions, including Athens, Bangalore, and China [52,53,54].

This paper aims to review the current progress of deep learning in the field of ionospheric modeling. It traces the development of ionospheric modeling based on deep learning technology from a historical perspective, discusses the data challenges facing this technology, and examines its applications and challenges in ionospheric modeling. Finally, it provides an outlook on future development directions.

2. Data Challenges in Ionospheric Modeling

2.1. Primary Data Sources

Ionospheric research began in the early 20th century and has gradually expanded with the development of science and technology and changing scientific needs. In the early years, the ionosonde was the primary instrument for ionospheric detection. The use of ionosondes dates back to the 1920s, when high-frequency radio waves were transmitted and their return time after reflection in the ionosphere was measured to obtain vertical profiles of ionospheric electron density. Currently, multiple ionosonde networks around the world, such as the Global Ionosphere Radio Observatory in the United States (https://giro.uml.edu/, accessed on 1 July 2024), continue to provide observational data.

Since the 1990s, the development of Global Navigation Satellite Systems (GNSS) has provided new means for ionospheric detection. GNSS ionospheric detection technology measures the delay of satellite signals as they pass through the ionosphere, allowing the calculation of TEC and enabling the large-scale monitoring of the ionosphere. GNSS observation networks have global coverage, providing continuous data support for ionospheric variation studies in different regions. The International GNSS Service (IGS) provides global GNSS observational data, and many countries or regions, such as the United States, China, the European Union, Japan, Australia, and New Zealand, have established dense GNSS networks that support multi-scale and multi-latitude studies of ionospheric changes [55].

In the 21st century, Radio Occultation (RO) technology has further enhanced the precision and coverage of ionospheric detection. RO technology utilizes low Earth orbit satellites to receive or transmit signals along their paths as they pass near the Earth’s edge. By analyzing the refraction effects that occur as the signals traverse the ionosphere, vertical electron density distributions of the ionosphere can be obtained. This method provides high-resolution three-dimensional ionospheric profiles, covering global regions, including low latitudes. Major RO constellations today include Challenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC-1), Constellation Observing System for Meteorology, Ionosphere, and Climate-2 (COSMIC-2), Swarm Satellite Constellation Mission (SWARM), Fengyun-3C (FY-3C), and Fengyun-3D (FY-3D). Some sources of ionospheric data are summarized in Table 1.

2.2. Data Preprocessing Algorithms

Due to the influence of external environments or instrument hardware errors, ionospheric data often contains noise. Therefore, it is a crucial step to eliminate observational noise before constructing ionospheric models. Common methods for ionospheric denoising include Long Short-Term Memory (LSTM) networks, Recurrent Neural Networks (RNN), wavelet transforms, Denoising Convolutional Neural Networks (DnCNN), and Fast Total Variation (FTV). Numerous studies have shown that after applying these denoising algorithms, the accuracy of ionospheric models is significantly improved [56,57].

The sparse or uneven distribution of observational data in the research region is a common phenomenon and an important preprocessing step in ionospheric modeling. Techniques such as spatial interpolation, Generative Adversarial Networks (GANs), and virtual reference stations are commonly used for data completion. For example, GANs can effectively improve the accuracy of TEC maps by filling in large missing areas of ionospheric data over oceans [58]. The use of virtual observation stations to fill data gaps enhances the spatial coverage of Global Ionosphere Models (GIMs), improving the model’s accuracy and real-time performance over large spatial areas. With the increasing diversification of ionospheric detection technologies, integrating multi-modal data to construct ionospheric models has become one of the trends. In this context, self-attention mechanisms help weight different modal data to ensure the complementarity of data from various sources, thus enhancing data fusion accuracy [59].

3. Progress of Ionospheric Modeling Based on Deep Learning Technology

The development of ionospheric modeling has primarily shifted from traditional empirical and physics-based models to data-driven methods. Traditional physics-based models (e.g., TIE-GCM) [60] and empirical models (e.g., IRI) [61] have demonstrated strong capabilities in reproducing multi-scale ionospheric dynamic features under various space conditions, playing a crucial role in advancing our understanding of global ionospheric convection. However, these traditional models are limited by their spatial-temporal resolution and prediction accuracy, making them insufficient to meet the demands of real-time, high-accuracy navigation services, particularly in the case of the TIE-GCM model. Ionospheric data-assimilation models, like the Global Assimilation of Ionospheric Measurements (GAIM) [62,63], Ionospheric Data Assimilation Three-Dimensional (IDA3D) [64], and Ionospheric Data Assimilation Four-Dimensional (IDA4D) [65,66], integrate observational data with physical and empirical models to estimate the ionosphere’s state. Compared to traditional models, these approaches utilize advanced statistical techniques, including Kalman filtering, ensemble methods, and variational approaches, to optimize predictions and achieve higher accuracy.

With advancements in satellite and ground-based monitoring technologies, ionospheric observation data have become increasingly abundant. Deep learning technology, known for its ability to handle complex nonlinear data, has found broader applications in ionospheric modeling. Deep learning models, built on Artificial Neural Networks (ANNs), offer superior capabilities in processing nonlinear functions compared to traditional ionospheric prediction methods [67]. By dynamically adjusting internal connection weights, ANNs can effectively capture and simulate nonlinear relationships within complex data, overcoming the limitations of traditional methods when dealing with nonlinear data [68,69,70]. The development and application of ANNs have provided new perspectives for ionospheric forecasting, significantly improving model accuracy and adaptability under complex spatiotemporal conditions.

Over the past three decades, numerous high-value models have emerged, with the majority of the model architectures focusing on the following types: Backpropagation Neural Networks (BPNN) [71], Convolutional Neural Networks (CNN) [72], RNN [73], LSTM [74], GANs [75], and Autoencoders [76]. These networks have further given rise to a variety of model structures, as illustrated in Figure 1. The following sections will provide a detailed discussion of the development of these neural networks in ionospheric modeling.

3.1. Backpropagation (BP) Neural Network

The BP neural network is a type of multi-layer feedforward neural network optimized through error backpropagation to minimize output error, allowing it to model and predict complex nonlinear problems effectively. The algorithm, proposed by Rumelhart et al. in 1986, addressed the challenge of weight adjustment in multi-layer neural networks, becoming one of the foundational methods in neural network algorithms [71]. In the field of ionospheric modeling, the application of BP neural networks dates back to the 1990s, when researchers began conducting preliminary experiments with limited ionospheric observation data to verify the network’s suitability for modeling ionospheric parameters. For example, in 1998, Cander et al. used a BP neural network to perform short-term predictions of single-station TEC data, achieving results that closely matched the observed values [70]. Entering the 21st century, with the widespread use of GNSS and other devices, researchers gained access to more extensive datasets, leading to breakthroughs in regional ionospheric modeling using BP neural networks. These advancements not only enhanced prediction accuracy but also enabled the capture of spatial distribution characteristics of ionospheric variations within regions [68,77,78,79]. For example, in 2007, Habarulema et al. developed a regional Vertical Total Electron Content (VTEC) model using data from multiple observation stations, achieving prediction accuracy that surpassed that of the IRI model [68].

After 2010, data fusion techniques began to integrate with BP neural networks, and optimization algorithms were introduced to enhance network stability and predictive accuracy [80,81,82,83]. For instance, in 2015, Huang et al. proposed a hybrid model optimized with a genetic algorithm (GA), achieving significantly lower prediction errors during periods of low solar activity [84]. Recently, BP neural networks have been increasingly combined with various optimization algorithms, leading to a trend in hybrid model applications. In 2023, Xu et al. applied a BP-NN-GA and RBF-NN to develop an Ionospheric Effective Height (IEH) model, which markedly improved prediction accuracy [85]. The same year, Weng et al. introduced a hybrid model combining BP neural networks with a Multi-Mutation, Multi-Model Adaptive Genetic Algorithm (MMAdapGA), and MMAdapGA-BP-NN. This model significantly reduced RMSE across different years, offering considerable performance gains over standalone models [52]. A timeline of BP neural network milestones in ionospheric modeling is shown in Figure 2. Additionally, Table 2 summarizes some typical BP neural network-based ionospheric models and their accuracy for reference.

In summary, the development of BP neural networks in ionospheric modeling has undergone a multi-stage evolution from single-site prediction to regional modeling and then to the integration of multiple optimization algorithms. This progression has steadily improved prediction accuracy and stability, providing a reliable technological approach for the precise forecasting of ionospheric parameters.

Figure 2

Milestone development of BP neural networks in ionospheric modeling. (a) The standard fully connected feed-forward network with backpropagation (from [86]); (b) The multi-layer feed-forward network architecture trained using BP neural networks (from [79]); (c) A BP neural network model with two hidden layers optimized through the EPB algorithm (from [87]); (d) A combined intelligent prediction model based on Multi-Mutation, Multi-Model Adaptive Genetic Algorithm (MMAdapGA) and BP neural network (BPNN) (from [52]).

[Figure omitted. See PDF]

Table 2

Some typical BP neural network-based ionospheric models and their accuracy.

Source Method Main Features and Results
Weng et al. [52] MMAdapGA-BP-NN

  • The MMAdapGA-BP-NN requires significantly fewer iterations compared to the neural network optimized by a single mutation genetic algorithm, typically ranging from 10 to 30.

  • The RMSE of MMAdapGA-BP-NN in 2015 and 2020 are 2.84 TECU and 0.85 TECU.
Lei et al. [88] GA-BP

  • The GA-BP algorithm can better address the issues of low accuracy in empirical models, cumbersome calculations in spherical harmonic function models, and insufficient computational efficiency in other models.

  • The RMSEs of short-term prediction of GA-BP model proposed in this paper are 67.61%, 36.33%, and 73.68%, higher than that of ARIMA model in different latitudes.
Zhang et al. [89] AdaBoost-BP

  • The AdaBoost-BP overcomes the issues of local minimization and weak network generalization ability in BPNN.

  • The AdaBoost-BP model improves the accuracy by 1.66%, and the error rate decreases by 3.25% compared to the BPNN model.
Huang et al. [84] GA-BP

  • The GA-BP algorithm overcomes the issue of BPNN being prone to falling into local minima.

  • The average relative error of BJFS and XIAN is within 10%, and the RMSE does not exceed 2 TECU.
Long et al. [90] Inte-BP

  • The Inte-BP model can produce more stable and accurate predictions compared to the BPNN model, which only obtains weights and bias parameters after a specific training session.

  • The Inte-BP model improves RMSE by 17%, 13%, and 23% over the BPNN model.
Xu et al. [85] BP-NN-GA

  • The flexible IEH model of RBF-NN and BP-NN-GA addresses the issue of the fixed IEH model being unreasonable in fitting the variations in the ionosphere.

  • The RMSE values calculated based on the flexible IEH models of RBF-NN and BP-NN-GA are approximately 1.8 and 1.9 TECU.
Zhao et al. [80] AdaBoost-BP

  • The AdaBoost-BP can improve accuracy by averaging the decisions of a group of BPNN.

  • The AdaBoost-BP prediction absolute error at Taipei station from the low latitude is 0.78 MHz.
Fang et al. [91] BP with Single Point Extrapolation

  • The BP with Single Point Extrapolation treats the prediction result of the last time as the real frequency value for the next time.

  • The average absolute error is 0.25234 MHz, the average relative error is 6.77812%, and the root mean square error is 0.40208 MHz.
Chen et al. [92] GA-BP

  • The genetic algorithm was applied to optimize the weights and thresholds of the BP neural network to obtain better predictive performance.

  • The RMSE of GA-BP reached 0.6059, reducing the prediction error by 50% compared to BP.

3.2. Convolutional Neural Networks (CNNs)

CNNs are a deep learning model that excels at processing data with grid-like structures, such as images. Through multiple layers of convolutional operations, CNNs can extract local features, and they have been widely used in applications such as image classification, object detection, and speech recognition. In 1998, Yann LeCun et al. proposed the LeNet-5 network, which demonstrated the advantages of convolutional layers in feature extraction for handwritten digit recognition, laying the foundation for CNNs in data processing [93]. However, hardware limitations at the time made it difficult to train large-scale CNNs, and the understanding of CNNs was still limited, hindering their practical applications. In 2012, Krizhevsky et al. introduced AlexNet, which won the ImageNet ILSVRC image classification challenge and propelled CNNs into the spotlight [94]. Since then, models such as Google’s GoogLeNet [95] and Microsoft’s ResNet [96] have further increased the complexity and accuracy of CNNs, significantly advancing the development of CNNs. CNNs have also demonstrated excellent feature extraction capabilities in ionospheric modeling, effectively capturing global spatial distribution features and regional anomalies in the ionosphere, such as equatorial ionization anomalies and Weddell Sea anomalies. In severe space environments (e.g., solar flares, geomagnetic storms), CNNs, with the aid of activation functions like ReLU, can model small- to medium-scale ionospheric dynamics and enhance prediction accuracy. The development timeline of typical ionospheric models based on CNN networks is shown in Figure 3. Additionally, Table 3 summarizes some typical ionospheric models based on CNNs and their accuracy for reference.

Figure 3

The development history of CNN in ionospheric modeling. (a) CNN-LSTM hybrid deep learning model architecture (from [53]); (b) Mask R-CNN neural network architecture (from [97]); (c) WOA-CNN-LSTM neural network architecture (from [98]).

[Figure omitted. See PDF]

Although CNNs perform exceptionally well in modeling spatial features of the ionosphere, they are less sensitive to temporal dimensions and struggle to capture time-related features. To address this limitation, researchers typically employ hybrid models based on CNNs to enhance their spatiotemporal feature extraction capabilities, such as CNN-LSTM [99], ED-ConvLSTM [51,100], CNN-GRU [101], and CNN-BiLSTM-TPA [102]. Despite this, CNNs still face several challenges in ionospheric modeling applications. Firstly, unlike BP neural networks, CNNs require grid-like data as input, whereas ionospheric observation data are often sparse and unbalanced, necessitating the use of strategies such as multi-source data integration or interpolation. Secondly, with increasing network depth and parameters, the computational complexity of CNNs rises, resulting in higher demands on computational resources, making them unsuitable for near-real-time navigation and positioning services. Additionally, CNNs have limited generalization ability and may perform poorly under varying spatiotemporal conditions, requiring optimized training strategies to improve their adaptability. The commonly used research schemes and accuracy of CNNs in ionospheric modeling are summarized in Table 3 for reference.

In summary, the CNN model, through the combination of other algorithms and optimization strategies, has shown significant potential in ionospheric modeling, although there is still room for improvement in its generalization ability and real-time processing capabilities.

Table 3

Some typical ionospheric models based on CNN neural networks and their accuracy.

Source Method Main Features and Results
Ren et al. [44] Mixed-CNN-BiLSTM

  • The model is trained using the longest available (25 years) Global Ionospheric GIM-TEC from storm periods.

  • The model increased R2 by 3.49% and reduced the RMSE by 13.48% in long-term forecasting.
Xia et al. [51] ED-ConvLSTM

  • The ED-ConvLSTM model is used to forecast TEC maps 1–7 days in advance through iterations.

  • The RMSE of the ED-ConvLSTM model was reduced by 51.5% in 2014 and 43% in 2018 compared to the IRI2016 model.
Boulch et al. [103] CNN+RNN

  • The model is used to predict a sequence of global TEC maps that are consecutive to an input sequence of TEC maps, without introducing any prior knowledge other than Earth rotation periodicity.

  • The proposed model has better predictive performance in high-latitude regions.
Ruwali et al. [53] LSTM-CNN

  • The LSTM-CNN addresses LSTM’s limitation of passing only temporal information, often missing spatial features from previous TEC values.

  • The LSTM-CNN outperformed the other models, achieving a minimum RMSE of 1.5 TECU and R2 = 0.99.
Li et al. [100] ED-ConvLSTM

  • The ED-ConvLSTM can simultaneously consider spatiotemporal characteristics when predicting TEC.

  • The ED-ConvLSTM outperforms ConvGRU, LSTM, GRU, and C1PG in terms of RMSE, MAE, MAPE, and SSIM.
Tang et al. [104] CNN-LSTM-Attention

  • The model can optimize the weight distribution of the input information at the fully connected layer to predict ionospheric TEC and reflect the spatio-temporal relationships between GNSS stations.

  • The RMSE of CNN-LSTM-Attention is 1.87 TECU, and the R2 is 0.90.
Kaselimi et al. [101] CNN-GRU

  • The CNN-GRU model is capable of providing accurate predictions of TEC values even under intense conditions.

  • The MAE is relatively low, with a minimum MAE between 0.2 and 0.5 TECU.
Xu et al. [102] CNN-BiLSTM-TPA

  • The CNN-BiLSTM-TPA addresses the issue of typical attention mechanisms failing to identify temporal patterns that are valuable for prediction.

  • The CNN-BiLSTM-TPA reduced the RMSE by an average of 17.4%, 15.03%, 22.81%, and 14.33% across the three stations in January, March, June, and October of 2008, respectively, compared to the IRI-2020 model.
Mao et al. [99] CNN-LSTM

  • The CNN-LSTM has good generalization ability in predicting electron density profiles.

  • The maximum improvement in RMSE in 2017 reached 68.53%, and the average improvement reached 69.55%.

3.3. Recurrent Neural Network (RNNs) and Long Short-Term Memory Network (LSTM)

RNNs are deep learning models designed to process time-series data. Their internal self-connection mechanism allows them to retain information from previous time steps, which influences current computations, making them suitable for tasks such as time-series analysis and natural language processing. The concept of RNNs was first introduced by John Hopfield in 1982, but early applications of RNNs were limited due to computational resource constraints [105]. With advancements in computational power, the application of RNNs in time-series data processing has become increasingly widespread. Particularly in ionospheric modeling, RNNs have been employed for the temporal prediction of electron density, owing to their ability to retain time-dynamic information. For instance, in 2018, Tianjiao Yuan et al. constructed the first single-site ionospheric TEC 24 h prediction model using RNNs. The results demonstrated that RNNs outperformed traditional BPNN in predicting ionospheric disturbances [106].

Despite the advantages of RNNs in time-series modeling, their recurrent structure makes them prone to issues such as vanishing or exploding gradients. In 1997, Hochreiter et al. proposed LSTM networks to address these problems [107]. By introducing mechanisms such as the input gate, forget gate, and output gate, LSTM effectively mitigates the vanishing gradient issue, enabling the network to capture long-term dependencies. This makes LSTM particularly suitable for modeling time-series data with long-term dependencies. The ionosphere, influenced by multiple factors such as solar radiation, ionization, and the geomagnetic field, exhibits distinct periodic variations and nonlinear disturbances, which LSTM is well-equipped to handle. In 2017, Sun et al. used LSTM to predict the vertical TEC in the Beijing area, achieving accuracy with a root mean square error (RMSE) below 3.5 during periods of low solar activity [74]. Additionally, in 2020, Tang et al. found that under complex space weather conditions such as geomagnetic storms, LSTM outperformed ARIMA and seq2seq models, providing accurate predictions of ionospheric dynamics [108]. In recent years, the application of LSTM in ionospheric modeling has expanded. In 2021, Wen et al. used LSTM for single-site ionospheric TEC prediction, addressing long-term dependency issues with significant results [109]. In 2022, Reddybattula et al. developed an LSTM model for ionospheric TEC prediction in the low-latitude ionosphere of India, demonstrating superior performance compared to the IRI-2016 model, with results closely aligned with GPS-TEC data and a lower average RMSE [6]. A milestone in using LSTM for ionospheric modeling is illustrated in Figure 4. Additionally, Table 4 summarizes several typical LSTM-based ionospheric models and their accuracy levels for the reader’s reference.

In summary, RNNs and LSTM provide powerful tools for time-series modeling, with LSTM in particular excelling in complex, dynamic ionospheric environments by capturing the ionosphere’s long-term and nonlinear variation characteristics.

Figure 4

Typical development of LSTM neural networks in ionospheric modeling. (a) Single LSTM network architecture (from [74]); (b) Sequence-to-sequence LSTM model composed of two stacked LSTM layers (from [110]); (c) CNN-LSTM-Attention neural network (from [104]); (d) Structure diagram of the Bidirectional Long Short-Term Memory (BiLSTM) network (from [111]).

[Figure omitted. See PDF]

Table 4

Some typical ionospheric models based on LSTM neural networks and their accuracy.

Source Method Main Features and Results
Liu et al. [9] LSTM-NN

  • The LSTM-NN is able to improve the prediction of SH coefficients by including solar and magnetic indices.

  • The first/second hour TEC RMSE is 1.27/2.20 TECU during storm time and 0.86/1.51 TECU during quiet time.
Sun et al. [112] Bi-LSTM

  • The Bi-LSTM can learn from both past and future information so that it can predict TEC more precisely.

  • The Bi-LSTM can capture the cyclic change feature of TEC successfully.
Xie et al. [14] Piecewise LSTM

  • The piecewise LSTM model differs from the regular temporal LSTM model in that the forecast error is independent of the number of hours in the forecast day.

  • The piecewise LSTM has a forecast error of less than 3 TECU.
Yuan et al. [106] RNN

  • The first 24 h forecasting model for the TEC at Beijing station based on RNN.

  • The RMSE of RNN model is decreased by 0.36∼0.47 TECU
NATH et al. [113] EEMD-LSTM

  • The EEMD-LSTM overcomes the issue that single methods are relatively inadequate in predicting ionospheric parameters due to the dynamic nature of ionospheric time series data.

  • The RMSE of EEMD-LSTM reached 0.6904, and the R2 reached 0.9969.
Ruwali et al. [53] LSTM-CNN

  • The LSTM-CNN addresses the issue that LSTM only passes temporal information to its layers, often missing the spatial or local hidden features from the TEC values of previous hours.

  • The LSTM-CNN outperformed the other models, achieving a minimum RMSE of 1.5 TECU and R2 = 0.99.
Reddybattula et al. [6] LSTM

  • The LSTM is an improved regional and global ionospheric forecasting model.

  • The RMSE of the LSTM is 1.6149, and the highest CC is 0.992.
Shi et al. [114] ICEEMDAN-LSTM

  • The model can utilize the ICEEMDAN decomposition algorithm to expand foF2 time series data into multi-dimensional space and use the LSTM algorithm to preserve long-term data information.

  • The model has an RMSE of 0.40 MHz and an R2 of 0.98 across the four stations in 2014.
Lu et al. [115] Seq2Seq-LSTM-Attention

  • The Seq2Seq-LSTM-Attention model could focus on the importance of different parts of the sequence.

  • The prediction accuracy of the Seq2Seq-LSTM-Attention model is superior to that of LSTM, BiLSTM, and Seq2Seq-CNN-Attention.

3.4. Autoencoder and Generative Adversarial Network (GAN)

An Autoencoder is a neural network used for data compression and reconstruction, capable of extracting efficient, abstract features from unlabeled data. In recent years, Autoencoders have shown significant potential in ionospheric modeling. For example, studies have employed Autoencoder algorithms to convert IGS-TEC maps into MIT-TEC maps, yielding predictions that outperform the IRI model [76]. Abri et al. used a deep Autoencoder to extract features from TEC data and explored the relationship between earthquakes and the ionosphere in combination with a stacked LSTM model [116]. Additionally, Reid et al. introduced a ConvLSTM Autoencoder that could reproduce nominal TEC data sequences, further demonstrating its capability in ionospheric data reconstruction [117]. However, the complexity and nonlinearity of ionospheric data present challenges in training Autoencoder models effectively.

The Generative Adversarial Network (GAN), proposed by Goodfellow et al. in 2014, is capable of generating new samples based on a learned model and is widely applied in image and video generation [75]. GAN has also proven effective in ionospheric modeling. For instance, Pan et al. used GAN to restore missing data in TEC maps, demonstrating superior performance over traditional methods, particularly in areas with extensive data gaps [118]. Yang et al. combined DCGAN and WGAMN-GP to generate MIT global TEC maps, achieving performance that surpassed IGS rapid products [119]. The DCGAN model can be referenced in Figure 5.

3.5. Comparative Performances of Global or Regional Models

Section 3.1, Section 3.2, Section 3.3 and Section 3.4 demonstrate that various neural networks have been applied to develop global and regional ionospheric models, achieving different levels of prediction accuracy. To enhance readers’ understanding of the performance of these models in specific regions, this study summarizes the prediction accuracy of various ionospheric models at single-station, regional, and global scales. The comparative results are presented in Table 5.

From Table 5, several key conclusions can be drawn: (1) Deep learning outperforms empirical models. Deep learning techniques significantly outperform empirical models in ionospheric modeling. This is attributed to their powerful data-fitting capabilities, which enable them to effectively handle complex nonlinear relationships and diverse data influenced by multiple factors in the ionosphere. Additionally, their strong generalization ability and self-updating capacity allow them to adapt to varying ionospheric conditions across regions and incorporate new data for real-time training and updates. (2) Suitability for multi-scale ionospheric modeling. Deep learning techniques are well-suited for developing ionospheric models at various scales. For example, the global ionospheric models developed using LSTM-NN [9], ED-ConvLSTM [51], and Mixed-CNN-BiLSTM [44] achieved accuracy ranging from 0.86 to 3.122 TECU, significantly surpassing the performance of traditional models such as IRI-2016 and NeQuick-2. (3) Regional variations in model performance. Different deep learning models exhibit varying levels of performance across different regions. These discrepancies may be influenced by the capabilities of the selected neural network architectures, as well as by differences in their internal configurations and structural designs.

4. Applications of Ionospheric Models Based on Deep Learning Techniques

Ionospheric models constructed by deep learning techniques demonstrate significant application potential across various fields. These models not only enhance predictive capabilities for complex spatiotemporal dynamics but also provide technical support for improving navigation accuracy, advancing space weather monitoring, and developing disaster early-warning systems. This paper provides a detailed discussion of the applications of deep learning in enhancing navigation service quality, monitoring space weather, and providing short-term natural disaster warnings, as illustrated in Figure 6.

4.1. Enhancing Navigation Service Quality

Ionospheric models based on deep learning have broad applications in enhancing navigation service quality, particularly in correcting ionospheric delays and improving navigation accuracy. When navigation signals pass through the ionosphere, electromagnetic waves experience delays due to effects such as reflection, refraction, and scattering, which adversely impact positioning accuracy. Traditional ionospheric models, such as IRI-2016, perform well under specific conditions. However, due to their limited ability to model complex nonlinear features, they struggle to maintain consistent prediction accuracy across different geographical regions and spatial environments. Deep learning models, with their powerful capabilities in nonlinear feature extraction and spatiotemporal dynamic modeling, have gradually become an important tool for addressing ionospheric modeling challenges.

Studies have shown that deep learning-based ionospheric models achieve higher accuracy in predicting TEC compared to traditional models [14,15,16,123]. Shi et al. developed a TEC prediction model combining particle swarm optimization and neural networks, which significantly improved prediction accuracy compared to the IRI-2016 model, demonstrating the superiority of deep learning models in ionospheric correction [124]. Li et al. integrated CNN and LSTM structures to build the WOA-CNN-LSTM model for precise TEC prediction in low-latitude regions. The results showed that the root mean square error (RMSE) was within 1.96 TECU, effectively improving regional navigation positioning accuracy [98]. Additionally, Xie et al. developed a piecewise LSTM model based on multi-latitude GNSS data, achieving robust TEC prediction in different regions. Compared to conventional LSTM and RNN models, the prediction errors were significantly reduced across various latitudes, further enhancing navigation accuracy in low-, middle-, and high-latitude regions [14].

Deep learning also excels in modeling ionospheric dynamics under complex space weather conditions. Srivani et al. investigated an LSTM-based deep learning model, and experiments demonstrated that this model achieved a correlation coefficient of 0.99 with observed values in predicting ionospheric delays in GPS signals, with a prediction error within 2–3 TECU, significantly outperforming the traditional IRI model [16]. Nevertheless, deep learning still faces challenges in global ionospheric modeling, particularly in improving prediction accuracy in high-latitude regions. Future research could optimize ionospheric models and further enhance navigation service quality by employing strategies such as multi-source data fusion and multi-model collaboration.

Figure 6

Applications of ionospheric models based on deep learning. In the area of enhancing navigation service quality, (a,b) depict the impact of machine learning-based ionospheric tomography on positioning accuracy and convergence time (from [123]). while (c) shows GNSS positioning data trajectories predicted by a DNN (from [125]); For space weather monitoring, (d,e) display VTEC distribution differences between four GIMs predicted by the Ion-LSTM model and CODG during geomagnetic storms at different times (from [10]). In the field of short-term natural disaster warnings, (f) demonstrates that changes in TEC are attributed to tsunami waves in time and space (from [25]), (g) shows four snapshots simulating TEC disturbances taken at different times during a tsunami (from [126]), (h,i) illustrate spatial TEC maps of seismic ionospheric anomalies at different UT hours before an earthquake epicenter (from [127]); (j) depicts volcanic surface deformation obtained using CNN (from [128]), and (k) shows volcanic surface displacement results predicted by GPS, CSK InSAR, and CNN methods (from [128]).

[Figure omitted. See PDF]

4.2. Space Weather Monitoring

As space weather events increasingly impact critical infrastructure such as aerospace, communication, and power systems, establishing an effective space weather forecasting system has become essential. In recent years, monitoring and analysis based on multi-source remote sensing data, including satellite observations, GNSS, and ground-based geomagnetic monitoring stations, have become a focal point in this field. Studies indicate that events like solar storms and coronal mass ejections (CMEs) can trigger ionospheric disturbances, which subsequently affect the stability of high-frequency communications, satellite navigation, and power systems. Therefore, constructing a real-time warning system using multi-source data fusion and advanced machine learning techniques can enhance forecasting capabilities for extreme events, thereby reducing economic losses and mitigating the impact on critical infrastructure.

The application of deep learning techniques in space weather forecasting is advancing rapidly, with significant progress made in predicting the impacts of ionospheric disturbances, geomagnetic storms, and solar activity on Earth’s space environment [5,6,8,9,10,76,129,130,131]. Yuan Tianjiao et al. pioneered a 24 h single-station TEC forecasting model using RNN, leveraging interplanetary solar wind parameters, geomagnetic activity indices, and ionospheric TEC data. This model substantially reduced forecast errors during ionospheric storms, with an RMSE of 0.2 TECU lower than that of traditional BPNN models [106]. The study demonstrated that incorporating solar wind parameters as predictors can further reduce ionospheric forecasting errors, providing a valuable reference for applying deep learning to short-term ionospheric forecasting.

In the field of space weather forecasting using multi-source data, Tang et al. proposed a CNN-LSTM-Attention model that integrates GNSS data and TEC time series, along with geomagnetic indices such as Bz, Kp, and Dst. This model achieved high predictive accuracy under varying geomagnetic conditions, with a coefficient of determination (R2) of 0.9 and a RMSE of only 1.87 TECU [104]. The model demonstrated strong predictive capability during both geomagnetic storm and quiet periods, showcasing the broad applicability of deep learning in space weather forecasting.

Overall, the application of deep learning in space weather forecasting has shown great potential, particularly in achieving high accuracy in ionospheric TEC prediction and geomagnetic storm detection. However, key challenges remain in real-time data processing, model interpretability, and multi-source data integration for practical applications. Although deep learning in space weather forecasting is still in a rapid developmental phase and has yet to reach full maturity, its future application prospects are highly promising.

4.3. Short-Term Early Warning of Major Natural Disasters

The gases, radiation releases, and atmospheric gravity waves generated before and after geological disasters can disrupt the dynamic equilibrium of the ionosphere. Monitoring these ionospheric disturbances caused by geological activities provides a new perspective for disaster monitoring. In the study of ionospheric anomalies, the powerful nonlinear processing capabilities of neural networks offer a crucial method for analyzing the coupling mechanisms of ionospheric anomalies induced by geological activities.

Geological activities such as earthquakes, tsunamis, and volcanic eruptions propagate upward to the ionosphere through acoustic and gravity waves, causing significant electron density disturbances that can even reach global scales [132]. Tsunamis triggered by earthquakes generate gravity waves, and their interference characteristics in the ionosphere contribute to tsunami early warning systems [133]. Similarly, Acoustic-Gravity waves produced by volcanic eruptions can also disturb the ionosphere, such as the persistent impact of the shockwave from the 2022 Tonga eruption on the global ionosphere [134]. Additionally, an “ionospheric hole” phenomenon, where the electron density rapidly decreases, may occur above the epicenter of earthquakes and tsunamis [135].

Deep learning neural networks have shown tremendous potential in analyzing ionospheric disturbances triggered by geological activities. These technologies can effectively classify and identify the signal features of events such as earthquakes and volcanic eruptions, extracting patterns from complex nonlinear data to reveal the coupling mechanisms between geological activities and the ionosphere, while enhancing the effectiveness of early warning systems. For example, CNN and LSTM have been used to classify volcanic and seismic signals, demonstrating exceptional classification performance [136]. Bayesian Neural Networks (BNN) can quantify uncertainties during the monitoring process, providing reliable support for volcanic eruption predictions [137]. Furthermore, LSTM networks have been employed to detect ionospheric anomalies induced by earthquakes, successfully capturing the abnormal changes in electron density and magnetic fields before and after the disaster [138]. In specific applications, Deep Convolutional Neural Networks (DCNN) combined with RNN have shown high accuracy in classifying different types of seismic signals [139]. CNN models have been used to identify ionospheric disturbance structures in satellite SAR signals, aiding in the monitoring of ionospheric responses after large-scale earthquakes [140]. Moreover, deep learning methods have demonstrated good performance in earthquake spatiotemporal clustering and aftershock pattern predictions, further verifying their potential in handling complex seismic data [141,142].

Deep learning, combined with GNSS monitoring and machine learning technologies, has shown enormous potential in the early warning of geological disasters. By integrating multi-source data, deep learning models can identify ionospheric anomalies before events such as earthquakes, volcanic eruptions, and tsunamis. This enables the real-time monitoring and early detection of anomalies, providing technical support for the development of efficient geological disaster early warning systems. This, in turn, advances the modernization of disaster prevention and reduction efforts, enhancing the ability to mitigate the impacts of natural disasters.

5. Conclusions and Prospects

The application of deep learning in ionospheric modeling has advanced significantly, particularly in ionospheric detection, geological disaster monitoring, and satellite navigation system enhancement. However, challenges remain in model construction, including the complexity and nonlinearity of ionospheric height, diverse training data requirements, and limited model interpretability, all of which affect prediction reliability. The literature suggests that deep learning shows promising trends in modeling complex ionospheric features, data fusion, and real-time monitoring [143]. With advancements in technology, including improved network architectures and richer training data, the accuracy and reliability of ionospheric modeling are expected to further improve.

  • (1). Integrating multi-modal data fusion with deep learning effectively combines data from diverse sources, such as ground observations, satellite data, and space weather parameters, capturing the spatiotemporal dynamics of the ionosphere. For instance, the hybrid model RFGAN utilizes multi-source TEC data for global fusion, enhancing data integrity and prediction accuracy [144]. Furthermore, deep learning in multi-modal remote sensing data fusion has significantly improved the interpretability of Earth observation data [145]. Multi-modal networks like MANET, which combine meteorological and imagery data, enhance the accuracy of weather system classification [146]. These methods highlight deep learning’s advantages in multisource data fusion, contributing to more precise ionospheric modeling and prediction.

  • (2). The integration of deep learning and transfer learning techniques in data-limited areas effectively addresses shortages and enhances predictive performance. Combining GANs with transfer learning significantly improves ionospheric modeling in data-scarce regions. GANs generate synthetic data that closely resembles real distributions, compensating for deficiencies and enhancing model stability in low-latitude areas [58]. Transfer learning, by utilizing pretrained models and fine-tuning them for specific domains, greatly enhances generalization and prediction accuracy [147]. This combination offers significant advantages in managing spatiotemporal inhomogeneity, thereby enhancing the precision and reliability of ionospheric predictions [148].

  • (3). By integrating traditional physics-based models with deep learning techniques, hybrid models leverage the strengths of both approaches, enhancing the accuracy and feasibility of ionospheric modeling. This integration allows for the reliable application of physical features alongside deep learning’s ability to manage complex nonlinear data, improving model accuracy and stability. Such models excel in data-scarce environments and extreme space weather conditions, significantly enhancing the prediction accuracy of ionospheric TEC and other parameters [51,108]. This hybrid model has promising applications in creating robust real-time early warning systems and supporting navigation and communication.

  • (4). Research on adaptive learning algorithms focuses on real-time adjustment of deep learning model parameters and structures to better handle the complex and unpredictable variations of the ionosphere. This includes online parameter tuning and trajectory tracking via the Lyapunov method, enhancing stability in nonlinear systems [149]. Integrating reinforcement learning techniques allows for dynamic adjustment of the action space and reward function, improving convergence speed and control stability of real-time tuning [150]. Additionally, adaptive activation functions optimize the learning process, accelerating convergence and enhancing accuracy in complex problem-solving [151]. These methods provide a solid foundation for improving the flexibility and responsiveness of models.

Author Contributions

Conceptualization, W.L.; validation, W.L. and R.Z.; formal analysis, Y.S., J.Y. and H.L.; writing—original draft preparation, R.Z. and H.L.; writing—review and editing, W.L., D.Z. and A.H.; supervision, W.L.; funding acquisition, W.L. All authors have read and agreed to the published version of the manuscript.

 Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

 Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables
View Image - Figure 1. Key network model structures in ionospheric modeling based on deep learning.Enlarge this image.

Figure 1. Key network model structures in ionospheric modeling based on deep learning.

View Image - Figure 5. DCGAN model architecture. Blue arrows denote training of DCGAN using the IGS-TEC maps. The discriminator (D) takes both the TEC maps produced by the generator (G) and the true IGS TEC maps and makes prediction whether it is an authentic (true) TEC map or a fake (false) one. Both the discriminator and generator are learned in a competitive way to improve their performance. The brown arrows denote the mapping from z to z* in the context of a particularly incomplete TEC map y, while the red arrows denote the Poisson blending applied the generator produces the fake TEC map G(z*) with the incomplete TEC map y (from [120]).Enlarge this image.

Figure 5. DCGAN model architecture. Blue arrows denote training of DCGAN using the IGS-TEC maps. The discriminator (D) takes both the TEC maps produced by the generator (G) and the true IGS TEC maps and makes prediction whether it is an authentic (true) TEC map or a fake (false) one. Both the discriminator and generator are learned in a competitive way to improve their performance. The brown arrows denote the mapping from z to z* in the context of a particularly incomplete TEC map y, while the red arrows denote the Poisson blending applied the generator produces the fake TEC map G(z*) with the incomplete TEC map y (from [120]).

Some ionospheric data sources and access links.

Date Type Affiliations Date Access URL
GNSS Networks Australian Space Weather Services https://downloads.sws.bom.gov.au/wdc/gnss/data/, accessed on 1 July 2024
Can-Net https://www.can-net.ca/, accessed on 1 July 2024
Canadian High Arctic Ionospheric Network http://chain.physics.unb.ca/chain/pages/data_download, accessed on 1 July 2024
Crustal Dynamics Data Information System https://cddis.nasa.gov/archive/gnss/data/daily/, accessed on 1 July 2024
Dutch Permanent GNSS Array http://gnss1.tudelft.nl/dpga/rinex, accessed on 1 July 2024
GeoNet New Zealand https://www.geonet.org.nz/data/types/geodetic, accessed on 1 July 2024
INGV-Rete Integrata Nazionale GPS (RING) http://ring.gm.ingv.it/, accessed on 1 July 2024
Institute of Geodynamics, National Observatory of Athens https://www.gein.noa.gr/services/GPSData/, accessed on 1 July 2024
Instituto Tecnologico Agrario de Castilla y Leon ftp://ftp.itacyl.es/RINEX/, accessed on 1 July 2024
International GNSS Service(IGS), UNAVCO https://www.unavco.org/data/gps-gnss/gps-gnss.html, accessed on 1 July 2024.
National Geodetic Survey https://geodesy.noaa.gov/corsdata/, accessed on 1 July 2024.
Pacific Northwest Geodetic Array (PANGA) https://www.geodesy.org/about, accessed on 1 July 2024.
Scripps Orbit and Permanent Array Center http://garner.ucsd.edu/, accessed on 1 July 2024.
SWEPOS Sweden https://swepos.lantmateriet.se/, accessed on 1 July 2024.
The Western Canada Deformation Array (WCDA) ftp://wcda.pgc.nrcan.gc.ca/pub/gpsdata/rinex, accessed on 1 July 2024.
TrigNet South Africa ftp://ftp.trignet.co.za, accessed on 1 July 2024.
Ionosonde Global Ionospheric Radio Observatory (GIRO) http://giro.uml.edu/, accessed on 1 July 2024.
CHAMP CHAMP Mission Data from ISDC https://isdc.gfz-potsdam.de/champ-isdc/, accessed on 1 July 2024.
COSMIC University Corporation for Atmospheric Research https://www.cosmic.ucar.edu, accessed on 1 July 2024.
GRACE International Science Data Center (ISDC) https://isdc.gfz-potsdam.de/, accessed on 1 July 2024.
FY-3C National Center for Space Weather (NCSW) http://www.nsmc.org.cn/, accessed on 1 July 2024.

Comparison of prediction performance of various models in different regions.

Scope Author Model RMSE (TECU)
High Low
global Liu et al. [9] LSTM-NN 1.510 0.860
global Xie et al. [51] ED-ConvLSTM 4.360 1.650
global Ren et al. [44] Mixed-CNN-BiLSTM 3.589 3.122
Global Liu et al. [9] IRI-2016/Nequick-2 9.210 5.500
China Li et al. [98] WOA-CNN-LSTM 1.960 0.740
Athens Weng et al. [52] MMAdapGA-BP-NN 2.840 0.850
Bangalore Ruwali et al. [53] LSTM-CNN 3.430 1.490
East Asia Li et al. [121] ED-AttConvLSTM 4.613 1.610
China Tang et al. [54] BiConvGRU 5.009 1.636
Beijing Bilitza et al. [122] IRI-2016 11.516 4.720

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© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

Abstract

With the continuous advancement of deep learning algorithms and the rapid growth of computational resources, deep learning technology has undergone numerous milestone developments, evolving from simple BP neural networks into more complex and powerful network models such as CNNs, LSTMs, RNNs, and GANs. In recent years, the application of deep learning technology in ionospheric modeling has achieved breakthrough advancements, significantly impacting navigation, communication, and space weather forecasting. Nevertheless, due to limitations in observational networks and the dynamic complexity of the ionosphere, deep learning-based ionospheric models still face challenges in terms of accuracy, resolution, and interpretability. This paper systematically reviews the development of deep learning applications in ionospheric modeling, summarizing findings that demonstrate how integrating multi-source data and employing multi-model ensemble strategies has substantially improved the stability of spatiotemporal predictions, especially in handling complex space weather events. Additionally, this study explores the potential of deep learning in ionospheric modeling for the early warning of geological hazards such as earthquakes, volcanic eruptions, and tsunamis, offering new insights for constructing ionospheric-geological activity warning models. Looking ahead, research will focus on developing hybrid models that integrate physical modeling with deep learning, exploring adaptive learning algorithms and multi-modal data fusion techniques to enhance long-term predictive capabilities, particularly in addressing the impact of climate change on the ionosphere. Overall, deep learning provides a powerful tool for ionospheric modeling and indicates promising prospects for its application in early warning systems and future research.

Details

Title
Deep Learning Applications in Ionospheric Modeling: Progress, Challenges, and Opportunities
Author
Zhang, Renzhong 1   VIAFID ORCID Logo  ; Li, Haorui 1 ; Shen, Yunxiao 1 ; Yang, Jiayi 1 ; Wang, Li 2   VIAFID ORCID Logo  ; Zhao, Dongsheng 3   VIAFID ORCID Logo  ; Hu, Andong 4 

1  Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming 650093, China; [email protected] (R.Z.); [email protected] (H.L.); [email protected] (Y.S.); [email protected] (J.Y.) 
2  Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming 650093, China; [email protected] (R.Z.); [email protected] (H.L.); [email protected] (Y.S.); [email protected] (J.Y.); Yunnan Province Key Laboratory of Intelligent Monitoring of Natural Resources and Spatiotemporal Big Data Governance (Under Preparation), Kunming 650093, China 
3  School of Environmental Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China; [email protected] 
4  Cooperative Institute for Research in Environmental Sciences (CIRES), CU Boulder, Boulder, CO 80309, USA; [email protected] 
First page
124
Publication year
2025
Publication date
2025
Publisher
MDPI AG
e-ISSN
20724292
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.3390/rs17010124
ProQuest document ID
3153683481
Copyright
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.