## 1 Introduction  
Total Electron Content (TEC), defined as the integrated electron count within a vertical column of unit cross-sectional area along a signal propagation path (unit: TECU, 1 TECU = 10\({}^{16}\) electrons/m\({}^{2}\)), characterizes the horizontal distribution of ionospheric electron content and serves as a path-integrated parameter describing the macroscopic state of the ionosphere [1]. Compared to macroscale TEC, electron density (Ne), a microscopic parameter quantifying local ionization levels (unit: electrons/m\({}^{3}\)), precisely delineates the fine vertical structural characteristics of the ionosphere by revealing altitude-dependent stratification (e.g., D, E, and F layers) and diurnal ionization variations (e.g., nocturnal F-layer density decay) [2]. In recent years, efforts in TEC-to-Ne modeling have focused on developing data-driven approaches. For instance, studies have utilized GNSS-TEC data to optimize ionospheric models like the International Reference Ionosphere (IRI-2016) for more accurate electron density profile estimations [3]. As a macroscopic observable factor, TEC holds critical operational value in space weather services. In satellite navigation, real-time TEC monitoring provides ionospheric delay correction parameters for GNSS systems. For instance, abrupt global TEC enhancements during geomagnetic storms can amplify GPS positioning errors to tens of meters [4], while TEC anomaly-based early warnings effectively mitigate ionospheric disturbances caused by solar events (e.g., solar flares, coronal mass ejections) in navigation and communication systems [5]. In comparison, the vertical distribution of Ne carries greater physical significance for radio wave propagation: Electron density gradients directly govern radio wave refraction paths and propagation losses. For example, shortwave communication systems require dynamic selection of optimal operating frequencies based on Ne peaks in the E-layer (90-150 km) and F-layer (>150 km) to avoid signal attenuation [6]. TEC and Ne describe ionospheric characteristics through two distinct dimensions: path-integrated quantities and spatial gradients, respectively. Their synergistic study forms the foundation of ionospheric multi-scale modeling; while TEC provides critical input parameters for Global Navigation Satellite Systems (GNSS) and space weather monitoring, Ne underpins research on ionospheric dynamic mechanisms and the optimization of communication systems. Consequently, achieving joint inversion of TEC and Ne constitutes a central challenge in enhancing the spatiotemporal precision of ionospheric models. Traditional physics-based approaches have also analyzed electron density gradients by investigating their mapping relationships [7]. However, the current vertical profiling of electron density faces significant technological bottlenecks: While incoherent scatter radar (ISR) can provide high-precision Ne profile data, its exorbitant single-station deployment costs and sparse global coverage [8; 9; 10] limit its widespread application. Conversely, GNSS radio occultation techniques using low-Earth-orbit satellites (e.g., COSMIC-2) achieve global coverage but are characterized by specific spatial resolution limitations. COSMIC-2 electron density profiles typically have a vertical resolution of about 0.5 km and a horizontal resolution of about 200 km. Although the mission provides approximately 5000 soundings per day with high density, these spatial limitations, primarily imposed by orbital parameters and the radio occultation technique itself, can still hinder their ability to fully capture rapid transient processes or small-scale structures of ionospheric parameters [11; 12; 13]. By comparison, ground-based GNSS-TEC observation networks have attained global continuous monitoring capabilities with high spatiotemporal resolution [14; 15; 16; 1]. Against this backdrop, electron density inversion methods based on global ionospheric TEC grid products (e.g., IGS-TEC) demonstrate unique application advantages.