Compositional Exploration of Combinatorial Scientific Models

TL;DR

This paper introduces a new framework for exploring complex scientific model spaces using categorical diagrams, enabling systematic construction and selection of models, demonstrated through epidemiological data fitting.

Contribution

It presents a novel categorical approach to model space representation and exploration, including implementation of diagram categories and their limits/colimits.

Findings

Successfully generated a tool for fitting epidemiological models.

Demonstrated systematic exploration of model spaces using categorical structures.

Enabled automated selection of models fitting experimental data.

Abstract

We implement a novel representation of model search spaces as diagrams over a category of models, where we have restricted attention to a broad class of models whose structure is presented by \C-sets. (Co)limits in these diagram categories allow the creation of composite model spaces from more primitive spaces. We present a novel implementation of the computer algebra of finitely presented categories and diagram categories (including their limits and colimits), which formalizes a notion of model space exploration. This is coupled with strategies to facilitate the selection of desired models from these model spaces. We demonstrate our framework by generating a tool which fits experimental data, searching an epidemiology-relevant subspace of mass-action kinetic models.