Spatio-temporal Graph Neural Networks for Ionospheric TEC Prediction Using Global Navigation Satellite System Observables

Precise modeling of the ionospheric Total Electron Content (TEC) is critical for reliable and accurate GNSS applications. TEC is the integral of the location-dependent electron density along the signal path and is a crucial parameter that is often used to describe ionospheric variability, as it is strongly affected by solar activity. TEC is highly depended on local time (temporal variability), latitude, longitude (spatial variability), solar and geomagnetic conditions. The propagation of the signals from GNSS (Global Navigation Satellite System) satellites throughout the ionosphere is strongly influenced by temporal changes and ionospheric regular or irregular variations. Here, we propose a deep learning architecture for the prediction of the vertical total electron content (VTEC) of the ionosphere based on GNSS data. 

The data used in many deep learning tasks until recently where mostly represented in the Euclidean space. However, geodesy studies data that have an underlying structure that is non-Euclidean space. Geospatial data are large and complex, as in the case of GNSS networks data, and their non- Euclidean nature has imposed significant challenges on the existing machine learning algorithms. The task of VTEC prediction is challenging mainly due to the complex spatiotemporal dependencies and an inherent difficulty in temporal forecasting. Spatial-temporal graph neural networks (STGNNs) aim to learn hidden patterns from spatial-temporal graphs. The key idea of STGNNs is to consider spatial and temporal dependency at the same time. Spatial Dependency: Assuming a network of permanent stations of International GNSS Service (IGS), each station represents a node of the graph, and their Euclidean distance is used to formulate the set of edges of the graph. Thus, we achieve exchange between nodes and their neighbors. Temporal dependency: The graph operates in a dynamic environment. Thus, we leverage the recurrent neural networks (RNNs) to model the temporal dependency. As a result, time series of VTEC data can be predicted to future epochs. Solar and geomagnetic indices are formulated as node attributes and are also present temporal variability.

Topics to be discussed in the study include the design of the graph neural network structure, the training methods exploiting steepest descent algorithms, data analysis, as well as preliminary testing results of the VTEC predictions as compared, with state-of-the-art graph architectures.