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Equation-free analysis of agent-based models and systematic parameter determination

Thomas, SA, Lloyd, David and Skeldon, AC (2016) Equation-free analysis of agent-based models and systematic parameter determination Physica A: Statistical Mechanics and its Applications, 464. pp. 27-53.

EFNCpaper_resubmission_2.pdf - Accepted version Manuscript

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Agent based models (ABM)s are increasingly used in social science, economics, mathematics, biology and computer science to describe time dependent systems in circumstances where a description in terms of equations is difficult. Yet few tools are currently available for the systematic analysis of ABM behaviour. Numerical continuation and bifurcation analysis is a well established tool for the study of deterministic systems. Recently, equation-free (EF) methods have been developed to extend numerical continuation techniques to systems where the dynamics are described at a microscopic scale and continuation of a macroscopic property of the system is considered. To date, the practical use of EF methods has been limited by; 1) the over-head of application-specific implementation; 2) the laborious configuration of problem-specific parameters; and 3) large ensemble sizes (potentially) leading to computationally restrictive run-times. In this paper we address these issues with our tool for the EF continuation of stochastic systems, which includes algorithms to systematically configuration problem specific parameters and enhance robustness to noise. Our tool is generic and can be applied to any `black-box' simulator and determine the essential EF parameters prior to EF analysis. Robustness is significantly improved using our convergence-constraint with a corrector-repeat method (C3R) method. This algorithm automatically detects outliers based on the dynamics of the underlying system enabling both an order of magnitude reduction in ensemble size and continuation of systems at much higher levels of noise than classical approaches. We demonstrate our method with application to several ABM models, revealing parameter dependence, bifurcation and stability analysis of these complex systems giving a deep understanding of the dynamical behaviour of the models in a way that is not otherwise easily obtainable. In each case we demonstrate our systematic parameter determination stage for configuring the system specific EF parameters.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 15 December 2016
Funders : Engineering and Physical Sciences Research Council
DOI : 10.1016/j.physa.2016.07.043
Grant Title : Evolution and Resilience of Industrial Ecosystems (ERIE)
Copyright Disclaimer : © 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Uncontrolled Keywords : Equation free methods; Agent-based models; Numerical continuation; Stochastic systems
Depositing User : Symplectic Elements
Date Deposited : 02 Aug 2016 08:05
Last Modified : 24 Feb 2021 05:04

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