Journal Article

Deep Neural Network-Based Inversion Method for Electron Density Profiles in Ionograms

Wei, Na, Niu, Longlong, Deng, ZhongXin, Zhou, Chen, Han, Guosheng, Liu, Wen

2026

Overview

Accurate inversion of ionograms of the ionosonde is of great significance for studying ionospheric structure and radio wave propagation. Traditional inversion methods usually describe the electron density profile based on preset polynomial functions, but such functions are difficult to fully match the complex dynamic distribution characteristics of the ionosphere, especially in accurately representing special positions such as the F2 layer peak. To this end, this paper proposes an inversion model based on a Variational Autoencoder, named VSII-VAE, which realizes the mapping from ionograms to electron density profiles through an encoder–decoder structure. To enable the model to learn inversion patterns with physical significance, we introduced physical constraints into the latent variable space and the decoder, constructing a neural network inversion model that integrates data-driven approaches with physical mechanisms. Using multi-class ionograms as input and the electron density measured by Incoherent Scatter Radar as the training target, experimental results show that the electron density profiles retrieved by VSII-VAE are highly consistent with ISR observations, with errors between synthetic virtual heights and measured virtual heights generally below 5 km. On the independent test set, the model evaluation metrics reached R2 = 0.82, RMSE = 0.14 MHz, rp = 0.94, outperforming the ARTIST method and verifying the effectiveness and superiority of the model inversion.

• Publisher: MDPI AG
• Subject: Artificial intelligence / Artificial neural networks / Comparative analysis / Datasets / Density profiles / Electron density / Electron density profiles / Electrons / Environmental aspects / F 2 region / Forecasts and trends / Functions (mathematics) / Incoherent scatter radar / inversion / ionogram / Ionograms / Ionosondes / Ionosphere / Ionospheric electron density / Ionospheric structure / Measurement / Methods / Neural networks / Polynomials / Propagation / Radio wave propagation / Radio waves / Variational Autoencoder / Wave propagation