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Machine Learning for the Physical Sciences
Forecasting the Ionosphere from Sparse GNSS Data with Temporal-Fusion Transformers
Giacomo Acciarini
Advanced Concepts Team
European Space Agency (ESA)
[email protected]
&Simone Mestici
Department of Physics
Università degli Studi di Roma Sapienza
[email protected]
&Halil S. Kelebek
Department of Engineering Science
University of Oxford
[email protected]
&Linnea M. Wolniewicz
Department of Information and Computer Science
University of Hawai’i at Mānoa
[email protected]
&Michael D. Vergalla
Free Flight Research Lab
[email protected]
&Madhulika Guhathakurta
NASA Headquarters
[email protected]
&Umaa Rebbapragada
NASA Jet Propulsion Laboratory
[email protected]
&&Bala Poduval
University of New Hampshire
[email protected]
&Atılım Güneş Baydin
Department of Computer Science
University of Oxford, UK
[email protected]
&Frank Soboczenski
Department of Computer Science
University of York & King’s College London
[email protected]
Abstract
The ionosphere critically influences Global Navigation Satellite Systems (GNSS), satellite communications, and Low Earth Orbit (LEO) operations, yet accurate prediction of its variability remains challenging due to nonlinear couplings between solar, geomagnetic, and thermospheric drivers. Total Electron Content (TEC), a key ionospheric parameter, is derived from GNSS observations, but its reliable forecasting is limited by the sparse nature of global measurements and the limited accuracy of empirical models, especially during strong space weather conditions. In this work, we present a machine learning framework for ionospheric TEC forecasting that leverages Temporal Fusion Transformers (TFT) to predict sparse ionosphere data. Our approach accommodates heterogeneous input sources, including solar irradiance, geomagnetic indices, and GNSS-derived vertical TEC, and applies preprocessing and temporal alignment strategies. Experiments spanning 2010–2025 demonstrate that the model achieves robust predictions up to 24 hours ahead, with root mean square errors as low as 3.33 TECU. Results highlight that solar EUV irradiance provides the strongest predictive signals. Beyond forecasting accuracy, the framework offers interpretability through attention-based analysis, supporting both operational applications and scientific discovery. To encourage reproducibility and community-driven development, we release the full implementation as the open-source toolkit ionopy.
1 Introduction
The ionosphere, Earth’s charged atmospheric layer extending from ∼50 to 1,000 km altitude, plays a crucial role in modern technological infrastructure and daily life [1]. This plasma layer, mainly influenced by solar radiation, magnetospheric convection and thermospheric neutral dynamics [2], directly affects critical systems including Global Navigation Satellite Systems (GNSS) accuracy, satellite communications, and Low Earth Orbit (LEO) orbital stability [3, 4].
A fundamental parameter for characterizing ionospheric behavior is the Total Electron Content (TEC), defined as the integrated electron density along a given path. TEC data are often converted to vertical TEC (vTEC) using a shell approximation and mapping function to account for ray path obliquity [5]. Figure 1 illustrates this process, showing slant paths from GNSS satellites projected to their vertical equivalent. Accurate vTEC prediction is essential for correcting GNSS signal delays, particularly during highly dynamic space weather events.
The Madrigal database [6], maintained by CEDAR and hosted at MIT Haystack Observatory, is among the largest repositories of upper atmospheric data. It integrates multi-decade observations from over 159 instruments, including incoherent scatter radars and GNSS-based vTEC, providing global (albeit sparse) coverage with 5-minute temporal resolution. This unique dataset is used by the Jet Propulsion Laboratory (JPL) to generate Global Ionospheric Maps (GIM) of vTEC [7] and provides an invaluable resource for machine learning applications in space weather research.
Despite rich observations, TEC prediction remains challenging due to nonlinear coupling between solar activity, geomagnetic conditions, and ionospheric response. Empirical models like the International Reference Ionosphere (IRI) [8, 9], though useful for climatology, show reduced accuracy during geomagnetic disturbances when ionospheric dynamics are most critical. This motivates machine learning approaches that can capture complex patterns from multi-source data.
Here, we focus on accurate ionospheric TEC prediction by forecasting vTEC using a time-fusion transformer architecture, with the sparse GNSS Madrigal dataset serving as the target. Our framework provides a flexible benchmarking platform that supports probabilistic forecasting, heterogeneous input sources, and scientific experimentation by accommodating varying input features, time histories, and resolutions. To foster reproducibility and community-driven innovation, we publicly release our implementation as ionopy111https://github.com/spaceml-org/ionopy
, accessed 30 August 2025, offering a foundation for both applied forecasting and fundamental ionospheric research.
2 Background
2.1 Machine Learning and Ionosphere Modeling
The application of machine learning to ionospheric modeling has gained significant momentum in recent years, driven by the limitations of traditional physics-based and empirical approaches and the increasing availability of datasets.
Early studies have applied classical algorithms such as gradient boosting (XGBoost) and Multi-Layer Perceptrons (MLP) to predict the global state of the ionosphere [10, 11], while more advanced methods, such as Bi-directional Long-Term-Short-Term Memory (BiLSTM) and transformers, have shown promising results in modeling temporal dependencies, though sometimes restricted to limited geographic areas. Part of these studies have leveraged the JPL-GIM as a target data source since it provides a homogeneous set with respect to latitude and longitude [12]. Instead, some of the regional forecasting models have also used the sparse GNSS-derived vTEC and demonstrated that modern ML models trained on Madrigal TEC data could significantly outperform traditional models [13, 14].
The ability to ingest heterogeneous, multi-source data represents a key advantage of machine learning approaches over empirical and physics-based models. Modern ML models can potentially simultaneously incorporate solar activity indices (F10.7, sunspot numbers), geomagnetic activity parameters (Dst, Kp indices), solar wind parameters, historical TEC observations, or even SDO images, to create comprehensive predictive frameworks. This multi-modal capability is particularly important for ionospheric and thermosphere modeling, where the complex interplay between solar, magnetospheric, and thermospheric processes requires consideration of numerous input variables [15].
2.2 Temporal Fusion Transformers
We employ Temporal Fusion Transformers (TFT) [16] to forecast vTEC behavior, leveraging their state-of-the-art design for multi-horizon time series forecasting with built-in interpretability. TFT integrates specialized components such as the variable selection network, sequence-to-sequence LSTM layers to replace positional encodings, and multi-head attention to handle heterogeneous inputs and temporal patterns common in real-world forecasting.
Key features include the variable selection network, which identifies and weights relevant input features, critical for ionospheric modeling, where parameter importance varies across conditions. Moreover, static covariate encoders incorporate time-invariant factors such as location, conditioning temporal processing with geographic and seasonal/daily contexts. Finally, the sequence-to-sequence LSTM layers replace positional encoding, better capturing local trends enriched with static information. Most importantly, TFT’s interpretable multi-head attention highlights influential time steps and features, offering transparent insights into relationships between solar activity, geomagnetic disturbances, and vTEC behavior.
3 Data & Methodology
In terms of input features, day-of-year, longitude, and seconds-in-day are sine/cosine encoded to preserve cyclical relationships, while other coordinates are standardized or log-normalized depending on their statistical properties. Target vTEC values are log-transformed and standardized using pre-computed statistics to address typical skewness in ionospheric measurements.
The framework integrates diverse data sources with different temporal resolutions, including Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics (TIMED) Solar EUV Experiment (SEE) Level 3, OMNI solar wind, indices and magnetic field data, JPLD Global Ionospheric Maps, solar activity proxies (F10.7, M10.7, S10.7, Y10.7), and geomagnetic indices (Dst, Ap). Temporal alignment and resampling are applied, followed by standardization or log-transformation for highly skewed data. JPLD data is subsampled to 10 equally spaced global points, reducing input features to 10. Static features (latitude, longitude, day-of-year) and temporal features (geomagnetic and solar inputs) are aligned, normalized, and prepared for input into a TFT model.
Input datasets include NASA’s OMNIWeb 1-minute high-resolution data [17], Ap index from Celestrack [18, 19], F10.7, M10.7, S10.7, Y10.7 solar proxies [20], TIMED SEE Level 3 solar irradiance data up to 190nm at 1nm resolution [21], and JPL-GIM data [7]. For training (80%), validation (10%), and testing (10%), a temporal split based on monthly rotations across years ensures models are evaluated on genuinely unseen periods while maintaining seasonal and solar activity representativeness, critical for assessing generalization to future space weather conditions.
4 Results
Table 1 summarizes the outcomes of experiments using the Temporal Fusion Transformer (TFT) with two attention heads, two LSTM layers, a hidden state size of 64, and a 10% dropout rate. Each row of the table corresponds to a different experimental setup, where the input features, their historical time windows (lag), and temporal resolutions (res) were varied. Model performance was evaluated on a completely held-out test set spanning 2010–2025, using root mean squared error (RMSE) and mean absolute error (MAE). Both the mean (μ) and standard deviation (σ) of vTEC (in TEC units, 1 TECU=1016 electrons/m2) are reported, since these values are available in the Madrigal dataset and predicted by the TFT. Prediction horizons ranged from 60 minutes up to 24 hours.
Overall, models that incorporated the full set of features and longer historical time windows achieved the best performance, as expected. Importantly, the results demonstrate that TIMED SEE L3 irradiance data can effectively replace traditional solar proxies, providing comparable predictive accuracy while offering direct EUV irradiance measurements. Moreover, solar irradiance seems to be the most critical input for ionospheric forecasting: when JPL-GIM data, TIMED irradiance, and solar proxies were excluded, model errors nearly doubled (up to about 5.6 TECU in RMSE for the mean).
While the inclusion of JPL-GIM features provided a modest performance boost, the improvement was marginal. This suggests that EUV irradiance and geomagnetic activity alone are sufficient to enable reliable ionospheric forecasts up to one day ahead.
Figure 2 further illustrates the TFT’s predictions with a one-hour lead time (left column) compared against GNSS-derived ionospheric data (right column) under four different geomagnetic storm conditions (based on NOAA geomagnetic storm G-classes). The central column displays corresponding JPL-GIM maps (calibrated on sparse data, not predictions). Qualitatively, the model successfully reproduces key ionospheric structures, such as the equatorial double crest enhancement (also called Equatorial Ionization Anomaly) and day–night variations during geomagnetic storm conditions.
More detailed performance metrics are provided in Appendix, where Tables 2, 3, and 4 present loss values aggregated by latitude, geomagnetic storm conditions, and solar activity levels.
5 Conclusions
In this work, we introduce and release the open-source framework ionopy, designed to preprocess, temporally align, and integrate solar and geomagnetic data to predict GNSS-derived sparse vTEC using Temporal Fusion Transformers. Solar EUV irradiance emerges as the most influential predictor, enabling accurate forecasts from 1 to 24 hours lead time, with RMSE as low as 3.33 TECU in the best experiments. These results highlight the potential of machine learning to outperform traditional ionospheric models and demonstrate the framework’s flexibility for testing scientific hypotheses, including the impact of varying input features, lags, and temporal resolutions.
Acknowledgments
This work is a research product of Heliolab (heliolab.ai), an initiative of the Frontier Development Lab (FDL.ai), delivered by Trillium Technologies in partnership with NASA, Google Cloud, and NVIDIA. The authors also thank NASA’s Jet Propulsion Laboratory for their continuing support.
Appendix
