An empirical nonlinear dynamics approach to analyzing emergent behavior of agent-based models

Agent-based models (ABMs) simulate the behavior of complex systems from bottom to top so that macro-scale patterns emerge from randomized micro-scale interactions among autonomous agents and their environment. However, our ability to construct complex ABMs currently exceeds our capacity to evaluate their emergent dynamics, contributing to an explainability problem in convincing policymakers that in silico experimentation with ABMs can be trusted to correspond to the real world they are charged with regulating. While there is no universally agreed-upon approach for analyzing or benchmarking ABM dynamics, past work has emphasized statistical and probabilistic analyses. Consistent with a key feature of ABMs—the macro-level order emerges from micro-level randomness—we propose a deterministic analytical framework built from nonlinear time series methods to reveal an emergent low-dimensional dynamical structure concealed in complex ABM output. In particular, embedding ABM dynamics (time series) in a nonlinear state space enables diagnosis of a low-dimensional structure, inference of causal interaction regimes among macro-level variables, extraction of a phenomenological meta-model consisting of a system of ordinary differential equations, and benchmarking of ABMs against real-world systems, to establish credibility in the eyes of policymakers and stakeholders. We demonstrate the deterministic approach with a canonical model for virus outbreaks.