Learning differential equation models from stochastic agent-based model simulations

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