Modeling volcanomagnetic dynamics by recurrent least-squares support vector machines

Nonlinear dynamic systems can be described by means of statistical learning theory: neural networks and kernel machines. In this work the recurrent least-squares support vector machines are chosen as learning system. The unknown dynamic system is a mapping of past states into the future. The recurrent system is implemented by special data preparation in the learning phase. The next iterations can be calculated but the convergence is usually not guaranteed. Due to the fact that the predicted trajectory can diverge from the real trajectory the semi-directed mode can be applied, i.e. after several prediction steps the system is updated by using the current values of the considered process as new initial conditions. The idea was tested on the data generated by the chaotic dynamic system ‐ the Chua’s circuit. The methodology was then applied to real magnetic data acquired at Etna volcano.