Complementary Characterization of Agent-Based Models via Computational Mechanics and Diffusion Models

• URL: http://arxiv.org/abs/2512.04771v1
• Date: Thu, 04 Dec 2025 13:14:49 GMT
• Title: Complementary Characterization of Agent-Based Models via Computational Mechanics and Diffusion Models
• Abstract summary: This article introduces diffusion models as computation and complementary tools for characterizing the output of agent-based models (ABMs)<n>We provide a formal analysis demonstrating that the two approaches operate on distinct mathematical domains.<n>This is the first framework to integrate computational mechanics with score-based generative modeling for the structural analysis of ABM outputs.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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