Model reduction of uncertain complex dynamical systems

In this paper we consider the problem of finding a low dimensional approximate model for a discrete time Markov process. This problem is of particular interest in systems that exhibit a so-called metastable behavior, i.e. systems whose behavior is principally concentrated on a finite number of disjoint components of the state space. The developed approach is based on a proper orthogonal decomposition and, unlike most existing approaches, does not require the Markov chain to be reversible. An example is presented to illustrate the effectiveness of the proposed method