Hetero-functional Graph Theory for Convergent Systems of Systems: Model-Based Applications in Watershed and Economic Systems

Abstract

Modern societal challenges defined by the Sustainable Development Goals of the United Nations are deeply interconnected. Addressing issues such as water scarcity, ecosystem degradation, or food security requires understanding the coupled systems that shape them, including hydrology, infrastructure, ecology, economics, and governance. While modelers within each discipline develop increasingly accurate representations of individual systems, real-world problems arise from the feedbacks between them. Actions intended to improve one domain can unintentionally disrupt another; for instance, reducing fertilizer to prevent eutrophication may also affect agricultural productivity. To address such interdependencies, this dissertation develops a unified, ontology-based modeling framework that integrates Model-Based Systems Engineering (MBSE) with Hetero-functional Graph Theory (HFGT). The dissertation progresses from domain-specific modeling studies toward a general convergence paradigm, illustrating how environmental and economic systems can be represented within a consistent system of systems architecture. The framework is first demonstrated in the context of simplified hydrological systems, where lakes, rivers, land segments, and outlet points are modeled using resistance-based transport laws and continuity equations adapted into the Hetero-functional Network Minimum Cost Flow (HFNMCF) optimization problem. This initial study establishes that environmental processes can be represented as a class of engineering systems within the HFGT meta-architecture when defined by an MBSE-based reference architecture. The approach is then extended to larger watershed systems and instantiated for the Chesapeake Bay Watershed. The approach classifies watershed systems under the HFGT meta-architecture then develops a watershed-specific Weighted Least Squares Error HFGT State Estimator to infer nitrogen and phosphorus flows across land–river–estuary networks under data sparsity and structural uncertainty. The paper then simulates the Chesapeake Bay Watershed using spatially and temporally resolved data from the Chesapeake Assessment Scenario Tool (CAST). This chapter demonstrates the scalability of the MBSE–HFGT framework and highlights its capacity for transparent, extensible environmental modeling at regional watershed scales. Having established the methodology through hydrologic and watershed applications, the dissertation then introduces a broader convergence paradigm. This chapter presents the meta-cognition map, which explains how scientific knowledge is generated across observation, abstraction, visualization, mathematics, and computation. The convergence paradigm draws directly on insights from the hydrology and watershed work as well as other domain applications to articulate the characteristics required for modeling complex Anthropocene systems of systems, including ontology, transparency, extensibility, and cross-domain alignment. The final chapters extend the MBSE–HFGT framework beyond environmental systems as preliminary steps to advance the cross-domain convergence paradigm. An economic input–output model is likewise classified as an engineering system under the HFGT meta-architecture and simulated as an HFNMCF optimization problem. Similarly, a system dynamics representation of the Mono Lake system is then translated into the MBSE–HFGT formalism, allowing a structural comparison between traditional causal-loop modeling and the capability-based, ontology-driven approach developed in this dissertation. Together, these studies establish a coherent, extensible methodology for representing and estimating complex systems across environmental and economic domains. By integrating system structure and function through a common ontology and demonstrating this integration across multiple domains, this dissertation provides a pathway toward convergent modeling of coupled human–natural systems in the Anthropocene.