Compositional Modeling

An SEIR model and a quarantine policy, drawn as two Petri nets, composed into a third
An SEIR model composed with a quarantine policy, from the AlgebraicPetri.jl documentation.

AlgebraicPetri.jl · AlgebraicDynamics.jl

A scientific model is usually written as a whole and then edited as a whole. Adding an age structure to an epidemic model, or a second species to a reaction network, means rewriting the equations by hand, which is slow and leaves no record of what the change was supposed to mean.

In this project we build models whose structure survives that kind of change. We represent a model as a Petri net, an undirected wiring diagram, or a regulatory network, which turns the operations modelers already perform into operations on the representation: stratifying by age or region, composing two subsystems, refining one species into several. The dynamics are then generated from the representation.

Three formalisms recur across this work. Petri nets carry epidemiological and reaction models, regulatory networks carry the promoting and inhibiting interactions of a biochemical system, and threshold-linear networks carry the dynamics of neural codes. Each has a composition operation, and for each we ask the same question: what does the whole do, given what the parts do?

Much of this work was carried out with the wider AlgebraicJulia community, including Sophie Libkind and Evan Patterson at the Topos Institute.

Project team

Project articles

  1. Aduddell, R., Fairbanks, J., Kumar, A., Ocal, P. S., Patterson, E., & Shapiro, B. T. (2024). A compositional account of motifs, mechanisms, and dynamics in biochemical regulatory networks. Compositionality, 6, 2. https://doi.org/10.32408/compositionality-6-2
  2. Libkind, S., Baas, A., Patterson, E., & Fairbanks, J. (2022). Operadic Modeling of Dynamical Systems: Mathematics and Computation. Electronic Proceedings in Theoretical Computer Science, 372, 192-206. https://doi.org/10.4204/EPTCS.372.14
  3. Libkind, S., Baas, A., Halter, M., Patterson, E., & Fairbanks, J. P. (2022). An algebraic framework for structured epidemic modelling. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380(2233), 20210309. https://doi.org/10.1098/rsta.2021.0309
  4. Libkind, S., Baas, A., Halter, M., Patterson, E., & Fairbanks, J. (2022). Typed and stratified models with slice categories. In Applied Category Theory (pp. 1-3). https://msp.cis.strath.ac.uk/act2022/papers/ACT2022_paper_3530.pdf
  5. Brown, K., Hanks, T., & Fairbanks, J. (2022). Compositional Exploration of Combinatorial Scientific Models. In Applied Category Theory. https://doi.org/10.48550/ARXIV.2206.08755
  6. Halter, M., Herlihy, C., & Fairbanks, J. (2020). A Compositional Framework for Scientific Model Augmentation. In Electronic Proceedings in Theoretical Computer Science (pp. 172-182). Opn Publishing Association. https://doi.org/10.4204/EPTCS.323.12
  7. Halter, M., Patterson, E., Baas, A., & Fairbanks, J. (2020). Compositional Scientific Computing with Catlab and SemanticModels. In Applied Category Theory. http://arxiv.org/abs/2005.04831
  8. Halter, M., Raparti, S., Cao, K., Herlihy, C., & Fairbanks, J. (2020). SemanticModels. jl: a julia package for scientific model augmentation. In Proceedings of the JuliaCon conferences (pp. 57).
  9. Herlihy, C., Cao, K., Reparti, S., Briscoe, E., & Fairbanks, J. (2019). Semantic Program Analysis for Scientific Model Augmentation. Modeling the World’s Systems, 7.