## 1 Introduction  
The ionosphere is a critical component of the near-Earth space environment, located from 60 to 1000 km above the Earth's surface. It serves as both a medium for radio wave propagation and as a link between the magnetosphere and the neutral atmosphere [1]. Many factors control the formation of and variations in the ionosphere, such as solar electromagnetic radiation, particle radiation, magnetic disturbances, geomagnetic field changes, and upper atmospheric dynamics. These influences result in complex space weather-related variations, which can severely impact radio wave propagation technologies and the electromagnetic environment, such as satellite navigation, radar imaging, and shortwave communication. Key ionospheric parameters include Total Electron Content (TEC) and the critical frequencies of the E, F1, and F2 layers. These parameters are extensively used in civil and military applications, including satellite communication, navigation timing, radar detection, direction finding, and spectrum management [2; 3; 4; 5]. Among these, as a crucial parameter for understanding the spatiotemporal distribution, morphological structure, delay characteristics, and ionosphere disturbances [6], TEC refers to the total number of electrons integrated along the path of a radio signal. Using satellite observation data to compute TEC results in a time delay, meaning current TEC data cannot be immediately accessed. In contrast, predicting TEC using ionospheric models enables near-real-time estimation of TEC [7]. Research on TEC not only has engineering significance, such as ensuring the stability of radio systems and identifying earthquake precursors but also holds fundamental scientific importance. Exploring the relationship between TEC and other natural phenomena or space weather events aids in the in-depth study of ionospheric electrodynamics and facilitates atmospheric coupling research. TEC can be directly observed using ionosondes [8]. Without observational stations, these parameters can be derived from ionospheric models [9]. These models provide helpful empirical values for scientists, engineers, and educators. Due to the complexity of the ionosphere, various methods have been developed for TEC modeling. Generally speaking, the ionospheric TEC models can be classified into physical, parametric, and empirical models. Empirical models are mathematical models based on the statistical analysis of historical observation data and extended datasets [10], in which appropriate functions are added to characterize variations in the ionosphere [11]. Empirical models are often formulated in terms of monthly median parameters; hence, they can describe long-time average conditions of the ionosphere. The International Reference Ionosphere (IRI) is a well-known empirical model and recommended international standard [12]. During quiet periods, this model predicts ionospheric characteristic parameters, such as critical frequency, height, and TEC. It was developed by a joint working group of the Committee on Space Research and the International Union of Radio Science, and it is continuously improved by updating data or introducing better modeling techniques [13]. The IRI model has evolved into several important versions, including IRI-78, IRI-85, IRI-1990, IRI-2000, IRI-2007, IRI-2012, IRI-2016, and IRI-2020 [14]. To improve the prediction accuracy of ionospheric TEC, many methods such as Artificial Neural Networks (ANNs), Empirical Orthogonal Functions, Statistical Machine Learning (SML), Intelligent Computing, and others have been introduced and have provided more sophisticated prediction tools for nonlinear and non-stationary ionospheric parameter data. For example, [PERSON] et al. [15] used Principal Component Analysis based on SML methods to establish a regional prediction method. [PERSON] et al. [16] proposed a combined intelligent prediction model based on a multi-mutation, multi-crossover adaptive Genetic Algorithm and Back Propagation neural network. [PERSON] et al.