🤖 AI Summary
This study addresses the insufficient output representation of agent-based models (ABMs). To this end, we propose a dual-axis analytical framework integrating temporal structure and distributional geometry. Methodologically, we first couple ε-machines from computational mechanics with score-based generative diffusion models, jointly leveraging Kolmogorov complexity analysis and score matching to simultaneously model ABM time-series predictability and high-dimensional state-distribution morphology. Theoretically, we provide formal definitions and derive key propositions; empirically, we validate the framework on a geriatric care ABM dataset, demonstrating its effectiveness in behavioral interpretation, long-horizon forecasting, and distributional synthesis. Our core contribution lies in a cross-domain, dual-dimensional representation paradigm—bridging computational mechanics and generative modeling—which overcomes the limitations of conventional univariate temporal or static distribution analyses. This advances ABM interpretability and enables controllable, physics-informed generative modeling.
📝 Abstract
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.