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

2025/12/04 by R. Garrone, Garrone, Roberto
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #37A35 #60G10 #62M05 #68T42 68T42 #94A17 #Complex Systems and Time Series Analysis #F.1.1 #FOS: Computer and information sciences #G.3 #I.2.11 #I.6.5 #Machine Learning (cs.LG) #Mathematical Biology Tumor Growth #Multiagent Systems (cs.MA) #Opinion Dynamics and Social Influence

paper · pdf · doi:10.48550/arxiv.2512.04771

openalex publication_date 2025/12/04 · openalex created_date 2025/12/06 · openalex updated_date 2026/07/28

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.

Citations

• Characterizing Agent-Based Model Dynamics via ε-Machines and Kolmogorov-Style Complexity
• Maximum Likelihood Training of Score-Based Diffusion Models
• Score-Based Generative Modeling through Stochastic Differential Equations
• Denoising Diffusion Probabilistic Models
• Generative Modeling by Estimating Gradients of the Data Distribution
• Variational Inference with Normalizing Flows
• Deep Unsupervised Learning using Nonequilibrium Thermodynamics
• Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index
• Computational Mechanics: Pattern and Prediction, Structure and Simplicity
• Least squares quantization in PCM

Related

• Characterizing Agent-Based Model Dynamics via ε-Machines and Kolmogorov-Style Complexity
• Learning Individual Behavior in Agent-Based Models with Graph Diffusion Networks
• Diffusion models learn distributions generated by complex Langevin dynamics
• Combining complex Langevin dynamics with score-based and energy-based diffusion models
• On the Generalization Properties of Diffusion Models