755 ANNALS OF GEOPHYSICS, VOL. 51, N. 5/6, October/December 2008 Using neural networks to study the geomagnetic field evolution Bejo Duka and Niko Hyka Department of Physics, Faculty of natural Sciences, University of Tirana Abstract Considering the three components of the geomagnetic field as stochastic quantities, we used neural networks to study their time evolution in years. In order to find the best NN for the time predictions, we tested many differ- ent kinds of NN and different ways of their training, when the inputs and targets are long annual time series of synthetic geomagnetic field values. The found NN was used to predict the values of the annual means of the geomagnetic field components beyond the time registration periods of a Geomagnetic Observatory. In order to predict a time evolution of the global field over the Earth, we considered annual means of 105 Geomagnetic Observatories, chosen to have more than 30 years registration (1960.5-2005.5) and to be well distributed over the Earth. Using the NN technique, we created 137 «virtual geomagnetic observatories» in the places where real Geomagnetic Observatories are missing. Then, using NN, we predicted the time evolution of the three components of the global geomagnetic field beyond 2005.5. Key words Geomagnetic Field – Geomagnetic Observatory – neural networks (nn) – time series – time prediction 1. Introduction Artificial Neural networks (ANN or shortly NN) are sets of connected neuron layers, which contain one or more neurons. Each neuron rep- resents a known function 1 f which transfers the input quantity p, multiplied by a weight w and added by a bias b, to the output a: a fpw b = ⋅ + ⋅ ( ) 1 w and b are both adjustable parameters of the neuron. Commonly, neural networks are adjusted, or trained, so that a particular input leads to a spe- cific target output. During training the weights and biases of the network are iteratively ad- justed to minimize the network performance function. The default performance function is the mean square error (mse) (Demuth and Beale, 2004). The neural networks have been used to study time series and predictions of different quantities that have a stochastic behavior (Frank et al., 2001). The geomagnetic field components have such behavior not only in the time scale of seconds or minutes (Hongre et al., 1999), but even in the larger time scale of years (Duka, 2005). For our intentions, the network inputs are the annual time series of the geomagnetic field component values and the targets are the known annual values of the geomagnetic field components that are shifted in some way from the input values. The pre- dicted values of the geomagnetic field compo- nents are simulated by the trained networks when the inputs are shifted from the initial inputs. ( 1 ) The most known functions are: purelin, logsig, tan- sig (Demuth and Beale, 2004). Mailing address: Prof. Bejo Duka, Fakulteti i Shken- cave Natyrore, Bulevardi Zogu I, Tirana, Albania; e-mail: bduka@fshn.edu.al