Coarse-grained variables for particle-based models

diffusion maps and animal swarming simulations

Ping Liu, Hannah R. Safford, Iain D. Couzin, Yannis Kevrekidis

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

As microscopic (e.g. atomistic, stochastic, agent-based, particle-based) simulations become increasingly prevalent in the modeling of complex systems, so does the need to systematically coarse-grain the information they provide. Before even starting to formulate relevant coarse-grained equations, we need to determine the right macroscopic observables—the right variables in terms of which emergent behavior will be described. This paper illustrates the use of data mining (and, in particular, diffusion maps, a nonlinear manifold learning technique) in coarse-graining the dynamics of a particle-based model of animal swarming. Our computational data-driven coarse-graining approach extracts two coarse (collective) variables from the detailed particle-based simulations, and helps formulate a low-dimensional stochastic differential equation in terms of these two collective variables; this allows the efficient quantification of the interplay of “informed” and “naive” individuals in the collective swarm dynamics. We also present a brief exploration of swarm breakup and use data-mining in an attempt to identify useful predictors for it. In our discussion of the scope and limitations of the approach we focus on the key step of selecting an informative metric, allowing us to usefully compare different particle swarm configurations.

Original languageEnglish (US)
Pages (from-to)425-440
Number of pages16
JournalComputational Particle Mechanics
Volume1
Issue number4
DOIs
StatePublished - Dec 1 2014

Fingerprint

Diffusion Model
Data mining
Animals
Coarse-graining
Swarm
Data Mining
Large scale systems
Emergent Behavior
Manifold Learning
Simulation
Particle Swarm
Differential equations
Breakup
Data-driven
Quantification
Stochastic Equations
Predictors
Complex Systems
Differential equation
Metric

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Fluid Flow and Transfer Processes
  • Numerical Analysis
  • Computational Mechanics
  • Civil and Structural Engineering
  • Modeling and Simulation

Cite this

Liu, Ping ; Safford, Hannah R. ; Couzin, Iain D. ; Kevrekidis, Yannis. / Coarse-grained variables for particle-based models : diffusion maps and animal swarming simulations. In: Computational Particle Mechanics. 2014 ; Vol. 1, No. 4. pp. 425-440.
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Coarse-grained variables for particle-based models : diffusion maps and animal swarming simulations. / Liu, Ping; Safford, Hannah R.; Couzin, Iain D.; Kevrekidis, Yannis.

In: Computational Particle Mechanics, Vol. 1, No. 4, 01.12.2014, p. 425-440.

Research output: Contribution to journalArticle

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