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Learning differential equation models from stochastic agent-based model simulations.

Authors
  • Nardini, John T1
  • Baker, Ruth E2
  • Simpson, Matthew J3
  • Flores, Kevin B1
  • 1 North Carolina State University, Mathematics, Raleigh, NC, USA.
  • 2 Mathematical Institute, University of Oxford, Oxford, UK.
  • 3 School of Mathematical Sciences, Queensland University of Technology, Brisbane 4001, Australia. , (Australia)
Type
Published Article
Journal
Journal of The Royal Society Interface
Publisher
The Royal Society
Publication Date
Mar 01, 2021
Volume
18
Issue
176
Pages
20200987–20200987
Identifiers
DOI: 10.1098/rsif.2020.0987
PMID: 33726540
Source
Medline
Keywords
Language
English
License
Unknown

Abstract

Agent-based models provide a flexible framework that is frequently used for modelling many biological systems, including cell migration, molecular dynamics, ecology and epidemiology. Analysis of the model dynamics can be challenging due to their inherent stochasticity and heavy computational requirements. Common approaches to the analysis of agent-based models include extensive Monte Carlo simulation of the model or the derivation of coarse-grained differential equation models to predict the expected or averaged output from the agent-based model. Both of these approaches have limitations, however, as extensive computation of complex agent-based models may be infeasible, and coarse-grained differential equation models can fail to accurately describe model dynamics in certain parameter regimes. We propose that methods from the equation learning field provide a promising, novel and unifying approach for agent-based model analysis. Equation learning is a recent field of research from data science that aims to infer differential equation models directly from data. We use this tutorial to review how methods from equation learning can be used to learn differential equation models from agent-based model simulations. We demonstrate that this framework is easy to use, requires few model simulations, and accurately predicts model dynamics in parameter regions where coarse-grained differential equation models fail to do so. We highlight these advantages through several case studies involving two agent-based models that are broadly applicable to biological phenomena: a birth-death-migration model commonly used to explore cell biology experiments and a susceptible-infected-recovered model of infectious disease spread.

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