Complementary Characterization of Agent-Based Models via Computational Mechanics and Diffusion Models
This provides a principled methodology for researchers in complex systems and simulation modeling to better understand ABM behavior, though it is incremental as it extends prior work by combining existing tools.
The paper tackles the problem of characterizing agent-based model (ABM) outputs by integrating computational mechanics (via ε-machines) and diffusion models, resulting in a two-axis representation that jointly analyzes temporal predictability and high-dimensional distributional structure, validated on an elder-caregiver ABM dataset.
This article extends the preprint "Characterizing Agent-Based Model Dynamics via $ε$-Machines and Kolmogorov-Style Complexity" by introducing diffusion models as orthogonal and complementary tools for characterizing the output of agent-based models (ABMs). Where $ε$-machines capture the predictive temporal structure and intrinsic computation of ABM-generated time series, diffusion models characterize high-dimensional cross-sectional distributions, learn underlying data manifolds, and enable synthetic generation of plausible population-level outcomes. We provide a formal analysis demonstrating that the two approaches operate on distinct mathematical domains -- processes vs. distributions -- and show that their combination yields a two-axis representation of ABM behavior based on temporal organization and distributional geometry. To our knowledge, this is the first framework to integrate computational mechanics with score-based generative modeling for the structural analysis of ABM outputs, thereby situating ABM characterization within the broader landscape of modern machine-learning methods for density estimation and intrinsic computation. The framework is validated using the same elder-caregiver ABM dataset introduced in the companion paper, and we provide precise definitions and propositions formalizing the mathematical complementarity between $ε$-machines and diffusion models. This establishes a principled methodology for jointly analyzing temporal predictability and high-dimensional distributional structure in complex simulation models.