## 1 Introduction  
The critical frequency of the F2 layer of the ionosphere (or known as plasma frequency of the F2 layer, identified as \(f_{o}\)F\({}_{2}\)) is a very important characteristic parameter in various civil and military applications such as high-frequency communications [1], satellite communications [2], navigation [3], timing, radar tracking, detections, locations, and spectrum management [4]. The accuracy in predicting \(f_{o}\)F\({}_{2}\) is an important way to improve the efficiency for the above- mentioned electronics-based information systems. For example, it can be used to improve the predictions of the receiving area, usable frequency and the group-delay, distribution and therefore help to determine the suitability of the communication [1]. The critical frequency can be measured using vertical [5; 6] and oblique incidence sounding ionosonde [7], global navigation satellite systems. In the absence of real-time measurements, the ionospheric models play an important role in all parts of related research fields. For this reason, many empirical models were developed in the past to predict \(f_{0}\)F\({}_{2}\)[8]. Among these models, some provide global coverage whereas some are regional. The models describing the temporal and spatial characteristics of the ionosphere are divided into two main categories: (1) Theoretical or physical, and (2) mathematical or empirical and can be derived from ionosonde data. There are various empirical ionosphere models to obtain \(f_{0}\)F\({}_{2}\)[4; 9; 10]. Moreover, these models provide long-term predictions of the monthly median values of the \(f_{0}\)F\({}_{2}\) and have been used to a certain degree as reference quiet time values [8; 11], for both global and regional models. As is well-known, the International Reference Ionosphere (IRI) model is the most representative global model. Initially, [PERSON] and [PERSON] [12; 13] proposed a global model that expressed the measurements for each station as a Fourier series with special Legendre functions dependent on latitude and longitude for each Fourier coefficient. This model was later adopted for international use by the International Radio Consultative Committee (CCIR) and recommended as International Telecommunications Union (ITU) standard [14]. On the basis of this global model, the IRI was proposed by a joint working group of the CCIR and the International Union of Radio Science (URSI) [15]. The IRI model is currently the most popular model and has been steadily developed and improved with newer data and more advanced techniques by the joint working group of the Committee on Space Research (COSPAR) and URSI. The IRI model has evolved to a number of important editions including IRI-78 [16], IRI-1990 [15], IRI-2000 [17], IRI-2007 [18], IRI-2012 [19], and IRI-2016 [20]. As the latest version, IRI-2016 includes significant improvements not only to the representation of the electron density, but also for the description of the electron temperature and ion composition [21]. In recent years, neural-network (NN) based global models for \(f_{0}\)F\({}_{2}\) are being developed and evaluated as a possible replacement for the IRI models presently in modeling [17; 22]. [PERSON] [23] proposed a model for ionospheric \(f_{0}\)F\({}_{2}\) that uses an empirical orthogonal function (EOF) analysis. At the same time, each developed model is compared with the IRI model to ensure that the replacement solution has greater accuracy than the IRI solution [17]. The purpose in all the above research is to achieve more accurate prediction of the parameters by developing new models and optimizing the existing models. Compared with global models, regional models give in general better results with better agreement with observations [8; 24; 25]. The development of these regional models arose: (1) With the demand for improved performances for specific areas, (2) in response to the availability of denser network of stations, and (3) to simplify the complex ionospheric morphology over a restricted area [25].