Simulation of Complex Systems Using the Observed Data Based on Recurrent Artificial Neural Networks

Abstract

We propose a new approach to reconstructing complex, spatially distributed systems on the basis of the time series generated by such systems. It allows one to combine two basic steps of such a reconstruction, namely, the choice of a set of phase variables of the system using the observed time series and the development of the evolution operator acting in the chosen phase space with the help of an artificial neural network with special topology. This network, first, maps the initial high-dimensional data onto the lower-dimension space and, second, specifies the evolution operator in this space. The efficiency of this approach is demonstrated by an example of reconstructing the Lorenz system representing a high-dimensional model of atmospheric dynamics.