Enabling Compositional System Dynamics Modeling via Category Theory
Date
2025-06-02
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
0000-0002-4206-098X
Type
Thesis
Degree Level
Doctoral
Abstract
This dissertation develops a novel, modular, compositional, and relational framework for System Dynamics (SD) modeling, leveraging the higher mathematics of Applied Category Theory (ACT). System Dynamics, a methodology for understanding and managing complex systems over time, has been widely used in various fields such as public health, business, and environmental management. Despite its strengths, traditional SD modeling methods face several critical limitations, including a lack of modularity, inadequate representation of complex relationships, stratification that obscures model transparency, rigid coupling of model syntax and semantics, and limited support for model composition and reuse. These challenges hinder the scalability, flexibility, and accuracy of models, especially for large or interdisciplinary systems. To address these limitations, this dissertation introduces a new framework based on ACT, which provides a mathematical foundation for representing, relating, composing, and stratifying complex systems. Key contributions include the development of a categorical framework for modular representation of commonly used SD tools such as Causal Loop Diagrams, System Structure Diagrams, and Stock and Flow Diagrams using co-presheaves; a compositional framework for open systems based on Decorated / Structured Cospans, enabling modular design and reuse; and a separation of graphical syntax (diagrams) from mathematical semantics (e.g., Ordinary Differential Equations), enhancing clarity and adaptability. Additionally, the dissertation defines functor mappings to establish relationships among SD diagrams, introduces a stratification framework for constructing hierarchical models from aggregate structures, and implements these theoretical advancements in the Julia-based software \texttt{StockFlow.jl}. The utility of this framework is demonstrated through several case studies, mainly focused on models of communicable diseases and other models in public health area, highlighting the efficiency and flexibility of the modular approach compared to traditional methods. While addressing many challenges in SD modeling, this dissertation also acknowledges limitations, such as the need for enhanced representation of feedback loops in Causal Loop Diagrams and improved support for stratified systems with complex mixing structures. Future work will aim to refine the mathematical frameworks, enhance software implementation, and explore broader applications across other domains. This research establishes a next-generation SD modeling approach, bridging mathematical rigor and practical utility, and significantly advances the capabilities and scope of System Dynamics for researchers and practitioners in diverse fields.
Description
Keywords
System Dynamics, Category Theory, Dynamical System Modelling, Applied Category Theory, Structured Cospan, Stock and Flow Diagrams, Causal Loop Diagrams, Epidemiological Models
Citation
Degree
Doctor of Philosophy (Ph.D.)
Department
Computer Science
Program
Computer Science