STATISTICAL APPROACH TO MODELING OF SPATIOTEMPORAL DYNAMICS

Abstract

Often in the analysis of spatially extended dynamic systems, we do not know an analytical model of the system dynamics, but we can provide spatiotemporal records of the characteristic state variable. The question then arises of how to extract a model of the system dynamics from the corresponding data. As a quite general solution of this problem, we propose a nonparametric statistical method of local modeling. The performance of the proposed method is demonstrated by predicting typical examples of spatiotemporal chaotic data. The results of modeling indicate that the statistical method can be applied to modeling the deterministic properties of spatiotemporal dynamics in terms of recorded data.