Title: A Compositional Framework for System Dynamics Modeling using Category Theory
Abstract: This presentation will introduce a modular and compositional framework for system dynamics, developed using category theory. System dynamics is a computer-aided approach for decision and policy making in complex dynamical systems. By leveraging categorical constructions, we establish a separation between syntax—the diagrammatic languages such as stock-and-flow diagrams—and semantics, such as ordinary differential equations (ODEs). Stock-and-flow diagrams (closed) are represented categorically as C-Sets (also known as copresheaves), enabling structure-preserving mappings via homomorphisms and functorial translations across different diagrammatic tools.
We further extend closed dynamical systems to open ones using decorated/structured cospans, which allows large, complex systems to be built compositionally from smaller components applying pushouts. Pullbacks in the category of closed diagrams are applied to support stratification, enabling the construction of refined model structures.
Finally, I will demonstrate applications of this framework to real-world problems in the public health domain, using the Julia package StockFlow.jl, which is implemented within the AlgebraicJulia ecosystem and built on Catlab.jl. This work illustrates how categorical methods provide a principled foundation for modular, compositional, and scalable modeling in system dynamics.
