Ionosphere is a layer in the upper part of atmosphere wide-ranging from 60 km to 2000 km. It has a very significance in radio wave propagation because of, its electromagnetic attributes. Ionosphere is mainly affected by solar zenith angle and solar activity. In the day-time ionization in ionosphere is at the highest level and the ionospheric effects are stronger. In the night-time ionization decreases and the effects of ionosphere gets weaker. One of the most important parameters that define the physical structure of ionosphere is total electron content (TEC). TEC is a line integral of electron density along signal path between satellites to the receiver on the ground. The unit of TEC is TECU and 1 TECU equals 1016 electrons/m2. The TEC values can be computed from dual frequency global positioning system (GPS), which are the most available observations for studying the earth’s ionosphere. However, because of scatter repartition of dual frequency GPS stations, precise information on TEC over the favorable region is unknown.
     Artificial neural networks appeared in the 1980 of the 20th century, it uses physical systems which can be realized to simulate the human brain structure and function of nerve cells. With distributed storage, parallel processing, the ANN has good self-earning, adaptive and associative function, can adapt to the complex and ever-hanging dynamics characteristics. Figure 1 shows the scheme of a three-layer perceptron network. For training of the network and modifications of the weights, there are so many ways. One of the most famous and simplest methods is back-propagation algorithm which trains network in two stages: feed-forward and feed-backward. In feed-forward process, input parameters move to output layer. In this stage, output parameters are compared with known parameters and the errors is identified. The next stage is done feed-backward. In this stage, the errors move from output layer to input layer. Again, the input weights are calculated. These two stages are repeated until the errors reaches a threshold expected for output parameters. 
    Particle swarm optimization (PSO) is a population based (evolutionary) stochastic optimization technique in which a collection of particles move around in search of space looking for the best solution to an optimization problem. The concept is derived from the motion of a flock of birds that communicates and learns from each other in search for food. This algorithm proposed by Eberhart et al., (2001). A PSO algorithm is inspired on the movements of the best member of the population and at the same time also on their own experience. The metaphor indicates that a set of solutions is moving in a search space with the aim to achieve the best position or solution.
In this paper, 3-layer MLP-ANN with 18 neurons in hidden layer is used to modeling the ionosphere TEC time series variations. For this purpose, observations from 36 GPS station in 11 successive days of 2012 (DOY# 220 to 230) are used to processes. To accelerate training step and also enhance the accuracy of the results, particle swarm optimization (PSO) algorithm is used. GPS TEC is used to validate the accuracy of results. Also results of ANN compared with international reference ionosphere (IRI-2012) and universal Kriging method. Analysis of the results showed that the PSO training algorithm has a high-speed in convergence to the optimal solutions. To evaluate the error of ANN results, dVTEC=VTEC_GPS - VTEC_M is used. Minimum dVTEC is computed 0.55, 1.57 and 0.70 TECU for ANN, IRI-2012 and universal kriging methods. Also, maximum dVTEC obtained 5.45, 7.16 and 5.51 TECU, respectively. The results of this paper suggest that the artificial neural network with PSO training algorithm has high accuracy in modeling of ionosphere electron content time series.