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<p>Reconstructing vertical ionospheric electron density profiles from ground-based GNSS-derived total electron content (TEC) is a fundamentally ill-posed inverse problem, as TEC represents only an integral constraint on the electron density distribution. In this study, we propose TEC2Ne, a physics-informed deep learning framework that reconstructs station-level electron density profiles by explicitly embedding the intrinsic coupling between TEC and vertical ionospheric structure. The key innovation of TEC2Ne is the introduction of a physically fitted TEC feature (TEC<sub><i>fit</i></sub>), derived using a genetic programming–based symbolic regression algorithm. TEC<sub><i>fit</i></sub> quantitatively bridges global TEC maps and locally integrated digisonde electron densities, effectively constraining the solution space of the inverse problem and guiding the neural network toward physically consistent reconstructions. The model also incorporates empirical background profiles from IRI-2020, solar and geomagnetic indices, and lunar-phase–related parameters, forming a hybrid, data-driven and physics-guided reconstruction framework. TEC2Ne is validated against more than one solar cycle of digisonde observations at representative mid- and low-latitude stations. The reconstructed electron density profiles exhibit strong agreement with observations, achieving coefficients of determination (<i>R</i><sup>2</sup>) exceeding 0.85 and substantially reducing reconstruction errors compared with the IRI-2020 model, empirical-NmF2 methods, and state-of-the-art data assimilation products. Feature attribution analysis based on integrated gradients demonstrates that TEC<sub><i>fit</i></sub> is the dominant non-spatiotemporal contributor, accounting for over 20% of the model influence and consistently outperforming traditional geophysical indices, while lunar phase–related features contribute non-negligibly (~ 7.5%). By explicitly encoding the physical relationship between TEC and electron density, TEC2Ne moves beyond black-box learning and provides a robust framework for reconstructing ionospheric electron density profiles from global TEC observations, offering a practical solution to mitigate digisonde data gaps and support real-time ionospheric specification for high-frequency communication and satellite navigation.</p>

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TEC2Ne: a physics-informed deep learning framework for reconstructing ionospheric electron density profiles from global TEC maps

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Chenghao Li,
  • Hanxian Fang,
  • Chao Xiao,
  • Die Duan,
  • Yang Lin,
  • Hongtao Huang,
  • Ganming Ren,
  • Han Wu,
  • Chuyue Zhou,
  • Haiyang Zheng,
  • Xuhui Shen,
  • Xiaoqun Cao

摘要

Reconstructing vertical ionospheric electron density profiles from ground-based GNSS-derived total electron content (TEC) is a fundamentally ill-posed inverse problem, as TEC represents only an integral constraint on the electron density distribution. In this study, we propose TEC2Ne, a physics-informed deep learning framework that reconstructs station-level electron density profiles by explicitly embedding the intrinsic coupling between TEC and vertical ionospheric structure. The key innovation of TEC2Ne is the introduction of a physically fitted TEC feature (TECfit), derived using a genetic programming–based symbolic regression algorithm. TECfit quantitatively bridges global TEC maps and locally integrated digisonde electron densities, effectively constraining the solution space of the inverse problem and guiding the neural network toward physically consistent reconstructions. The model also incorporates empirical background profiles from IRI-2020, solar and geomagnetic indices, and lunar-phase–related parameters, forming a hybrid, data-driven and physics-guided reconstruction framework. TEC2Ne is validated against more than one solar cycle of digisonde observations at representative mid- and low-latitude stations. The reconstructed electron density profiles exhibit strong agreement with observations, achieving coefficients of determination (R2) exceeding 0.85 and substantially reducing reconstruction errors compared with the IRI-2020 model, empirical-NmF2 methods, and state-of-the-art data assimilation products. Feature attribution analysis based on integrated gradients demonstrates that TECfit is the dominant non-spatiotemporal contributor, accounting for over 20% of the model influence and consistently outperforming traditional geophysical indices, while lunar phase–related features contribute non-negligibly (~ 7.5%). By explicitly encoding the physical relationship between TEC and electron density, TEC2Ne moves beyond black-box learning and provides a robust framework for reconstructing ionospheric electron density profiles from global TEC observations, offering a practical solution to mitigate digisonde data gaps and support real-time ionospheric specification for high-frequency communication and satellite navigation.