Mean Field Theory For Non-Equilibrium Network Reconstruction

TL;DR

This paper develops a mean-field theoretical framework and iterative algorithms for reconstructing network interactions in non-equilibrium systems, exemplified by an asymmetric Sherrington-Kirkpatrick model, advancing beyond equilibrium assumptions.

Contribution

It introduces an exact iterative inversion method and efficient approximations for inferring interactions in non-equilibrium networks using correlation functions.

Findings

Derived an exact iterative inversion algorithm.

Developed approximations based on dynamical mean-field and TAP equations.

Expressed interactions in terms of correlation functions.

Abstract

There has been recent progress on the problem of inferring the structure of interactions in complex networks when they are in stationary states satisfying detailed balance, but little has been done for non-equilibrium systems. Here we introduce an approach to this problem, considering, as an example, the question of recovering the interactions in an asymmetrically-coupled, synchronously-updated Sherrington-Kirkpatrick model. We derive an exact iterative inversion algorithm and develop efficient approximations based on dynamical mean-field and Thouless-Anderson-Palmer equations that express the interactions in terms of equal-time and one time step-delayed correlation functions.