2015/05/31 by Christian Kuehn · 4 citations
Physics and Astronomy · Mathematics · Biochemistry, Genetics and Molecular Biology · #cond-mat.stat-mech #math.DS #nlin.AO #q-bio.QM
paper · pdf · doi:10.1007/978-3-319-28028-8
published as Control of Self-Organizing Complex Systems (editors: E. Schoell, S. Klapp and P. Hoevel), Springer, pp. 253-271, 2016 · short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biology
arxiv created 2015/09/29 · arxiv updated 2018/12/24
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.