English

Moment Closure - A Brief Review

Statistical Mechanics 2018-12-24 v2 Dynamical Systems Adaptation and Self-Organizing Systems Quantitative Methods

Abstract

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.

Keywords

Cite

@article{arxiv.1505.02190,
  title  = {Moment Closure - A Brief Review},
  author = {Christian Kuehn},
  journal= {arXiv preprint arXiv:1505.02190},
  year   = {2018}
}

Comments

short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biology