A closure for the Master Equation starting from the Dynamic Cavity Method

TL;DR

This paper introduces a new systematic closure method for the Master Equation in classical spin systems on tree-like graphs, improving upon existing cavity-based approaches.

Contribution

A novel, systematically derived closure method for the Master Equation that outperforms previous cavity-based techniques in classical spin systems.

Findings

The new method shows improved accuracy on key problem classes.

Systematic derivation enhances theoretical understanding.

Performance benchmarks indicate better results than prior methods.

Abstract

We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We introduce a new such method which can be derived in a more systematic manner, and which performs better on several important classes of problems.