On the acceleration of spatially distributed agent-based computations: A patch dynamics scheme
Authored by Ioannis G Kevrekidis, Giovanni Samaey, Ping Liu, C William Gear
Date Published: 2015
DOI: 10.1016/j.apnum.2014.12.007
Sponsors:
United States Department of Energy (DOE)
Platforms:
MATLAB
Model Documentation:
Other Narrative
Mathematical description
Model Code URLs:
Model code not found
Abstract
In recent years, individual-based/agent-based modeling has been applied
to study a wide range of applications, ranging from engineering problems
to phenomena in sociology, economics and biology. Simulating such
agent-based models over extended spatiotemporal domains can be
prohibitively expensive due to stochasticity and the presence of
multiple scales. Nevertheless, many agent-based problems exhibit smooth
behavior in space and time on a macroscopic scale, suggesting that a
useful coarse-grained continuum model could be obtained. For such
problems, the equation-free framework {[}16-18] can significantly reduce
the computational cost. Patch dynamics is an essential component of this
framework. This scheme is designed to perform numerical simulations of
an unavailable macroscopic equation on macroscopic time and length
scales; it uses appropriately initialized simulations of the fine-scale
agent-based model in a number of small ``patches{''}, which cover only a
fraction of the spatiotemporal domain. In this work, we construct a
finite-volume-inspired conservative patch dynamics scheme and apply it
to a financial market agent-based model based on the work of Omurtag and
Sirovich {[}22]. We first apply our patch dynamics scheme to a continuum
approximation of the agent-based model, to study its performance and
analyze its accuracy. We then apply the scheme to the agent-based model
itself. Our computational experiments indicate that here, typically, the
patch dynamics-based simulation needs to be performed in only 20\% of
the full agent simulation space, and in only 10\% of the temporal
domain. (C) 2015 IMACS. Published by Elsevier B.V. All rights reserved.
Tags
algorithms
models
Equation-Free
Optimization
population
systems
Homogenization problems
Multiscale computation
Bifurcation-analysis
Time-steppers