Solving the inverse problem of noise-driven dynamic networks

TL;DR

This paper introduces the double correlation matrix (DCM) method for accurately inferring the structure and noise correlations of stochastic dynamic complex networks from kinetic data, addressing a central inverse problem.

Contribution

The paper presents a novel, analytically derived universal inference formula (DCM) method for network structure and noise correlation estimation from data.

Findings

DCM method accurately infers network structures

DCM captures noise correlations effectively

Method validated through numerical simulations

Abstract

Nowadays massive amount of data are available for analysis in natural and social systems. Inferring system structures from the data, i.e., the inverse problem, has become one of the central issues in many disciplines and interdisciplinary studies. In this Letter, we study the inverse problem of stochastic dynamic complex networks. We derive analytically a simple and universal inference formula called double correlation matrix (DCM) method. Numerical simulations confirm that the DCM method can accurately depict both network structures and noise correlations by using available kinetic data only. This inference performance was never regarded possible by theoretical derivation, numerical computation and experimental design.