Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session L70: Poster Session II (11:15am-2:15pm)
Wednesday, March 6, 2019
BCEC Room: Exhibit Hall
Abstract: L70.00267 : Coarse-graining of Dynamics in Weakly Non-linear Processes on Networks
In linear and weakly non-linear processes these transient states appear at time scales associated with inverse of the so-called community eigenvectors of the quadratic piece of the Hamiltonian.
We show that these transient states can be exploited to coarse-grain the network during the dynamics and reduce the time complexity of estimating the outcome of a dynamical process from $O(N^3)$ down to a lower complexity in most hierarchical networks, and possibly to $O(N^2\log N)$ in tree-like networks.
We outline the coarse-graining procedure, which relies on spectral methods and can be computed efficiently.
We also discuss potential relations with graph learning and regression on graphs.
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