Spectral learning of dynamic systems from nonequilibrium data

TL;DR

This paper extends spectral learning methods for stochastic systems to handle nonequilibrium data and continuous observations, enabling efficient and consistent estimation of equilibrium dynamics without assuming data is identically distributed.

Contribution

It introduces a novel approach to spectral learning that relaxes the i.i.d. assumption and proposes a binless algorithm for continuous data, improving efficiency and applicability.

Findings

Successfully extracts equilibrium dynamics from nonequilibrium data

Achieves linear complexity in continuous data spectral learning

Provides consistent estimation of system dynamics

Abstract

Observable operator models (OOMs) and related models are one of the most important and powerful tools for modeling and analyzing stochastic systems. They exactly describe dynamics of finite-rank systems and can be efficiently and consistently estimated through spectral learning under the assumption of identically distributed data. In this paper, we investigate the properties of spectral learning without this assumption due to the requirements of analyzing large-time scale systems, and show that the equilibrium dynamics of a system can be extracted from nonequilibrium observation data by imposing an equilibrium constraint. In addition, we propose a binless extension of spectral learning for continuous data. In comparison with the other continuous-valued spectral algorithms, the binless algorithm can achieve consistent estimation of equilibrium dynamics with only linear complexity.