Project Overview

This project establishes a category-theoretic foundation for complex system-of-systems (SoS) design, treating system architectures as first-class mathematical objects and emergent behavior (EB) as a computable quantity rather than an after-the-fact anomaly. To achieve this, the research utilizes cellular sheaves to attach local data across networks and ensure consistency, alongside enriched profunctors that evaluate subsystem operability on a continuous, graded scale rather than relying on simple yes-or-no feasibility. By scoring the discrepancy between theoretically predicted and practically observed system compositions, the framework quantifies and classifies emergent behaviors—distinguishing positive, negative, and neutral outcomes—while providing constructive techniques to optimize architectures, evaluate cascading effects, and mitigate negative emergent behaviors.

Funding Info

Agency: Air Force Research Lab
Program Manager: Marco Gamarra
Grant Number: FA8750-20-3-1004
My Role: Principal Investigator
Amount: $10,921 USD
Project Period: Jun 2026 - Jul 2026