Information-theoretic formulation of dynamical systems: causality, modeling, and control

TL;DR

This paper introduces an information-theoretic framework for analyzing causality, modeling, and control in chaotic dynamical systems, exemplified by turbulence, using Shannon entropy to quantify information flow and conservation.

Contribution

It formulates causality, modeling, and control problems within an information-theoretic context, providing new insights and methods for high-dimensional chaotic systems like turbulence.

Findings

Quantifies causality via information flux in dynamical systems.

Proposes information-preserving reduced-order models.

Applies framework to turbulence for energy transfer, modeling, and flow control.

Abstract

The problems of causality, modeling, and control for chaotic, high-dimensional dynamical systems are formulated in the language of information theory. The central quantity of interest is the Shannon entropy, which measures the amount of information in the states of the system. Within this framework, causality is quantified by the information flux among the variables of interest in the dynamical system. Reduced-order modeling is posed as a problem related to the conservation of information in which models aim at preserving the maximum amount of relevant information from the original system. Similarly, control theory is cast in information-theoretic terms by envisioning the tandem sensor-actuator as a device reducing the unknown information of the state to be controlled. The new formulation is used to address three problems about the causality, modeling, and control of turbulence, which stands as a primary example of a chaotic, high-dimensional dynamical system. The applications include the causality of the energy transfer in the turbulent cascade, subgrid-scale modeling for large-eddy simulation, and flow control for drag reduction in wall-bounded turbulence.