Reduced Markovian models of dynamical systems

Abstract

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, this paper addresses two problems for obtaining further reduced statistical representations. The first problem is to extract the most salient reduced-order dynamics for a given timescale by using a modified clustering algorithm from network theory. The second problem is to provide an alternative construction for the infinitesimal generator of a Markov process that respects statistical features over a large range of time scales. The methodology is demonstrated on three low-dimensional dynamical systems with stochastic and chaotic dynamics, as well as two high-dimensional systems the Kuramoto-Sivashinsky equations and fluid-flow data sampled via Particle Image Velocimetry. The presented method offers a robust reduced-order statistical representation of the underlying system.

Publication
Physica D: Nonlinear Phenomena, 134393