## 1 Introduction
First, by constructing cross-scale TEC-Ne mapping relationships through deep learning, these methods transform widely available TEC data into finely resolved vertical profile information, effectively compensating for the spatial coverage limitations of traditional observation techniques. Second, the high-resolution Ne data obtained from inversion serve dual purposes: acting as data assimilation sources for ISR and occultation observations, while also providing validation benchmarks for first-principles-based ionospheric numerical models. This technical approach--leveraging easily accessible parameters to infer difficult-to-measure ones--delivers an innovative solution to overcome ionospheric vertical structure monitoring bottlenecks. Furthermore, the rapid advancement of deep learning has spurred significant progress in ionospheric modeling, particularly in developing high-precision TEC prediction models [17; 18; 19; 20]. Studies in this area have demonstrated the effectiveness of deep learning architectures, often utilizing Recurrent Neural Networks like LSTM and incorporating diverse training data including historical TEC and indices of solar and geomagnetic activity, to forecast TEC with improved accuracy. Building upon these advancements in leveraging deep learning for ionospheric data analysis, our study applies these data-driven techniques to a complementary problem: establishing TEC-to-Ne inversion relationships. While TEC prediction focuses on forecasting future conditions [17, 18, 19, 20], our approach leverages widely available instantaneous TEC grid products to infer detailed vertical electron density profiles, offering a distinct but related application and highlighting the broad potential of deep learning in ionospheric characterization. This study proposes a deep learning-based Ionospheric Vertical Decomposition Framework (IVDF), which establishes a cross-scale mapping model from macroscale TEC to electron density vertical profiles by integrating IGS-TEC grid data with multi-source space environment parameters (AE, SYM-H, F10.7). The framework aims to rapidly and accurately derive globally distributed vertical electron density through the synergistic use of TEC, geomagnetic indices (AE, SYM-H), solar activity parameters (F10.7), and essential spatiotemporal information. The innovation of IVDF is threefold:  
1. Dynamic Magnetospheric Coupling: Geomagnetic activity indices (AE/SYM-H) are incorporated as dynamic drivers into the deep learning architecture to explicitly characterize the control mechanisms of magnetospheric energy injection on ionospheric Ne abrupt changes. 2. Adaptive Spatial Encoding: Longitude periodicity encoding (sine and cosine transformations) and a logarithmic Ne output layer are introduced to enhance the model's adaptability to ionospheric longitudinal-latitudinal variation patterns and Ne magnitudes spanning multiple orders. 3. Full-Profile Real-Time Inversion: A vertically decomposed network covering 60-800 km altitudes enables real-time global Ne profile retrieval using single-input TEC data. To validate the feasibility of TEC-based vertical decomposition, this study adopts a lightweight Multilayer Perceptron (MLP) model as a proof of concept. While more complex architectures (e.g., CNNs, RNNs, Transformers) could better capture spatiotemporal dependencies, they are reserved for future work aimed at further improving accuracy and generalization.