Work

Coarse-graining and reconstruction for Markov matrices

Year: 2025

Type: article

Abstract: We present an operator theoretic coarse-graining (or model order reduction) procedure for stochastic matrices by clustering. The method is consistent with the natural structure of Markov theory, preserving positivity and mass, and does not rely on any tools from Hilbert space theory. The reconstruction is provided by a generalized Penrose–Moore inverse of the coarse-graining operator incorporating the inhomogeneous invariant measure of the Markov matrix. As we will show, the method provides coarse-graining and reconstruction also on the level of tensor spaces, which is consistent with the notion of an incidence matrix and quotient graphs, and, moreover, allows to coarse-grain and reconstruct fluxes. Furthermore, we investigate the connection with functional inequalities and Poincaré-type constants.

Source: Zeitschrift für Analysis und ihre Anwendungen

DOI: 10.4171/zaa/1796

Author: Artur Stephan

Institution: TU Wien

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W3205602768

FWCI:

Cites: 12

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Related to: 10