Decorated Cospans at Work: Coupling Heterogeneous Dynamical Systems via Pushouts and Particle Filters

TL;DR

This paper demonstrates how decorated cospans can be used to compose and analyze heterogeneous dynamical systems, such as economic, epidemiological, and behavioral models, revealing structural properties and biases through coupling and bifurcation analysis.

Contribution

It introduces a computational framework using decorated cospans to couple diverse dynamical models via pushouts, enabling structural analysis of complex systems.

Findings

Coupled system exhibits rejection bifurcation with trajectories escaping or cycling.

Coupling shifts output gap by 0.78 percentage points and rejection by 22 points.

Bias decomposition identifies structural sources of asymmetry in the coupled system.

Abstract

Decorated cospans provide a categorical framework for composing open systems along shared interfaces. This paper is a computational proof of concept: we show that the framework produces a working coupled dynamical system when the decorations are quantitative models from different mathematical traditions. Specifically, we couple a linearised New Keynesian DSGE, a stochastic compartmental epidemic (multi-strain SEIR), and a nonlinear vaccine adoption model with hysteresis into a single sequential Monte Carlo sampler. Each model is a decorated cospan -- interior dynamics as decoration, exposed variables as interfaces. The composite system is the pushout along variable identifications, with coupling functions encoded as factor graph constraints. The coupled system produces a rejection bifurcation: some trajectories escape via vaccination, others enter a self-reinforcing cycle of mandate backlash, vaccine refusal, sustained infection, and recession. This is a structural property of the coupling, not an input assumption. Coupling shifts the output gap by 0.78 pp and rejection by 22 pp relative to the uncoupled system. A fourth narrative -- fiscal/political dynamics, calibrated to the US COVID fiscal response -- attaches via a second pushout and introduces the first positive coupling channel. With pandemic-scale spending parameters, 14% of trajectories overshoot into positive output gap territory; the bearish bias shrinks, but persists. A computable bias decomposition separates three sources of this asymmetry -- sampling, structural, and observational -- and localises the structural component to specific coupling functions whose directional asymmetry can be tested against historical analogues.