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.

基于代理的模型提供了一个灵活的框架，经常用于对许多生物系统进行建模，包括细胞迁移、分子动力学、生态学和流行病学。由于其固有的随机性和繁重的计算要求，模型动力学分析可能具有挑战性。分析基于代理的模型的常见方法包括模型的广泛蒙特卡罗模拟或粗粒度微分方程模型的推导，以预测基于代理的模型的预期或平均输出。然而，这两种方法都有局限性，因为对基于代理的复杂模型的大量计算可能不可行，并且粗粒度微分方程模型可能无法准确描述某些参数范围内的模型动态。我们提出，方程学习领域的方法为基于代理的模型分析提供了一种有前景、新颖且统一的方法。方程学习是数据科学的一个最新研究领域，旨在直接从数据推断微分方程模型。我们使用本教程来回顾如何使用方程学习方法从基于代理的模型模拟中学习微分方程模型。我们证明该框架易于使用，需要很少的模型模拟，并且可以准确预测粗粒度微分方程模型无法做到的参数区域中的模型动态。我们通过几个案例研究强调了这些优势，涉及两种广泛适用于生物现象的基于代理的模型：通常用于探索细胞生物学实验的出生-死亡-迁移模型和传染病传播的易感-感染-恢复模型。