TY - JOUR
T1 - Coarse-grained descriptions of dynamics for networks with both intrinsic and structural heterogeneities
AU - Bertalan, Tom
AU - Wu, Yan
AU - Laing, Carlo
AU - Gear, C. William
AU - Kevrekidis, Ioannis G.
N1 - Publisher Copyright:
© 2017 Bertalan, Wu, Laing, Gear and Kevrekidis.
PY - 2017/6/12
Y1 - 2017/6/12
N2 - Finding accurate reduced descriptions for large, complex, dynamically evolving networks is a crucial enabler to their simulation, analysis, and ultimately design. Here, we propose and illustrate a systematic and powerful approach to obtaining good collective coarse-grained observables—variables successfully summarizing the detailed state of such networks. Finding such variables can naturally lead to successful reduced dynamic models for the networks. The main premise enabling our approach is the assumption that the behavior of a node in the network depends (after a short initial transient) on the node identity: a set of descriptors that quantify the node properties, whether intrinsic (e.g., parameters in the node evolution equations) or structural (imparted to the node by its connectivity in the particular network structure). The approach creates a natural link with modeling and “computational enabling technology” developed in the context of Uncertainty Quantification. In our case, however, we will not focus on ensembles of different realizations of a problem, each with parameters randomly selected from a distribution. We will instead study many coupled heterogeneous units, each characterized by randomly assigned (heterogeneous) parameter value(s). One could then coin the term Heterogeneity Quantification for this approach, which we illustrate through a model dynamic network consisting of coupled oscillators with one intrinsic heterogeneity (oscillator individual frequency) and one structural heterogeneity (oscillator degree in the undirected network). The computational implementation of the approach, its shortcomings and possible extensions are also discussed.
AB - Finding accurate reduced descriptions for large, complex, dynamically evolving networks is a crucial enabler to their simulation, analysis, and ultimately design. Here, we propose and illustrate a systematic and powerful approach to obtaining good collective coarse-grained observables—variables successfully summarizing the detailed state of such networks. Finding such variables can naturally lead to successful reduced dynamic models for the networks. The main premise enabling our approach is the assumption that the behavior of a node in the network depends (after a short initial transient) on the node identity: a set of descriptors that quantify the node properties, whether intrinsic (e.g., parameters in the node evolution equations) or structural (imparted to the node by its connectivity in the particular network structure). The approach creates a natural link with modeling and “computational enabling technology” developed in the context of Uncertainty Quantification. In our case, however, we will not focus on ensembles of different realizations of a problem, each with parameters randomly selected from a distribution. We will instead study many coupled heterogeneous units, each characterized by randomly assigned (heterogeneous) parameter value(s). One could then coin the term Heterogeneity Quantification for this approach, which we illustrate through a model dynamic network consisting of coupled oscillators with one intrinsic heterogeneity (oscillator individual frequency) and one structural heterogeneity (oscillator degree in the undirected network). The computational implementation of the approach, its shortcomings and possible extensions are also discussed.
KW - Coarse-graining
KW - Networks heterogeneity
KW - Polynomial chaos
KW - Projective integration
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U2 - 10.3389/fncom.2017.00043
DO - 10.3389/fncom.2017.00043
M3 - Article
AN - SCOPUS:85027567708
SN - 1662-5188
VL - 11
JO - Frontiers in Computational Neuroscience
JF - Frontiers in Computational Neuroscience
M1 - 43
ER -