Suscripción a Biblioteca: Guest
Portal Digitalde Biblioteca Digital eLibros Revistas Referencias y Libros de Ponencias Colecciones
International Journal for Multiscale Computational Engineering
Factor de Impacto: 1.016 Factor de Impacto de 5 años: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimir: 1543-1649
ISSN En Línea: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2016015897
pages 291-302

MODELING HETEROGENEITY IN NETWORKS USING POLYNOMIAL CHAOS

Karthikeyan Rajendran
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ
Andreas C. Tsoumanis
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ
Constantinos I. Siettos
School of Applied Mathematics and Physical Sciences, NTUA, Athens, Greece
Carlo R. Laing
Institute for Natural and Mathematical Sciences, Massey University, Auckland, New Zealand
Ioannis G. Kevrekidis
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ; Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ

SINOPSIS

Using the dynamics of information propagation on a network as our illustrative example, we present and discuss a systematic approach to quantifying heterogeneity and its propagation that borrows established tools from uncertainty quantification, specifically, the use of polynomial chaos. The crucial assumption underlying this mathematical and computational "technology transfer" is that the evolving states of the nodes in a network quickly become correlated with the corresponding node identities: features of the nodes imparted by the network structure (e.g., the node degree, the node clustering coefficient). The node dynamics thus depend on heterogeneous (rather than uncertain) parameters, whose distribution over the network results from the network structure. Knowing these distributions allows one to obtain an efficient coarse-grained representation of the network state in terms of the expansion coefficients in suitable orthogonal polynomials. This representation is closely related to mathematical/computational tools for uncertainty quantification (the polynomial chaos approach and its associated numerical techniques). The polynomial chaos coefficients provide a set of good collective variables for the observation of dynamics on a network and, subsequently, for the implementation of reduced dynamic models of it. We demonstrate this idea by performing coarse-grained computations of the nonlinear dynamics of information propagation on our illustrative network model using the Equation-Free approach.


Articles with similar content:

LOW-COST MULTI-DIMENSIONAL GAUSSIAN PROCESS WITH APPLICATION TO UNCERTAINTY QUANTIFICATION
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 4
Guang Lin, Bledar A. Konomi
ORTHOGONAL BASES FOR POLYNOMIAL REGRESSION WITH DERIVATIVE INFORMATION IN UNCERTAINTY QUANTIFICATION
International Journal for Uncertainty Quantification, Vol.1, 2011, issue 4
Oleg Roderick, Mihai Anitescu, Fred Hickernell, Yiou Li
ADAPTIVE SELECTION OF SAMPLING POINTS FOR UNCERTAINTY QUANTIFICATION
International Journal for Uncertainty Quantification, Vol.7, 2017, issue 4
Casper Rutjes, Enrico Camporeale, Ashutosh Agnihotri
PRIOR AND POSTERIOR ROBUST STOCHASTIC PREDICTIONS FOR DYNAMICAL SYSTEMS USING PROBABILITY LOGIC
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 4
Alexandros Taflanidis, James L. Beck
COMPARISON OF LINEARIZATION AND GRAPH CLUSTERING METHODS FOR UNCERTAINTY QUANTIFICATION OF LARGE SCALE DYNAMICAL SYSTEMS
International Journal for Uncertainty Quantification, Vol.7, 2017, issue 1
Abani K. Patra, Puneet Singla, Rahul Rai, Arpan Mukherjee, Tarunraj Singh